GNSS for High-Precision and Reliable Positioning: A Review of Correction Techniques and System Architectures

Abstract

This paper provides a comprehensive review of the existing approaches to ensuring high-precision and reliable GNSS positioning. The purpose of this review is to examine modern approaches to mitigating the main factors affecting GNSS receiver accuracy, including atmospheric delays, ephemeris and clock errors, multipath, and receiver noise, and to highlight the key open challenges in high-precision positioning and error correction. The article presents various error correction techniques and provides their analysis. It presents modern architectural solutions for GNSS receivers aimed at providing high-precision and reliable positioning (conventional, software-defined, multi-frequency and multi-constellation, cloud/edge, integrated GNSS/INS/LiDAR, and integrated GNSS/IoT) and their comparative analysis. The resulting overview will be useful for further research in the field of high-precision navigation.

1. Introduction

The demand for high-precision satellite navigation technologies is growing every day. In particular, these technologies are used for autonomous robots designed for urban environments, where movement is complicated by the presence of buildings (limited GPS visibility), dynamic obstacles (people, vehicles), complex routes, and intersections [1], as well as for field mobile robots used in agriculture and open areas [2,3], commercial drones to improve navigation accuracy and stability in real flight conditions [4], aircraft-type UAVs [5], drones conducting topographic surveys [6], and autonomous vehicles in urban environments, including areas with limited GNSS signals [7], for collision avoidance [8]. However, most satellite navigation systems are quite sensitive to external conditions:

• Atmospheric delays (ionospheric and tropospheric), signal delays, etc. [9,10];
• The presence of obstacles in the form of vegetation [11,12] and civilian buildings [13,14] prevalent in populated areas;
• Problems with real-time availability and accuracy without correction services [15,16];
• Blocking of navigation satellite signals [17,18].

The factors listed above affect the accuracy of GNSS positioning, and some of them are caused by the poor geometry of visible navigation satellites when they are clustered on one side of the sky, which leads to errors from atmospheric delays and multipath effects [19,20]. Other errors are caused by the quality of ephemeris and time information and the noise characteristics of the GNSS receiver [20].

It is known that the accuracy of determining the distance between the navigation satellite and the receiver at a given moment in time plays an important role in determining the position of a navigation GNSS receiver. To determine this, modern receivers use measurements of the code or phase of the navigation signal carrier frequency.

In the case of code measurements, the receiver calculates the pseudorange directly based on ephemeris and time information (namely, the time of signal transmission and reception) extracted from the code. The accuracy of the coordinates obtained in this mode of receiver operation, named as single point positioning (SPP), is about 3–15 m [21]. In comparison, phase receivers provide a distance calculation that is implemented after resolving ambiguities (finding the integer number of wavelengths that fit within the measured distance), with the accuracy of the receiver coordinates being on the order of several centimeters, since the wavelength is ~19 cm (for L1) [22].

To improve the accuracy of coordinate determination by a code GNSS receiver, global or regional differential correction systems are used, which employ ground monitoring stations that determine corrections and transmit them to GNSS receivers, allowing them to achieve a meter-level positioning accuracy. These corrections may include corrections to the end user’s raw pseudorange measurements, corrections to clock and ephemeris data provided by the GPS satellite, and primary measurements from the reference station [20,23]. Differential correction systems typically provide sub-meter accuracy and are often used in marine navigation, agriculture, and railway monitoring. Differential correction systems operate in both post-processing and real-time modes: SBAS (WAAS, EGNOS, etc.).

Phase receivers, especially those operating at more than one frequency, can employ several positioning methods to achieve high accuracy. Among them, the Precise Point Positioning (PPP) approach is one of the most commonly used techniques for determining accurate coordinates. This approach provides corrections to the following GNSS data: satellite orbit errors, satellite clock inaccuracies, and ionospheric and tropospheric disturbances. These corrections can be obtained from various sources, including regional reference station networks (CORS), global reference station networks (IGS), spacecraft (SBAS), and the Internet. When applied properly, PPP corrections enable a centimeter-level accuracy for phase receivers [24] and are often used in geodetic applications. The PPP method is implemented in both a posteriori and real-time modes.

Another widely used technique for phase receivers is the Real-Time Kinematic (RTK) method, which uses ephemeris time data from a reference station with pre-calculated coordinates to determine corrections to the receiver’s navigation solution. Its network-based extension, known as network RTK (NRTK), further enhances performance by combining data from multiple reference stations to generate spatially interpolated corrections. The use of correction data allows for an accuracy of several millimeters for a phase receiver [25] and is used in aviation, unmanned technology, and geodesy. The RTK method is implemented in real time; in a posteriori mode, it is referred to as PPK.

In recent years, hybrid approaches such as PPP-RTK have also been developed, combining the advantages of both methods and providing additional opportunities for high-precision positioning, especially in areas without access to satellite differential station networks [26].

However, in conditions of temporary GNSS signal unavailability, the influence of the non-line-of-sight (NLOS) effect or multipath (in the presence of obstacles such as vegetation and civilian buildings), the performance, accuracy, and reliability of the above positioning methods can suffer significantly [27]. Therefore, to improve the accuracy and reliability of data obtained by a code or phase GNSS receiver, measurements are integrated with other sensors, for example, as follows:

• Integration with LiDAR to identify NLOS emissions, create virtual satellite corrections, and close integration with a GNSS receiver [27] to detect NLOS situations and integrate GNSS measurements into SLAM [28];
• Integration with INS using factor graph optimization (FGO) [29], and integration with INS supplemented by a vehicle motion detection module [30];
• INS/GNSS integration with visual data for sky segmentation and determining which satellites are actually in the line of sight (LOS), and which are most likely in the NLOS zone [31].

To mitigate the effects of multipath, NLOS, and signal unavailability, intelligent data processing techniques can be employed. For instance, these include convolutional neural networks (CNNs), which have been used to recognize reflected signals and suppress multipath effects [32]; the use of ML techniques, such as SVM, to classify LOS and NLOS signals [33]; nonlinear regression to develop a multipath prediction model [34]; SVM and NN techniques to determine NLOS multipaths [35], which are the cause of the largest errors in GNSS positioning in urban environments; and the application of machine learning methods (LSTM and GBDT) to ensure positioning in conditions where GNSS measurements are unavailable [36].

The use of multi-constellation GNSS receivers can solve some of the problems associated with reduced accuracy due to the blocking of navigation satellites by vehicles, buildings, terrain, or foliage, as they provide a sufficient number of satellites in the radio visibility zone to solve the navigation problem [37,38,39]. However, in cases where the signal is completely blocked due to use in tunnels, dense urban areas, or forests, inertial sensors can be used in conjunction with multi-constellation GNSS receivers to predict the position of an object based on the latest GNSS measurements.

Multi-frequency GNSS receivers are even more reliable in terms of mitigating ionospheric distortions [40]; their accuracy is the least affected by the multipath effect [41,42], and it increases naturally due to the access to measurements from the largest number of navigation satellites [43].

Recent studies on the integration of GNSS measurements with IoT technologies and cloud GNSS processing are transforming GNSS receivers from point instruments into a global spatial monitoring system, improving the functioning and accuracy of GNSSs in real time. In particular, [44] considers the idea of using cloud platforms (Cloud GNSS processing) for signal processing tasks, which reduces the receiver’s power consumption [45] and development budget, but not its accuracy. When using RTK, corrections provide a better accuracy [46]. However, due to delays and the dependence on a stable Internet connection, cloud processing is not always suitable for real-time tasks. Therefore, for real-time GNSS positioning tasks, the use of edge computing technologies is currently being considered [47], where calculations and signal processing are performed at the nearest edge nodes, which improves device reliability and operation with minimal delays.

Every year, the manufacturers of high-precision navigation equipment offer new models of high-precision GNSS receivers on the market. Most of them are multi-constellation and multi-frequency models, certified to industrial standards and correspondingly expensive, such as the Trimble R12i, equipped with support for all constellations and RTK [48]; the Leica GS18 T [49]; the Topcon HiPer HR multi-channel receiver [50]; high-precision receivers in the mid-price segment for integration, robots, and IoT, such as the Septentrio Mosaic-X5 with built-in interference suppression technology [51]; the NovAtel OEM7700 multi-frequency receiver with RTK corrections [52]; the RTK module with multi-frequency support and centimeter accuracy u-blox ZED-F9P [53]; etc. Given the high cost of the models presented, one of the main prospects for the development of GNSS positioning is to improve accuracy using consumer equipment aimed at mass application. In this regard, the direction of improving positioning accuracy based on budget, low-cost, and civilian GNSS receivers is represented by a large number of scientific works and continues to develop. As a rule, budget receivers are more susceptible to noise, which significantly degrades their positioning accuracy. For this reason, research into improving the accuracy of such devices includes technical solutions, such as the use of geodetic antennas with low-cost modules [54,55], which allow sub-centimeter horizontal accuracy to be achieved when using PPP or RTK. Architectural solutions are considered, such as improving the accuracy and reliability of budget navigation modules through an integration with INS [56] and an integration with IoT platforms with PPP-RTK correction [57]. Software solutions are also presented, in particular the adaptation of existing correction algorithms, navigation calculations (Kalman filter), and the development of algorithms for tracking outliers and cycle slips [58].

The review found that, despite the high quality of modern GNSS receiver models, multipath and satellite channel blocking continue to significantly impair positioning accuracy and reliability. Cloud GNSS processing requires a reliable Internet connection to obtain refined coordinates, but edge computing technology is more promising. Research on the application of deep learning (DL) and ML techniques is rapidly progressing. Budget receivers for mass use suffer most from interference, noise, and delays, which provides a strong motivation for further research aimed at improving their accuracy in the coming years. Jamming and spoofing, which cause significant navigation failures, remain serious threats to GNSS navigation receivers [59,60], while software-defined structures are more promising.

The purpose of this review is to systematize modern methods and technologies for high-precision positioning based on GNSS; to consider key sources of errors and the main approaches to their minimization for SPP, RTK, PPP, and PPP-RTK; to analyze the existing architectural solutions aimed at providing high-precision and reliable positioning, such as traditional hardware-based architecture, software-defined architecture, multi-frequency/multi-constellation architecture, architectural solutions with cloud or edge computing, GNSS/INS/LIDAR integrated architectures, and GNSS/IoT integrated architectures; and to identify research challenges and open problems in the field of high-precision and reliable GNSS navigation.

The literature analyzed in this review was selected using a systematic search strategy focusing on peer-reviewed journal papers and high-impact conference proceedings published between 2010 and 2024, with a particular emphasis on studies from the last five years (2020–2024). The search was performed in databases such as IEEE Xplore, MDPI, Elsevier, SpringerLink, and Google Scholar. The main keywords included GNSS, PPP, RTK, PPP-RTK, high-precision positioning, correction techniques, ionospheric and tropospheric errors, multipath mitigation, software-defined GNSS, edge/cloud GNSS, and integrated GNSS/INS/IoT architectures. Publications were prioritized based on their scientific contribution, experimental validation, and relevance to modern receiver architectures and correction methods. Older but fundamental works were cited selectively when they provided the theoretical or methodological background necessary to interpret recent research directions.

The review is organized as follows. Section 2 presents the basic principle of GNSS operation and describes the main sources of positioning errors and the existing methods for correcting error data and improving the accuracy of GNSS receivers. Section 3 presents modern architectural solutions for GNSS receivers. Section 4 highlights the current research challenges and open issues in high-precision GNSS navigation. Section 5 formulates the main conclusions of the review.

2. GNSS Accuracy Factors and Techniques of Accuracy Improvement

Global navigation satellite systems (GNSSs) include GPS (USA), GLONASS (Russia), Galileo (EU), and BeiDou (BDS) (China). Each system consists of three segments: the space segment (a constellation of satellites transmitting navigation signals), the ground segment (a network of control and monitoring stations), and the user segment (GNSS receivers) [20].

The principle of operation of satellite navigation systems is based on measuring the distance from the GNSS receiver to satellites whose positions are known with high accuracy. To determine this distance, modern receivers use measurements of the code or phase of the navigation signal carrier frequency.

When measuring by code, the receiver calculates the pseudorange directly based on ephemeris and time information (namely, the time of signal transmission and reception) extracted from the code. Thus, using the definition of the pseudorange as a function of the GNSS receiver coordinates and GNSS receiver clock errors, with a minimum of four pseudorange measurements to satellites, a system of equations can be constructed to determine the receiver coordinates [20,24]:

$${\rho }_i=R_i+c{\delta t}_{rx}-c{\delta t}_{sv,i}+d_{iono,i}+d_{tropo,i}+{\epsilon }_{\rho ,i},$$

(1)

where $R_i=\sqrt{{(x-x_i)}^2+{(y-y_i)}^2+{(z-z_i)}^2}$ respresents the true distance to the i-th satellite, $c{\delta t}_{rx}$ is the GNSS receiver clock error, $c{\delta t}_{sv,i}$ is the navigation satellite clock error, $d_{iono,i}$ is the ionospheric delay, $d_{tropo,i}$ is the tropospheric delay, and ${\epsilon }_{\rho ,i}$ represents the noise, multipath, and correlation errors.

The equations are solved using the least-squares method or a Kalman filter. The accuracy of the coordinates obtained by the code receiver is approximately 3–15 m [21]. This positioning mode is called single point positioning (SPP) and is used in smartphones, car navigators, and GPS trackers. To improve accuracy, differential correction methods based on the Wide Area Differential GNSS system (e.g., SBAS, DGNSS) can be used.

Carrier-phase measurements can be performed with millimeter accuracy, but the measurement is ambiguous because the total number of cycles (full wavelengths) between the satellite and the receiver is unknown a priori:

$${\Phi }_i=R_i+{\delta t}_{rx}-c{\delta t}_{sv,i}+d_{iono,i}+d_{tropo,i}+\lambda N_i+{\epsilon }_{\Phi ,i},$$

(2)

where $\lambda$ is the wavelength (~19 cm for L1 and 24 cm for L2), N is the integer number of wavelengths, and ${\epsilon }_{\Phi ,i}$ is the phase noise.

Resolving or evaluating carrier-phase ambiguity is key to achieving accurate positioning. With phase measurements from a single receiver, and using accurate satellite orbits and clocks (from IGS or commercial services), it is not possible to express the integer wavelength—only its real value (float) [61,62]. The positioning mode in this case is called float Precise Point Positioning (float PPP). The PPP method with integer ambiguity resolution of pseudophase measurements is called PPP-AR (Integer PPP), which, together with other absolute and relative positioning approaches, is shown schematically in Figure 1.

If phase measurements from another GNSS receiver are available, double differences (DD) are calculated between a pair of satellites and a pair of GNSS receivers, completely eliminating satellite clock errors. GNSS receiver clock errors also disappear (since they are the same for satellites i and j), and the integer ambiguity remains [24]. In this case, this corresponds to the Real-Time Kinematic (RTK) positioning mode, which allows centimeter-level positioning accuracy to be achieved. RTK is a relative positioning technique, as shown in Figure 1, and serves as the basis for its hybrid extension—the PPP-RTK method, which combines the advantages of absolute and relative positioning. It is also possible to use a comprehensive PPP-RTK approach (Figure 1).

The error in determining the coordinates of the GNSS receiver is determined by several parameters. One such parameter is the covariance matrix A of the navigation solution vector $x=[x,y,z,t_r]$. To improve the understanding of the positioning error, the term user equivalent range error (UERE) is introduced, which reflects all major ephemeris–time errors and atmospheric, noise, and multipath errors expressed in terms of distance [24]. That is, UERE is used as a metric for the contributions of different sources of error to the navigation solution. The main indicator determining the quality of the navigation solution is given as the sum of variances:

$${\sigma }_{UERE}=\sqrt{{\sigma }_r^2+{\sigma }_{dt}^2}=\sigma tr\left\{{\left(A^{T}A\right)}^{-1}\right\},$$

(3)

where ${\sigma }_r$ is the variance of the GNSS receiver position estimates, and ${\sigma }_{dt}$ is the variance of the clock offset estimate.

The final error in determining the coordinates of the GNSS receiver is recorded as follows [24]:

$${\sigma }_{GNSS}={\sigma }_{UERE}·DOP,$$

(4)

where $DOP$ (Dilution Of Precision) is an indicator of “satellite geometry quality”.

The factors that distort the determination of GNSS receiver coordinates can be classified by their origin into the following categories: atmospheric effects, ephemeris and clock errors, signal obstructions leading to multipath, and receiver noise. This section summarizes these influences on GNSS receiver accuracy in descending order of their error magnitude and outlines the main methods used to mitigate them.

2.1. Ionospheric Effects and Their Correction

The atmosphere affects signal delay, has different effects on code and phase, and directly affects accuracy. The ionosphere, as part of the atmosphere, is a dispersive medium: GNSS signals slow down and change phase depending on frequency, causing a delay error proportional to the free electron content (TEC). This error can cause positioning errors of up to 10–15 meters for single-frequency (L1) receivers [22]. For receivers operating in absolute and relative positioning modes, various methods of ionospheric correction are considered. Table 1 summarizes the main methods.

For single-frequency code receivers, ionospheric corrections are provided through the Klobuchar model included in the navigation message [24]. Improved empirical models such as Ref-Klobuchar and CODESH yield about 30–40% higher vertical accuracy (Ref-Klobuchar 1.41 m, CODESH 1.30 m versus 2.32 m without correction) [63]. However, their accuracy still degrades significantly during geomagnetic storms or in equatorial regions with a strong TEC variation.

For phase receivers, combining dual-frequency measurements enables ionosphere-free combinations (IF) that almost eliminate the first-order ionospheric effect [64] and provides an improvement in accuracy of 1–6 m. Namely, when using a single-frequency receiver (L1) with the Klobuchar ionosphere model, the RMSE is 7.7 m (winter)/9.8 m (summer), while for a dual-frequency receiver (L1, L2), the RMSE is 5.6 m (winter)/7.6 m (summer), respectively [64]. The superior performance of dual-frequency approaches is explained by their ability to directly estimate the dispersive component of the ionospheric delay.

When operating in PPP mode, the use of external ionospheric models enhances accuracy, allowing <3 m accuracy [65]. In particular, in a calm ionosphere, using IGS corrections provides ${\sigma }_N=1.2$, ${\sigma }_E=0.9$, and ${\sigma }_U=1.8$; global ionospheric map (GIM) products provide an accuracy of ${\sigma }_N=1.4$, ${\sigma }_E=0.9$, and ${\sigma }_U=1.9$; and a GIM with DMD enhancement based on CODE products with RMS statistics achieves ${\sigma }_N=1.8$, ${\sigma }_E=0.6$, and ${\sigma }_U=1.6$ [65]. The improvement in the GIM with DMD enhancement arises because this method captures short-term temporal variations in TEC, allowing for more accurate predictions during ionospheric fluctuations.

In [66], a neural network was trained to predict more accurate TEC maps based on GIM data, improving single-frequency positioning to ~1–2 m (horizontal) and 2–3 m (vertical). Machine learning approaches outperform empirical and statistical models since they dynamically learn nonlinear dependencies in the ionosphere, particularly under disturbed conditions, offering better regional adaptability.

For relative methods, ionospheric delay is also one of the main sources of error for RTK positioning, especially for medium and long baselines. In this case, the key factor is the fast and reliable resolution of phase ambiguities. The ionosphere-weighted model [67,68] introduces ionospheric delay as a random parameter, with network corrections (VRS, MAC, FKP) as priors. This hybrid approach performs better than the classic ionosphere-fixed or float models because it balances flexibility in error estimation with stability in ambiguity resolution. Under a calm ionosphere, the average time-to-fix (TTF) is 1–1.5 epochs with a 1–2 cm horizontal and 2–3 cm vertical accuracy. During disturbed conditions, the vertical errors rise to 5–7 cm.

The distance between correction stations is also important for RTK-PPP when accounting for ionospheric corrections. In [26], tests on CORS networks in the US with different distances between stations (68 km, 115 km, 174 km, 237 km) showed that using a linear unbiased predictor (BLUP) for the interpolation of undifferentiated ionospheric corrections enables a sub-decimeter accuracy (<10 cm) in less than 6 minutes at 68 km and in less than 20 m at 237 km. Kriging interpolation [69] showed ~1.3–3.2 cm error for large networks (>500 km). These methods are better than linear interpolation, as they statistically model the spatial correlation of ionospheric delay, minimizing the prediction variance.

Multi-frequency GNSS receivers operating in PPP-RTK mode generally show good accuracy, taking into account network correction of ionospheric delays calculated on the server. Provided that multiple frequencies and the data from several GNSSs (GPS, Galileo, BDS) are available, a sub-decimeter accuracy can be achieved almost instantly: ~2 cm horizontally and ~3.5 cm vertically in open terrain [70]. This approach allows for merging global consistency with local precision.

Table 1. Comparative summary of ionospheric correction models for high-precision GNSS positioning, grouped by type of solution (absolute/relative).

Correction Method for Absolute Positioning	Example Model/Product	Description/Principle	Accuracy
Broadcast ionospheric model [24,64,71]	Klobuchar (GPS), NeQuick-G (Galileo)	Empirical model broadcast in the navigation message; corrects ~50–70% of the ionospheric delay	Horizontal 5–7 m, vertical 8–12 m [24]; 7.7 m (winter)/9.8 m (summer) (single freq L1); 5.6 m (winter)/7.6 m (summer) (dual-freq L1/L2) [64]
Global ionospheric maps (GIM) [65]	IGS, CODE, ESA GIM	Data-driven global TEC maps updated every 15 min; applied for PPP and SBAS corrections	${\sigma }_N=1.4$, ${\sigma }_E=0.9$, ${\sigma }_U=1.9$ [65]
DMD-enhanced GIM forecast [65]	Dynamic Mode Decomposition	Supplementing ionospheric forecasts based on CODE products with RMS statistics	${\sigma }_N=1.8$, ${\sigma }_E=0.6$, ${\sigma }_U=1.6$ [65]
Use of ML [66]	ML (ANN, RF, LSTM) models	Improvement of ionospheric GIMs	Horizontal ~1–2 m, vertical ~2–3 m [66]
Regional interpolation models (PPP-RTK) [26,69]	BLUP, Kriging	Interpolate ionospheric delays from CORS stations	<10 cm at a distance of 237 km between stations; ≈1.3–3.2 cm at a distance of 500 km between stations [69]
Multi-frequency PPP (ionosphere-free IF) [70]	Dual-frequency L1/L2 PPP	Linear combination removes first-order ionospheric delay	~2 cm horizontally, ~3.5 cm vertically [70]
Correction Method for Relative Positioning	Example Model/Product	Description/Principle	Accuracy
Ionosphere-weighted network RTK [68]	VRS/MAC networks	Double-difference approach with network-wide corrections	Horizontal 1–2 cm, vertical 2–3 cm in calm atmosphere; vertical 5–7 cm in disturbed atmosphere [68]

Table 1. Comparative summary of ionospheric correction models for high-precision GNSS positioning, grouped by type of solution (absolute/relative).

Correction Method for Absolute Positioning	Example Model/Product	Description/Principle	Accuracy
Broadcast ionospheric model [24,64,71]	Klobuchar (GPS), NeQuick-G (Galileo)	Empirical model broadcast in the navigation message; corrects ~50–70% of the ionospheric delay	Horizontal 5–7 m, vertical 8–12 m [24]; 7.7 m (winter)/9.8 m (summer) (single freq L1); 5.6 m (winter)/7.6 m (summer) (dual-freq L1/L2) [64]
Global ionospheric maps (GIM) [65]	IGS, CODE, ESA GIM	Data-driven global TEC maps updated every 15 min; applied for PPP and SBAS corrections	${\sigma }_N=1.4$, ${\sigma }_E=0.9$, ${\sigma }_U=1.9$ [65]
DMD-enhanced GIM forecast [65]	Dynamic Mode Decomposition	Supplementing ionospheric forecasts based on CODE products with RMS statistics	${\sigma }_N=1.8$, ${\sigma }_E=0.6$, ${\sigma }_U=1.6$ [65]
Use of ML [66]	ML (ANN, RF, LSTM) models	Improvement of ionospheric GIMs	Horizontal ~1–2 m, vertical ~2–3 m [66]
Regional interpolation models (PPP-RTK) [26,69]	BLUP, Kriging	Interpolate ionospheric delays from CORS stations	<10 cm at a distance of 237 km between stations; ≈1.3–3.2 cm at a distance of 500 km between stations [69]
Multi-frequency PPP (ionosphere-free IF) [70]	Dual-frequency L1/L2 PPP	Linear combination removes first-order ionospheric delay	~2 cm horizontally, ~3.5 cm vertically [70]
Correction Method for Relative Positioning	Example Model/Product	Description/Principle	Accuracy
Ionosphere-weighted network RTK [68]	VRS/MAC networks	Double-difference approach with network-wide corrections	Horizontal 1–2 cm, vertical 2–3 cm in calm atmosphere; vertical 5–7 cm in disturbed atmosphere [68]

2.2. Orbit and Clock Errors and Their Correction

The next key component of GNSS positioning error is the orbit and clock errors, which can cause an error of up to 2.5 m [22]. Various methods are used to mitigate these errors, depending on the type of solution. The main modern approaches are summarized in Table 2.

In the classic SPP solution, data from the navigation broadcast is used to correct orbit and clock errors, from which the satellite position is estimated using the Keplerian orbit model (taking into account the perturbations specified in the ephemerides), and the satellite clock offset is modeled using a second-degree polynomial, whose coefficients are taken from the navigation message [22]. According to [71], the broadcast orbit error and clock errors are 1–2.5 m (UERE), resulting in an SPP accuracy of ~3–5 m horizontally and ~5–10 m vertically. Such models perform adequately for open-sky, single-frequency users but are limited by coarse update intervals and simplified orbital dynamics. To improve accuracy, differential correction systems (SBAS, DGPS, DGNSS) are primarily used, which utilize ground monitoring stations that determine corrections and transmit them to the GNSS receiver, providing 1–3 m accuracy [72]. Regional monitoring allows for the fast detection and compensation of local orbit or clock drifts, which broadcast parameters cannot capture.

By combining measurements with data from IGS services, which supply precise orbits and clocks updated every 15 min, the accuracy improves to the sub-meter or sub-decimeter level (<1 m or <10 cm) [73,74]. Precise IGS products are the basis for PPP solutions. According to [75], in static PPP, a horizontal accuracy of 1–2 cm and a vertical accuracy up to 2–4 cm are achieved; in kinematic mode, a 3–5 cm horizontal accuracy and 5–10 cm vertical accuracy are achieved, with a convergence time of ~30 min. The better temporal stability of IGS clocks compared to the broadcast data explains their superior PPP performance.

In [76], using IGS services for Galileo and BDS constellations and a linear clock model (instead of a piecewise-constant one) provided a similar accuracy: 1–2 cm (E/N) and 2–3 cm (U) in static, 1.9 cm (E), 2.4 cm (N), and 4.9 cm (U) in kinematic mode, with a convergence time under 1 hour. Linear modeling performs better because it avoids discontinuities in clock corrections and maintains a consistency between epochs.

At the same time, attempts are being made to achieve RTK accuracy for PPP solutions using global ephemeris–clock IGS corrections based on multi-constellation (GPS, Galileo, BeiDou, GLONASS) with the implementation of a flexible PPP-AR (ambiguity resolution) for different frequency combinations [77]. The work uses an extended Uncombined Decoupled Clock Model (UDCM) for four systems and four frequencies. The test results show that, in approximately 80% of cases, the user obtains a horizontal accuracy of <2.5 cm instantly (epoch-by-epoch, 1σ).

At the same time, efforts are also made to reach RTK-level accuracy in PPP using multi-constellation (GPS, Galileo, BeiDou, GLONASS) IGS corrections and flexible PPP-AR (ambiguity resolution) [77]. The Uncombined Decoupled Clock Model (UDCM) for four systems and four frequencies allowed 80% of users to achieve a <2.5 cm horizontal accuracy instantly (epoch-by-epoch, 1σ). This demonstrates that multi-frequency corrections accelerate ambiguity resolution by reducing the impact of inter-system clock biases.

For GNSS receivers operating in RTK mode with a short base, forming double differences almost eliminates orbit and clock errors [24,71]. Residual orbit and clock errors can only appear on long baselines (>50–100 km), where network corrections (NRTK, VRS, MAC) help. NRTK (network RTK) overcomes the problem of increasing errors with base length by using a network of stations. The VRS (Virtual Reference Station) network creates a “virtual station” near the user to model and compensate local orbit and clock effects. The MAC (Master Auxiliary Concept) network transmits “raw” data from the master station and corrections from the auxiliary stations, and the GNSS receiver itself reconstructs the error field. Using corrections from both networks results in a horizontal accuracy better than 2.5 cm and a vertical accuracy better than 5 cm [78]. These network-based approaches outperform single-baseline RTK by spatially interpolating orbit and clock errors across the region.

Unlike RTK, where errors are eliminated by double differentiation, in PPP-RTK they are compensated by State Space Representation (SSR) corrections generated at the service center. SSR corrections contain orbital corrections (updated every 30 s), high-frequency corrections to satellite clocks (updated every 5 s), and bias parameters. The advantage of SSR is its global consistency: it models each error source separately and transmits compact parameters, allowing users to correct orbits and clocks before filtering. The user’s GNSS receiver operating in PPP-RTK mode applies these corrections to its measurements, thus eliminating orbit and time errors even before Kalman filtering, allowing for the instantaneous fixing of ambiguities, and obtaining centimeter–decimeter level accuracy. In [79], the PPP-RTK solution with SSR corrections made achieved an accuracy of about 2–3 cm horizontally and 5–6 cm vertically in static mode, and 2–4 cm horizontally and 5–8 cm vertically in kinematic mode, with ambiguities resolved within 2 s in 90% of cases. Hence, PPP-RTK combines the global precision of IGS-based orbits with the rapid convergence of network RTK, representing the most efficient compromise between accuracy and coverage.

Table 2. Methods for correcting ephemeris and clock errors in GNSS positioning, grouped by type of solution (absolute/relative).

Correction Method for Absolute Positioning	Example Model/Product	Description/Principle	Accuracy
Broadcast ephemerides and clock data [71,72]	GPS LNAV, Galileo FNAV, BDS CNAV	Parameters transmitted in navigation message; updated periodically for SPP/PPP users	~3–5 m horizontally and ~5–10 m vertically [71], 1–3 m [72]
Post-processed precise products [73,74]	IGS Final	Derived from global tracking networks	Within <1 m or <10 cm [73,74]
Rapid/Ultra-rapid IGS products [75]	IGS Rapid	Near-real-time solutions for low-latency PPP applications	3–5 cm horizontally and 5–10 cm vertically [75]
Real-Time Service [76]	IGS services + linear clock model	Real-time corrections for PPP solutions	(E) ~1.9 cm, (N) ~2.4 cm, (U) ~4.9 cm in kinematic mode [76]
Multi-frequency PPP [77]	Uncombined Decoupled Clock Model (UDCM) for four systems and four frequencies for PPP	Real-time corrections for PPP solutions	<2.5 cm [77]
SSR corrections for PPP-RTK [79]	IGS RTS	Real-time State Space Representation corrections for PPP-RTK.	~2–4 cm horizontally, ~5–8 cm vertically in kinematic mode [79]
Correction Method for Relative Positioning	Example Model/Product	Description/Principle	Accuracy
RTK/Network RTK with orbit and clock corrections [78]	VRS, MAC	Double-differencing cancels satellite clock and ephemeris errors; network models extend precision to longer baselines	Horizontal accuracy < 2.5 cm; vertical accuracy < 5 cm [78]

Table 2. Methods for correcting ephemeris and clock errors in GNSS positioning, grouped by type of solution (absolute/relative).

Correction Method for Absolute Positioning	Example Model/Product	Description/Principle	Accuracy
Broadcast ephemerides and clock data [71,72]	GPS LNAV, Galileo FNAV, BDS CNAV	Parameters transmitted in navigation message; updated periodically for SPP/PPP users	~3–5 m horizontally and ~5–10 m vertically [71], 1–3 m [72]
Post-processed precise products [73,74]	IGS Final	Derived from global tracking networks	Within <1 m or <10 cm [73,74]
Rapid/Ultra-rapid IGS products [75]	IGS Rapid	Near-real-time solutions for low-latency PPP applications	3–5 cm horizontally and 5–10 cm vertically [75]
Real-Time Service [76]	IGS services + linear clock model	Real-time corrections for PPP solutions	(E) ~1.9 cm, (N) ~2.4 cm, (U) ~4.9 cm in kinematic mode [76]
Multi-frequency PPP [77]	Uncombined Decoupled Clock Model (UDCM) for four systems and four frequencies for PPP	Real-time corrections for PPP solutions	<2.5 cm [77]
SSR corrections for PPP-RTK [79]	IGS RTS	Real-time State Space Representation corrections for PPP-RTK.	~2–4 cm horizontally, ~5–8 cm vertically in kinematic mode [79]
Correction Method for Relative Positioning	Example Model/Product	Description/Principle	Accuracy
RTK/Network RTK with orbit and clock corrections [78]	VRS, MAC	Double-differencing cancels satellite clock and ephemeris errors; network models extend precision to longer baselines	Horizontal accuracy < 2.5 cm; vertical accuracy < 5 cm [78]

2.3. Multipath Effects and Their Mitigation

Another major source of error is multipath, which occurs because the signal from the satellite to the receiver antenna travels not only directly, but also via reflections from surrounding objects: buildings, metal structures, ground, water, snow, walls, vehicles. The typical error scale for code receivers is 1–5 m [22]. The main modern approaches for the effective correction of the multipath are listed in Table 3.

Multipath is a local error, so there are no network corrections for it. This means that differential correction systems (such as SBAS) are not suitable for compensating for multipath errors in urban environments for SPP solutions.

One of the new approaches being considered for aircraft navigation is the Advanced Receiver Autonomous Integrity Monitoring (ARAIM) method, which extends the classical RAIM concept by using multi-frequency and multi-constellation data with probabilistic failure models. This allows for a better isolation of inconsistent measurements and achieves an error of 4–10 m vertically and up to 30 m horizontally [80]. When combined with Kalman filtering [81], the method adapts dynamically to signal degradation, which explains the improvement of horizontal accuracy to 13–17 m. The joint use of ARAIM and NLOS-detection algorithms employing 3D urban models further reduces errors to 7.7 m in static and 4.7 m in kinematic modes [82]. Thus, combining integrity monitoring with contextual 3D modeling outperforms ARAIM algorithm by about 40%.

In urban environments, the clustering of satellite measurements and adaptive filtering also play a key role. In particular, in [83], the clustering and filtering of NLOS satellites made it possible to achieve an accuracy of about 2.4 m, demonstrating that adaptive methods outperform static weighting in multipath conditions.

Hardware solutions complement algorithmic ones. For SPP and PPP modes of receivers, it is important for the antenna to be able to receive signals from a large number of satellites, including low-angle ones, in order to improve geometry (GDOP). Antennas with choke-ring, Electromagnetic Bandgap (EBG), or pinwheel designs [84,85,86] physically suppress reflections, providing cleaner raw data before signal processing. Multi-frequency antennas further improve performance because reflected components at different frequencies have decorrelated phases, reducing the combined multipath interference by up to 70%.

Conventional receivers use a Delay-Locked Loop (DLL) with a classic Early–Prompt–Late correlator structure. DLL does not separate the direct signal from the reflected signal, resulting in pseudorange errors of up to 10–15 m. Replacing DLL with an improved correlator (e.g., Narrow Correlator, High-Resolution Correlator (HRC), Strobe Correlator) can reduce this error to 1 m. Using a multi-correlator structure with an Extended Kalman Filter (EKF) and estimating the code delay, Doppler shift, and channel propagation characteristics (Channel Impulse Response, CIR), including multipath components, allows for the lowering of GNSS positioning errors up to 0.5–1 m [87].

GNSS receiver algorithms typically use a C/N₀ threshold depending on the elevation angle to reject poor-quality satellite data. The adaptive C/N weighting model improves robustness by dynamically reassigning observation weights according to real-time signal quality, reducing urban positioning errors by 30–40% [88].

Machine learning (ML)-based algorithms now represent one of the effective approaches for suppressing multipath for SPP and PPP modes. In [89], multiple ML models (SVR, KNN, Random Forest, MLP, etc.) were trained to classify LOS/NLOS signals using C/N₀, elevation, and azimuth difference, reducing horizontal errors from 10–40 m to 5 m. In [90], the use of pseudorange bias correction via regression models further improved accuracy by 70% compared to classical C/N₀ weighting. These ML approaches outperform traditional filters because they exploit nonlinear relationships between signal features and multipath bias, enabling data-driven adaptation.

Integration with other sensors also significantly mitigates multipath for receivers working in SPP mode. In [91], GNSS was fused with LiDAR and INS through factor graph optimization (FGO), correcting NLOS reflections and maintaining accurate trajectories even when LOS satellites were limited. Errors decreased from 7.9 m to 2.8 m, showing that sensor fusion adds a spatial redundancy unavailable to standalone GNSS.

For the PPP solutions, hybrid signal decomposition methods such as wavelet and (Principal Component Analysis) PCA filtering [92] reduce both high-frequency noise and static multipath to a sub-millimeter accuracy of about 0.62 mm. Wavelet decomposition separates the signal into low-frequency and high-frequency components. PCA then extracts useful components and removes noise.

Likewise, sidereal filtering (SF) and multipath hemispherical maps (MHMs) exploit the repeatability of satellite geometry. Advanced SF (ASF) shows the average standard deviations (STD) 2.1 mm (N), 1.7 mm (E), and 4.3 mm (U) [93]. MHMs generally outperform SF in dynamic conditions because they account for azimuth–elevation correlations and reduce the dispersion of residuals by 86–90% [94]. Combining MHMs with outlier exclusion methods shows an accuracy 1.7 mm (E), 2.0 mm (N), and 4.0 mm (U) [95].

The use of ML for classifying reflected signals based on a set of features (e.g., SNR, elevation angle, code residuals) refers to software approaches for mitigating multipath in PPP solutions. In [96], K-means clustering is performed based on known features, and groups of LOS, weak multipath, and strong multipath/NLOS signals are identified. These results are then used to change the measurement weights within the EKF PPP.

Multi-constellation and multi-frequency receivers exploit carrier frequency overlapping to combine measurements from different constellations, increasing sky coverage and improving the geometry of observations. In [97], the MHM_GEC model, which integrates GPS, Galileo, and BDS data, achieved 0.34 cm (East), 0.46 cm (North), and 0.81 cm (Up) accuracy, which is superior to ASF under identical conditions due to the higher-frequency diversity and redundancy that decorrelate multipath errors.

Integrating receiver working in PPP mode with other sensors shows good results in mitigating the multipath. Article [98] discusses the integration of a multi-frequency receiver operating in PPP mode with LIDAR measurements and MEMS-IMU, which limits the growth of INS drift and compensates for GNSS degradation caused by multipath. LiDAR contributes geometric constraints and IMU provides short-term continuity, which helps to reduce errors threefold to 1.41 m (E), 1.25 m (N), and 1.70 m (U) in urban areas.

GNSS receivers operating in RTK mode often face difficulty in correctly fixing carrier-phase ambiguities in urban conditions. Besides hardware improvements (antennas, correlators), algorithmic solutions are used to exclude poor signals. In [99], temporal C/N₀ filtering rejected satellites whose SNR dropped 10 dB-Hz below the average, reducing errors from tens of meters to 2.8 m.

In RTK solutions, ML algorithms such as SVM, FCNN, and XGBoost successfully separate LOS and NLOS signals [100,101]. These models analyze features like C/N₀, elevation angle, and correlator outputs to identify multipath signatures. XGBoost provided the best results by capturing nonlinear dependencies between geometry and residuals, improving accuracy to 1.6 mm (E), 1.9 mm (N), and 4.5 mm (U) in kinematic mode [101].

The RAIM method originally designed for code receivers can be adapted to phase measurements for RTK. In [102], the MS-CRAIM algorithm, based on a Kalman filter with adaptive stochastic modeling, achieved a 2.8 mm horizontal and 4.7 mm vertical RMSE. Its advantage lies in dynamically tuning noise covariance, which enables the system to remain consistent even when multipath noise varies between epochs.

In conditions where EKF struggles with non-Gaussian phase errors, robust filters provide a more effective solution [103]. Replacing the float solution estimator with Robust Information Filters (RIFs), Generalized M-estimator KFs (GM-KFs), or Variational Bayesian KFs (V-KFs) increases the resilience to heavy-tailed multipath noise. In [104], testing these filters for water transport passing under bridges showed that V-KF achieved 10–15 mm horizontal and 20–25 mm vertical precision, outperforming RIF and GM-KF due to its adaptive update of uncertainty distributions. Such robust filters perform better because they reduce the influence of outliers instead of averaging them, which is crucial under irregular reflection patterns.

To improve the reliability and accuracy of RTK measurements in multipath conditions, integration with INS (IMU) and LiDAR is often considered. In [105], the tight integration of the GNSS receiver with INS, LiDAR, and an HD map is proposed in a tightly coupled particle filter, where LiDAR with an HD map allows the trajectory to be “fixed” even with strong GNSS reflections. This approach reduced errors to 0.21 m (E), 0.33 m (N), and 1.52 m (U). Likewise, [27] shows that factor graph optimization (FGO) with virtual satellites derived from LiDAR improved observation geometry, yielding a 0.44–0.79 m accuracy, which is about four times better than conventional RTK using low-cost receivers.

The PPP-RTK approach combines PPP and RTK benefits but requires local mitigation since multipath is not corrected by network models. In [106], the proposed method using single-difference preprocessing improved accuracy by ~40% compared with classical SF and MHM, reducing RMSE to 1.1 cm (E), 1.2 cm (N), and 3.2 cm (U).

Robust adaptive Kalman filters [107] further enhance performance by continuously estimating observation variance through a sliding window, automatically suppressing the influence of multipath through adaptive weighting. This approach achieved a ~1 mm horizontal and 2 mm vertical accuracy, superior to fixed-parameter EKFs, as it self-adjusts to time-varying observation quality.

ML-based signal classification methods have great potential for detecting NLOS signals in PPP-RTK solutions. In [108], a signal classifier based on a multilayer perceptron (MLP) is proposed, in which signal power, elevation, and pseudorange consistency are fed as input data, with a fisheye camera reference. This classifier improved 3D positioning by 36.7–42.3% over traditional PPP-RTK.

Tightly coupled PPP-RTK/INS integration [109] provides the highest reliability in poor GNSS visibility. Combining IMU and LiDAR constraints achieved 0.055 m (E), 0.048 m (N), and 0.037 m (U) accuracy (and 0.4–0.5 m for budget IMUs). Such hybrid systems perform best because they exploit the complementary error dynamics of INS for short-term stability and GNSS for long-term drift correction.

Table 3. Methods for correcting multipath in GNSS positioning, grouped by type of solution (absolute/relative).

Correction Method for Absolute Positioning	Example Model/Product	Description/Principle	Accuracy
Antenna design [84,85,86]	Multipath-resistant GNSS antenna, ground plane, choke-ring structure	Reduces reflections from the ground and nearby objects by suppressing low-elevation signals	-
Correlator optimization [87]	Multi-correlator structure	Creation a high-resolution “snapshot” of the signal’s full autocorrelation function	0.5–1 m [87]
RAIM, ARAIM [80,81,82]	Integrity monitoring	Detects faulty or multipath-affected satellites via consistency tests and exclusion	4–10 m vertically, 30 m horizontally [80], 13–17 m horizontally [81], horizontal 7.7 m in static mode and 4.7 m in kinematic mode [82]
Clustering of satellite measurements [83]	Cluster-based weighting	Groups satellites with similar error signatures to reduce multipath correlation in position estimation	2.4 m [83]
Adaptive filtering [88]	Elevation- and C/N0-dependent weighting of measurements	Dynamically updates observation weights based on signal strength and multipath indices	22 m [88]
Machine learning (ML) classification [27,89,96,101,108]	SVM, CNN, LSTM trained on C/N0, residuals, elevation	Classifies LOS/NLOS signals and dynamically suppresses reflected measurements	2.5 m horizontally, 3.3 m vertically [89], 1.6 mm (E), 1.9 mm (N), 4.5 mm (U) [101]
Model-based multipath detection for PPP [93,95]	Siderial Filtering, Multipath Hemispherical Map (MHM)	Exploits satellite geometry periodicity to detect/filter repeating multipath patterns	2.1 mm (N), 1.7 mm (E), 4.4 (U) [93], 1.7 mm (E), 2.0 mm (N), 4.0 mm (U) [95]
Integration with other sensors [91,98,109]	EKF [109], FGO-based GNSS/INS fusion [91]	Detects reflective surfaces; filters inconsistent pseudorange residuals	2.8 m [91], 0.055 m (E), 0.048 m (N), 0.037 m (U) [109], 1.41 m (E), 1.25 (N), 1.70 (U) [98]
Multi-frequency PPP [97]	Overlap frequency	Uses redundant multi-frequency carrier signals to decorrelate multipath and improve ambiguity fixing	0.34 cm (East), 0.46 cm (North), 0.81 cm (Up) [97]
Robust filters [107]	Robust adaptive Kalman filter for PPP-RTK	Filters inconsistent pseudorange residuals	~1 mm horizontally and ~2 mm vertically [107]
Correction Method for Relative Positioning	Example Model/Product	Description/Principle	Accuracy
Adaptive filtering [99]	Elevation- and C/N0-dependent weighting of measurements	Dynamically updates observation weights based on signal strength and multipath indices	2.8 m [99]
RAIM [102]	MS-CRAIM	Detects faulty or multipath-affected satellites via consistency tests and exclusion	Horizontally 2.8 mm; vertically 4.7 mm [102]
Robust filters [104]	RIF, GM-KF, V-KF	Filters inconsistent pseudorange residuals	10–15 mm horizontal and 20–25 mm vertical [104]
Integration with other sensors [27,105]	EKF [105], FGO [27]	Detects reflective surfaces, filters inconsistent pseudorange residuals	GNSS+INS+LiDAR+HD map: 0.21 m (E), 0.33 m (N), 1.52 m (U) [105], GNSS+LiDAR+IMU: 0.44–0.79 m [27]

Table 3. Methods for correcting multipath in GNSS positioning, grouped by type of solution (absolute/relative).

Correction Method for Absolute Positioning	Example Model/Product	Description/Principle	Accuracy
Antenna design [84,85,86]	Multipath-resistant GNSS antenna, ground plane, choke-ring structure	Reduces reflections from the ground and nearby objects by suppressing low-elevation signals	-
Correlator optimization [87]	Multi-correlator structure	Creation a high-resolution “snapshot” of the signal’s full autocorrelation function	0.5–1 m [87]
RAIM, ARAIM [80,81,82]	Integrity monitoring	Detects faulty or multipath-affected satellites via consistency tests and exclusion	4–10 m vertically, 30 m horizontally [80], 13–17 m horizontally [81], horizontal 7.7 m in static mode and 4.7 m in kinematic mode [82]
Clustering of satellite measurements [83]	Cluster-based weighting	Groups satellites with similar error signatures to reduce multipath correlation in position estimation	2.4 m [83]
Adaptive filtering [88]	Elevation- and C/N0-dependent weighting of measurements	Dynamically updates observation weights based on signal strength and multipath indices	22 m [88]
Machine learning (ML) classification [27,89,96,101,108]	SVM, CNN, LSTM trained on C/N0, residuals, elevation	Classifies LOS/NLOS signals and dynamically suppresses reflected measurements	2.5 m horizontally, 3.3 m vertically [89], 1.6 mm (E), 1.9 mm (N), 4.5 mm (U) [101]
Model-based multipath detection for PPP [93,95]	Siderial Filtering, Multipath Hemispherical Map (MHM)	Exploits satellite geometry periodicity to detect/filter repeating multipath patterns	2.1 mm (N), 1.7 mm (E), 4.4 (U) [93], 1.7 mm (E), 2.0 mm (N), 4.0 mm (U) [95]
Integration with other sensors [91,98,109]	EKF [109], FGO-based GNSS/INS fusion [91]	Detects reflective surfaces; filters inconsistent pseudorange residuals	2.8 m [91], 0.055 m (E), 0.048 m (N), 0.037 m (U) [109], 1.41 m (E), 1.25 (N), 1.70 (U) [98]
Multi-frequency PPP [97]	Overlap frequency	Uses redundant multi-frequency carrier signals to decorrelate multipath and improve ambiguity fixing	0.34 cm (East), 0.46 cm (North), 0.81 cm (Up) [97]
Robust filters [107]	Robust adaptive Kalman filter for PPP-RTK	Filters inconsistent pseudorange residuals	~1 mm horizontally and ~2 mm vertically [107]
Correction Method for Relative Positioning	Example Model/Product	Description/Principle	Accuracy
Adaptive filtering [99]	Elevation- and C/N0-dependent weighting of measurements	Dynamically updates observation weights based on signal strength and multipath indices	2.8 m [99]
RAIM [102]	MS-CRAIM	Detects faulty or multipath-affected satellites via consistency tests and exclusion	Horizontally 2.8 mm; vertically 4.7 mm [102]
Robust filters [104]	RIF, GM-KF, V-KF	Filters inconsistent pseudorange residuals	10–15 mm horizontal and 20–25 mm vertical [104]
Integration with other sensors [27,105]	EKF [105], FGO [27]	Detects reflective surfaces, filters inconsistent pseudorange residuals	GNSS+INS+LiDAR+HD map: 0.21 m (E), 0.33 m (N), 1.52 m (U) [105], GNSS+LiDAR+IMU: 0.44–0.79 m [27]

2.4. Tropospheric Effects and Their Correction

The troposphere (the lower 10–15 km of the atmosphere) contains nitrogen, oxygen, and water vapor. GNSS radio signals (L1, L2, etc.) slow down as they pass through it, causing tropospheric delay, which for code receivers results in an error of 2–3 m at the zenith [22]. Unlike ionospheric delay, tropospheric delay is not dispersive and does not depend on frequency, so special techniques are used to eliminate it. The main modern approaches to the effective correction of tropospheric errors are listed in Table 4.

Typically, tropospheric delay along the LOS is displayed in the zenith direction using a height-dependent mapping function. Therefore, modeling zenith tropospheric delay is an important step. The zenith tropospheric delay (ZTD) model is usually divided into two parts: zenith hydrostatic delay (ZHD) and zenith wet delay (ZWD). Currently, there are several models of zenith tropospheric hydrostatic delay (ZHD) [110]: models based on meteorological parameters, such as the Hopfield model [111] and the Saastamoinen model [112]; empirical tabular models, such as the University of New Brunswick (UNB) series models [113] and the European Geostationary Navigation Overlay System (EGNOS) model [114]; models based on numerical weather forecasts, VMF1 and VMF3 [115]; and the hybrid models GZTD2, IGGtrop_ri [116], TropGrid2 [117], and Improved Tropospheric Grid (ITG) [118]. Hybrid models based on the existing models were also developed, taking into account seasonality and humidity and calculating the wet zenith delay (ZWD): Saastamoinen and GPT2 [119], UNB3m [120], and others.

According to [110], empirical global models (Saastamoinen, GPT2) are simple but limited because they use average meteorological conditions and neglect short-term variability, producing RMS errors up to 20 cm. Global models GPT2, GPT2w, and GPT3 perform slightly better, with average errors of <1 cm and an RMS of up to 5 cm due to the inclusion of gridded temperature and humidity data, while UNB3m reduces bias through a humidity term but still lacks temporal adaptation and has an RMS of approximately 6 cm. The VMF3 model achieves the best overall accuracy (RMS ≈ 1.3 cm) because it assimilates real meteorological data. Hence, the more a model incorporates real-time atmospheric data, the better it performs, particularly for ZWD estimation.

Since ZWD is difficult to predict due to water vapor variability, data-driven forecasting methods using ML provide a promising alternative. In [121], Feedforward and LSTM Neural Networks trained on CODE data achieved an RMSE ≈ 1–2 cm throughout the year. These outperform empirical or static regression models because they capture nonlinear seasonal and meteorological dependencies. Such prediction models can be used for SPP to reduce vertical positioning errors.

Tropospheric delay also strongly affects the convergence time of PPP solutions. In classical PPP solutions, ZWD is estimated as a random walk parameter, which slows convergence. To address this, [122] proposed adding global ZTD values as “virtual observations” to the solution, constraining the tropospheric state and accelerating ambiguity resolution. This approach improves both the convergence speed and coordinate precision by reducing the correlation between tropospheric and geometric parameters.

Numerical Weather Model (NWM)-based methods [123,124] provide higher-fidelity corrections by integrating pressure, temperature, and humidity profiles from models such as WRF or ECMWF. In [124], combining WRF data with GNSS observations using least-squares collocation gives an accuracy of about 46 mm. Such combinations outperform empirical models because they account for real spatial and temporal gradients of refractivity. When combining WRF with a troposphere model (UNB3m, VMF1-FC, etc.), an accuracy of 13.7 mm was obtained.

Regional tropospheric models offer a compromise between accuracy and practicality. In [125], a method for correcting tropospheric delay in real-time PPP solutions is proposed, which calculates a real-time ZWD from CORS networks to generate local corrections, achieving 13 cm horizontal and 12.4 cm vertical accuracy. Although network coverage limits applicability, this approach performs better than global models, as it captures short-range weather variability. Similar techniques include optimal polynomial models (OFC) and grid-based interpolation [126,127]. The modified OFC (M-OFC) approach, which models exponential humidity decay with altitude, achieved <1.5 cm ZWD error, improving PPP accuracy by 25%. The grid-based interpolation method [127] using data from ERA-Interim (ECMWF reanalysis) and Chinese CMONOC network data yielded 2–3 cm horizontal and 4–5 cm vertical PPP accuracy, while reducing the convergence time by 30–65%.

Combining several types of troposphere models, while taking into account regional climate characteristics, also improves the accuracy of PPP. Thus, [128] presents a regional multi-source fusion model of tropospheric delay, combining GNSS, Saastamoinen, and the global GPT2w model, reducing ZTD error to 7.5 cm.

Since traditional Numerical Weather Models (GFS, WRF, etc.) rely on costly and often approximate calculations, machine learning (ML) is increasingly used to build data-driven Numerical Weather Prediction (NWP) models. In [129], the Pangu-Weather (Huawei), GraphCast (Google DeepMind), and FengWu (Shanghai AI Lab) models are trained on ERA5 reanalysis and provide rapid forecasts of atmospheric parameters, from which meteorological parameters (pressure, temperature, humidity, etc.) are extracted and ZHD and ZWD are calculated using ray tracing. The use of short-term forecasts reduces the PPP convergence time by an average of 6–7 min, while the accuracy of PPP coordinates remains at the standard centimeter level.

For short RTK bases (10–20 km), residual atmospheric errors are small and are almost completely eliminated by double differences. For long bases (50–100 km and more), the residual troposphere becomes critical. Global models (Saastamoinen, UNB3) give errors of several cm at zenith, so network corrections are employed, which use data from several reference stations and the real-time estimation of tropospheric delays using a Kalman filter based on GPS data [130]. In network RTK (NRTK), tropospheric delays are compensated through the network corrections of FKP (Flächen Korrektur Parameter), VRS (Virtual Reference Station), and MAC (Master Auxiliary Concept), which are transmitted to users [131]. Interpolation is performed on the network side, as in VRS, or on the user side, as in FKP or MAC, using various methods: LSM (Linear Surface Model)—a simple linear surface in space; IDW (Inverse Distance Weighting)—interpolation by weights inversely proportional to distance; and Kriging—a geostatistical method that takes into account the ZTD distribution variogram. It is Kriging that shows the best stable results in different weather conditions: a horizontal accuracy of 1–2 cm and a vertical accuracy of 2–4 cm [132].

The correction of tropospheric errors using NWP is particularly effective for long baselines of more than 200 km. Thus, in [133], regional NWP from the Shanghai Meteorological Bureau (based on WRF) was used; meteorological fields were taken from NWP, and the zenith tropospheric delay (ZTD) was calculated using the integral method, which used RTK for a priori values of wet delay (ZWD) with a given dispersion. This made it possible to achieve an accuracy of 2.3 cm (N), 2.1 cm (E), and 4.3 cm (U) on a long base and 1.3 cm (N), 1.0 cm (E), and 2.6 cm (U) on a short base.

For long baselines (>200 km), numerical model-based a priori corrections remain most effective. In [133], regional WRF data were selected to compute ZTD integrals using RTK for a priori values of wet delay (ZWD), and reduced the RTK error to 2.3 cm (N), 2.1 cm (E), and 4.3 cm (U) for a long base and 1.3 cm (N), 1.0 cm (E), and 2.6 cm (U) for a short base.

In PPP-RTK solutions, the hydrostatic part is modeled globally, while the wet part is interpolated from network grids via Kriging or DIM2. This yields a 2.5 cm horizontal and 5 cm vertical accuracy [134].

Weather prediction models additionally improve ambiguity-fixing speed and reliability, outperforming purely empirical PPP-RTK constraints by shortening the initialization time. For example, [79] uses data from the Global Forecast System (GFS) NWP model to calculate ZWD. This improved the accuracy of PPP-RTK positioning by about 3.3 cm. Likewise, SSR-based tropospheric products strengthen PPP-RTK models, achieving a 1–3 cm accuracy in static mode and ≈0.1 m in dynamic mode [79].

Table 4. Methods for correcting tropospheric errors in GNSS positioning grouped by type of solution (absolute vs. relative).

Correction Method for Absolute Positioning	Example Model/Product	Description/Principle	Accuracy
Empirical models [110]	Saastamoinen, Hopfield, UNB3m, GPT2, GPT2w, GPT3, VMF3	Empirical hydrostatic and wet delay models	Up to 20 cm UNB3m; up to 5 cm GPT2, GPT2w, GPT; 1.3 cm VMF3 [110]
Numerical Weather Prediction (NWP) models [124]	WRF, ERA5-based ZTD estimation	Combine WRF with UNB3m, VMF1-FC	13.7 mm [124]
ML for ZWD forecasting and NWP model building [121]	Feedforward Neural Network (FNN), Long Short-Term Memory RNN	Provide tropospheric parameter forecasts (ZHD, ZWD, ZTD)	1–2 cm [121]
Regional corrections ZTD/ZWD [125,126,127]	ZTD/ZWD estimation	Provide ZTD/ZWD corrections with network, grid, or polynomial models	Horizontal accuracy 13 cm, vertical accuracy 12.4 cm [125]; 2–3 cm horizontally, 4–5 cm vertically at PPP [127]
Network corrections [134]	Interpolation of ZTD gradients from dense networks	Global troposphere models + correction through network Interpolation models (e.g., Kriging or DIM2) for PPP-RTK	2.5 cm horizontally; 5 cm vertically
SSR products [79]	Interpolated SSR corrections for PPP-RTK	SSR products with tropospheric corrections to correct tropospheric delays in PPP-RTK	Horizontal accuracy 1–3 cm in static mode, 0.1 m in dynamic mode
Correction Method for Relative Positioning	Example Model/Product	Description/Principle	Accuracy
Network RTK interpolation [132]	VRS, MAC, FKP tropospheric interpolation	Networks estimate and interpolate tropospheric gradients	Horizontal accuracy 1–2 cm, vertical accuracy 2–4 cm [132]
Regional corrections [133]	Correction of tropospheric errors using regional NWP	Meteorological fields are used and the zenith tropospheric delay (ZTD)	on a long base 2.3 cm (N), 2.1 cm (E), 4.3 cm (U) and 1.3 cm (N), 1.0 cm (E), 2.6 cm (U) on a short base [133]

Table 4. Methods for correcting tropospheric errors in GNSS positioning grouped by type of solution (absolute vs. relative).

Correction Method for Absolute Positioning	Example Model/Product	Description/Principle	Accuracy
Empirical models [110]	Saastamoinen, Hopfield, UNB3m, GPT2, GPT2w, GPT3, VMF3	Empirical hydrostatic and wet delay models	Up to 20 cm UNB3m; up to 5 cm GPT2, GPT2w, GPT; 1.3 cm VMF3 [110]
Numerical Weather Prediction (NWP) models [124]	WRF, ERA5-based ZTD estimation	Combine WRF with UNB3m, VMF1-FC	13.7 mm [124]
ML for ZWD forecasting and NWP model building [121]	Feedforward Neural Network (FNN), Long Short-Term Memory RNN	Provide tropospheric parameter forecasts (ZHD, ZWD, ZTD)	1–2 cm [121]
Regional corrections ZTD/ZWD [125,126,127]	ZTD/ZWD estimation	Provide ZTD/ZWD corrections with network, grid, or polynomial models	Horizontal accuracy 13 cm, vertical accuracy 12.4 cm [125]; 2–3 cm horizontally, 4–5 cm vertically at PPP [127]
Network corrections [134]	Interpolation of ZTD gradients from dense networks	Global troposphere models + correction through network Interpolation models (e.g., Kriging or DIM2) for PPP-RTK	2.5 cm horizontally; 5 cm vertically
SSR products [79]	Interpolated SSR corrections for PPP-RTK	SSR products with tropospheric corrections to correct tropospheric delays in PPP-RTK	Horizontal accuracy 1–3 cm in static mode, 0.1 m in dynamic mode
Correction Method for Relative Positioning	Example Model/Product	Description/Principle	Accuracy
Network RTK interpolation [132]	VRS, MAC, FKP tropospheric interpolation	Networks estimate and interpolate tropospheric gradients	Horizontal accuracy 1–2 cm, vertical accuracy 2–4 cm [132]
Regional corrections [133]	Correction of tropospheric errors using regional NWP	Meteorological fields are used and the zenith tropospheric delay (ZTD)	on a long base 2.3 cm (N), 2.1 cm (E), 4.3 cm (U) and 1.3 cm (N), 1.0 cm (E), 2.6 cm (U) on a short base [133]

2.5. Receiver Noise and Methods of Correction

Receiver noise refers to positioning errors caused by the hardware and software of the GNSS receiver. High-end GNSS receivers typically have lower noise levels than cheaper receivers. In code receivers, noise can cause positioning errors of 0.2–1 m, in high-end phase receivers, 1–2 mm, and in budget receivers up to 10 mm [22]. The main modern approaches for the effective correction of tropospheric errors are listed in Table 5.

Receiver noise consists of random errors that occur when measuring pseudorange and carrier phase due to the internal limitations of the equipment (amplifiers, ADCs, generators, tracking algorithms). For SPP solutions, various filtering and denoising methods are applied. In [135], a Robust Adaptive Extended Kalman Filter with an updated covariance matrix R and adaptive weighting improved accuracy from 0.74 m (GPS-only) to 0.097 m (multi-GNSS). Adaptive filters outperform standard EKF because they tune the noise model in real time rather than assuming constant variance.

Wavelet decomposition [136] separates high-frequency noise from signal components, reducing error from 0.38 m to 0.21 m. Wavelet-based approaches are more effective for dynamic SPP, as they preserve low-frequency motion trends while removing stochastic fluctuations. Review [137] also notes other smoothing filters, Vondrak, RTSS, sidereal filtering, Singular Spectrum Analysis, and Multipath Hemispherical Map, which are mainly useful for post-processing.

Real-time noise suppression often relies on weighted observation models using satellite elevation (El) and carrier-to-noise ratio (C/N₀) [138]. Measurements with low redundancy or poor geometry receive reduced weight, limiting the influence of outliers. As a result, a horizontal RMS < 10 m was achieved, which is considered a high performance for SPP in degraded conditions.

For PPP solutions, robust and adaptive filters are particularly effective. In [139], an improved robust adaptive filter based on the χ² criterion forms a separate weight matrix for code and phase data. It achieved an RMS of 0.016 m (E), 0.014 m (N), and 0.022 m (U), with a more than 100% accuracy improvement compared to conventional robust filters. This improvement arises from the filter’s ability to adaptively limit the influence of heavy-tailed residuals while maintaining sensitivity to small errors.

Observation weighting by C/N₀ [140] or elevation [141] further increases PPP stability: C/N₀ weighting reduced RMS from 12.7 m to 4.6 m, while elevation weighting mainly improved vertical precision. Smoothing approaches such as inverse [142] and incremental smoothing [143] also enhance PPP by optimizing the temporal consistency of states, halving dynamic RMS from 3.74 m to 1.80 m [143] and giving RMS values of 0.139 m (N), 0.163 m (E), and 0.137 m [142]. Signal decomposition techniques, such as wavelet packet transform combined with MSPCA [92], isolate low-frequency components, achieving a 0.62 mm PPP error relative to reference sensors.

The classic Kalman filter assumes a constant noise level, which is unrealistic and leads to a degradation in accuracy. Therefore, for RTK solutions, improved filters like an adaptive Kalman filter based on Integer Ambiguity Validation (IAVAKF) [144] adjust covariance, improving accuracy by 26% on 15 km baselines. Similarly, robust adaptive Kalman filtering in [103] yielded a 0.5–1.5 m horizontal accuracy on smartphones.

New weighted stochastic models for observations are being developed for RTK solutions. In particular, [145] proposes a combined weight model for elevation and C/N₀ and an algorithm for sequentially excluding observations with low elevations and C/N₀. This reduces the influence of noise and provides a horizontal accuracy of 1–2.2 cm.

Increased noise characteristics are naturally inherent in cheaper GNSS receivers due to hardware limitations in terms of antenna properties, since the type of antenna critically affects the noise level and the number of cycle slips. Reference [55] provides an analysis of the use of various antennas (helix, microstrip patch, vertical dipole) in conjunction with a modified stochastic noise model for a receiver working in PPP-RTK mode. According to the research results, the best accuracy is observed when using a helix antenna: 0.32 m (E), 0.23 m (N), and 0.97 m (U).

Multi-sensor integration helps compensate for noisy observations and represents another way to improve accuracy and reduce noise for budget receivers working in PPP-RTK mode. In [146], a tight coupling model was created coupling a GNSS receiver working in PPP-RTK, INS, and a vision sensor, which allowed for the achievement of practically decimeter accuracy in “noisy conditions”: 11 cm (E), 7 cm (N), and 13 cm (U). Such hybrid approaches work better than GNSS-only filters because they use independent motion data to stabilize the solution and keep accuracy even in difficult conditions.

Table 5. Methods for correcting receiver noise in GNSS positioning, grouped by type of solution (absolute vs. relative).

Correction Method for Absolute Positioning	Example Model/Product	Description/Principle	Accuracy
Weighted filtering [138]	Elevation- and C/N0-dependent weighting of measurements	Weighting of observations by C/N0 and elevation angle and local redundancy of measurements [138]; C/N0 weighting and prediction of missing data for PPP [140]	Horizontal errors < 5 m [138], 4.6 m [140]
Kalman filtering [135,139]	Adaptive/Robust KF	Robust Adaptive Extended Kalman Filter [135]; robust adaptive filter for PPP [139]	0.74 m [135] 201 mm (E), 77 mm (N), 160 mm (U) [139]
Filtering and smoothing [142,143]	Smoothing methods	Classical inverse smoothing for PPP [142]; incremental smoothing [143]	RMS: 0.139 m (N), 0.163 m (E), 0.137 m [142] 1.80 m [143]
Noise component separation	Wavelet analysis	Wavelet signal transformation [136]	0.21 m [136]
Correction Method for Relative Positioning	Example Model/Product	Description/Principle	Accuracy
Weighted filtering [142]	Elevation- and C/N0-dependent weighting of measurements	Exclusion of observations with low elevation and C/N0	1–2.2 cm [142]
Kalman filtering [144]	Adaptive/Robust KF	Adaptive Kalman filter based on Integer Ambiguity Validation (IAVAKF)	Improved by 26% compared to classic KF [144]
Integration with other sensors [146]	GNSS/INS integration with EKF or factor graph	Tight coupling PPP-RTK, INS, vision sensor	11 cm (E), 7 cm (N), 13 cm (U) [146]
Hardware improvement [55]	Use of improved antennas	Use of helix antennas	0.32 m (E), 0.23 m (N), 0.97 m (U) [55]

Table 5. Methods for correcting receiver noise in GNSS positioning, grouped by type of solution (absolute vs. relative).

Correction Method for Absolute Positioning	Example Model/Product	Description/Principle	Accuracy
Weighted filtering [138]	Elevation- and C/N0-dependent weighting of measurements	Weighting of observations by C/N0 and elevation angle and local redundancy of measurements [138]; C/N0 weighting and prediction of missing data for PPP [140]	Horizontal errors < 5 m [138], 4.6 m [140]
Kalman filtering [135,139]	Adaptive/Robust KF	Robust Adaptive Extended Kalman Filter [135]; robust adaptive filter for PPP [139]	0.74 m [135] 201 mm (E), 77 mm (N), 160 mm (U) [139]
Filtering and smoothing [142,143]	Smoothing methods	Classical inverse smoothing for PPP [142]; incremental smoothing [143]	RMS: 0.139 m (N), 0.163 m (E), 0.137 m [142] 1.80 m [143]
Noise component separation	Wavelet analysis	Wavelet signal transformation [136]	0.21 m [136]
Correction Method for Relative Positioning	Example Model/Product	Description/Principle	Accuracy
Weighted filtering [142]	Elevation- and C/N0-dependent weighting of measurements	Exclusion of observations with low elevation and C/N0	1–2.2 cm [142]
Kalman filtering [144]	Adaptive/Robust KF	Adaptive Kalman filter based on Integer Ambiguity Validation (IAVAKF)	Improved by 26% compared to classic KF [144]
Integration with other sensors [146]	GNSS/INS integration with EKF or factor graph	Tight coupling PPP-RTK, INS, vision sensor	11 cm (E), 7 cm (N), 13 cm (U) [146]
Hardware improvement [55]	Use of improved antennas	Use of helix antennas	0.32 m (E), 0.23 m (N), 0.97 m (U) [55]

3. Architectures for GNSS High-Precision and Reliable Solutions

The GNSS structure for user positioning includes space, user, and control segments (Figure 2). The space segment provides navigation signals from satellites and the control segment monitors orbits, updates ephemerides, and corrects clocks, while the user segment uses a GNSS receiver to capture and track signals, decode navigation messages, and calculate the user’s coordinates, speed, and time.

The current development of global navigation satellite systems is characterized not only by the improvement of algorithms and the growth in the number of satellite constellations, but also by the improvement of receiver architectures to increase positioning accuracy and reliability.

Various approaches, ranging from hardware-based to software-defined solutions and integration with additional sensors, reflect the desire to adapt GNSS receivers to a variety of application scenarios: from mass-market mobile devices to geodesy, autonomous transport, and infrastructure monitoring tasks.

To identify trends in precision and reliability improvement, the following subsections analyze and compare key GNSS architectures, focusing on their implementation principles, advantages, and trade-offs.

3.1. Conventional GNSS Receiver Architecture

Conventional hardware-based GNSS receiver architecture includes an antenna, radio frequency front end, downconverter, analog-to-digital converter, basic correlator unit, and navigation processor [147]. This modular design ensures the high reliability and predictability of operation. In aviation, such receivers have been successfully certified and are operated in conjunction with SBAS/GBAS systems, where integrity and meter-level accuracy are guaranteed [148]. The use of auxiliary technologies such as A-GNSS further reduces time-to-first-fix (TTFF) and increases sensitivity, ensuring stable signal acquisition even at C/N₀ < 30 dB-Hz [149]. However, in modern conditions, architecture with hardware correlators demonstrates a limited flexibility. Thus, review [150] shows that single-frequency low-cost receivers (SF-LC) provide an accuracy comparable to geodetic analogs only in open sky conditions, but in the presence of shading and multipath, accuracy drops sharply to decimeters and sometimes meters. The use of structures with multi-correlators [87] allows for an accuracy of 0.5–1 m. Dual-frequency receivers (DF-LC) partially compensate for ionospheric errors and provide RTK solutions, but, with long baselines (>10 km) and in difficult conditions, the quality of observations remains significantly worse than that of geodetic devices [151].

In aviation applications, where resistance to ionospheric disturbances and multipath propagation is critical, hardware-based architecture is vulnerable to signal degradation. Ref. [148] shows that antenna shadowing by aircraft structural elements or the influence of the ionosphere can lead to temporary signal loss, and the use of only a classical scheme does not provide the required level of fault tolerance. To compensate for this, SBAS and GBAS system products and the use of RAIM methods are proposed, which allow the integrity and continuity of operation to be restored.

In geostationary orbit (GEO), rigid hardware architecture also limits effectiveness, as satellite visibility is limited and signals in geostationary orbit are weak and unstable, often coming through the side lobes of GNSS antennas. Thus, in [152], modeling and hardware tests using Galileo E1 and GPS L1/L5 signals showed that successful signal acquisition is only possible at C/N₀ > 28 dB-Hz. At lower values, the probability of successful tracking decreases, which directly affects the availability of navigation solutions. Even with the use of an adaptive orbital filter, the achievable accuracy was about 1 m, which is worse than the expected level of modern multi-frequency solutions.

Limitations have also been identified in agriculture applications. For example, in [153], the testing of precision farming systems showed that single-frequency receivers provide decimeter accuracy. Under favorable conditions, the average accuracy from pass to pass was 11.5 cm (WADGPS), 8.5 cm (PPP-SF3), and 4.5 cm (RTK). Under the worst conditions, the accuracy dropped to 25.5 cm (WADGPS), 65.5 cm (PPP-SF3), and 22.5 cm (RTK), confirming the inadequacy of standard hardware for precision agricultural applications.

Civilian conventional GNSS receivers for mass use usually provide only meter-level accuracy, as shown in [154]. The main limitations are related to signal attenuation indoors and the high cost of antennas for broadband reception. In such conditions, the hardware architecture does not provide the required positioning quality without hybridization with other technologies, such as INS or LiDAR.

3.2. Software-Defined GNSS Receivers

Software-defined (SD) GNSS receivers represent an architecture in which key functional blocks of the receiver path, such as the correlator, tracking system, and subsequent signal processing, are implemented in software on top of a universal hardware platform. This approach provides fundamental flexibility in researching, testing, and rapidly implementing new processing methods, including multi-system and multi-frequency signals (GPS, Galileo, BeiDou, etc.). A detailed overview of the history of SDR development, their current status, and standardization efforts is presented in [155], which also notes that software-defined architecture contributes to the unification of receiver description methods and the development of generally accepted standards. From the point of view of hardware implementation, SD receivers cover a wide range of architectures, from CPU-oriented systems to hybrid solutions using GPUs and FPGAs [156].

Practical applications of SD structures in GNSS receivers cover both research and applied tasks. In the context of security, SD structures are used to develop methods for detecting and mitigating spoofing. They allow protection algorithms to be updated or replaced without hardware redesign, which is a critical advantage over rigid hardware solutions. Ref. [157] provides an overview of SDR tools for implementing anti-spoofing algorithms. As a case study, the MMSE correlator mitigates cross-correlation and spoofing effects but requires higher computational resources, demonstrating a direct trade-off between adaptability and processing cost.

Another promising direction of SDR applications lies in the localization and suppression of radio frequency interference (RFI). The authors of [158] confirmed the possibility of using inexpensive off-the-shelf SDRs for the rapid detection of RFI sources and their localization in real operating conditions. Compared to conventional receivers, SDR-based approaches enable near-real-time adaptation of detection thresholds and filtering algorithms, improving resilience to new types of interference.

The open development community is making a significant contribution to the development of SDR technologies. Projects such as GNSS-SDR and PocketSDR [159,160] make experimentation reproducible and foster the cross-validation of algorithms, creating a feedback loop between research and implementation. In contrast to proprietary systems, open SDR ecosystems accelerate the translation of new algorithms into practical receivers and enhance transparency in performance evaluation. Ref. [159] emphasizes that it is the open source system that contributes to the consolidation of efforts in the field of standardization.

The prospects for the development of GNSS-SD are linked to the further standardization of interfaces and modular descriptions of receiver blocks [155], which will improve the compatibility and interchangeability of components; the optimization of hybrid hardware–software architectures [156], which open up opportunities for the implementation of SDR solutions in critical navigation systems; and the expansion of the open source community [159], which will contribute to the accelerated dissemination of new methods. Thus, SD is a promising technology for both fundamental GNSS research and applied navigation solutions.

3.3. Multi-Frequency and Multi-Constellation Architectures

Multi-frequency and multi-constellation architectures (Figure 3) of global navigation satellite systems (GNSSs) have become a key area of development for high-precision positioning. The growth in the number of satellite constellations (GPS, GLONASS, Galileo, BeiDou) and the emergence of new civil signals at multiple frequencies have made it possible to significantly improve the stability of solutions, reduce convergence time, and increase accuracy even in challenging urban or natural environments. For example, [134] shows that the use of multi-GNSS and multi-frequency measurements allows for a convergence time of less than 9 minutes for floating PPP solutions and less than 5 minutes for fixed solutions, providing centimeter accuracy. For dynamic condition car experiments, PPP-RTK maintains accuracy within 10 cm, which meets the requirements of intelligent transport and unmanned systems.

Multi-frequency and multi-constellation architectures are of considerable interest in the field of unmanned aviation. In [161], a comparative analysis of the use of individual constellations (GPS, GLONASS, Galileo, BeiDou, SBAS) for UAV localization was conducted. The results showed that combining GPS and Galileo provides a noticeable increase in accuracy; adding BeiDou increases availability and reduces errors at low horizons, and GLONASS can improve solution stability in urban canyons.

Additional benefits are provided by integrating GNSS with inertial systems and odometry. In [162], it is demonstrated that the use of multi-frequency GPS (L1, L2C, L5) and Galileo (E1, E5a, E5b) in a tightly integrated GNSS/IMU/odometry algorithm reduces RMS positioning errors to 3.6 m/2.1 m compared to 5.2 m/2.9 m for single-frequency GPS. The effectiveness is particularly high in poor GNSS reception conditions, when odometry reduces the 95% horizontal positioning error from 6.2 m to 4.2 m.

Triple-frequency PPP models are the most promising for static tasks. In [163], triple-frequency solutions for Galileo and BDS-3 were tested: the TIF (triple-frequency ionosphere-free combination) model provides an accuracy of 4.9–12.1 mm with a convergence time of ~11 min, which makes it comparable to geodetic RTK methods. For dynamic conditions, [164] shows that combining GPS, GLONASS, Galileo, and BeiDou with GFZ (Geo Forschungs Zentrum) products allows for centimeter accuracy to be achieved.

However, multi-frequency solutions are sensitive to signal degradation in complex environments. Ref. [165] shows that leafy canopies and metal structures significantly reduce the quality of GPS L2 signals (C2W, L2WW), while more modern signals (L2C, L1 C/A) demonstrate a better stability. These results highlight the need for adaptive filters and algorithms that combine different methods to maintain solution quality in multipath conditions. Thus, the use of multi-constellation and multi-frequency solutions for the more efficient construction of the Multipath Hemispherical Map provides accuracy of <1 cm [97] in dense urban environments.

The characteristics of multi-frequency and multi-constellation solutions are shown in Table 6. Based on the analysis, it has been determined that multi-frequency and multi-constellation GNSS architectures combine the advantages of high-precision global services, integration with additional sensors, and resistance to difficult reception conditions.

Table 6. Characteristics of multi-frequency and multi-constellation solutions.

Solution Type	Correction Methods/Features	Examples of Configurations/Services	Convergence Time	Positioning Accuracy	Experimental Conditions
Absolute PPP (single frequency) [163]	IF model PPP, basic ionospheric correction	GPS L1	>30 min	Decimeter level	Static processing
Absolute PPP (dual-frequency) [163]	IF model PPP, ionospheric error correction	GPS + Galileo	~15 min	Horizontal accuracy 7–12 mm	Static processing (160 stations)
Absolute PPP (triple-frequency) [163]	TIF PPP model, using BDS-3 and Galileo	BDS-3 (triple-frequency)	~11 min	4.9–12.1 mm	Static processing
PPP with multi-GNSS [134]	Combination of orbital and temporal products + multi-frequency signals	GPS + Galileo + BeiDou	<10 min (floating solution)	1–2 cm	Vehicle testing
Hybrid PPP-RTK [134]	PPP-AR + network corrections	GPS + Galileo + BeiDou, HAS, BDS-3 PPP-B2b	<5 min (fixed solution)	~2.5 cm	Vehicle testing
Multi-GNSS PPP (dynamic) [164]	MGEX products (GFZ), multi-constellation	GPS + GLONASS + Galileo + BeiDou	~10–15 min	Centimeter -decimeter level	Sea trials
PPP (dynamics, single constellation) [164]	GPS-only, standard PPP products	GPS	~20–30 min	0.3–0.5 m	Bathymetric mapping
GNSS in interference conditions [165]	Analysis of signal degradation in multipath and under foliage	GPS L2 vs. L2C, Galileo	-	Accuracy degradation	Stationary tests on construction equipment

Table 6. Characteristics of multi-frequency and multi-constellation solutions.

Solution Type	Correction Methods/Features	Examples of Configurations/Services	Convergence Time	Positioning Accuracy	Experimental Conditions
Absolute PPP (single frequency) [163]	IF model PPP, basic ionospheric correction	GPS L1	>30 min	Decimeter level	Static processing
Absolute PPP (dual-frequency) [163]	IF model PPP, ionospheric error correction	GPS + Galileo	~15 min	Horizontal accuracy 7–12 mm	Static processing (160 stations)
Absolute PPP (triple-frequency) [163]	TIF PPP model, using BDS-3 and Galileo	BDS-3 (triple-frequency)	~11 min	4.9–12.1 mm	Static processing
PPP with multi-GNSS [134]	Combination of orbital and temporal products + multi-frequency signals	GPS + Galileo + BeiDou	<10 min (floating solution)	1–2 cm	Vehicle testing
Hybrid PPP-RTK [134]	PPP-AR + network corrections	GPS + Galileo + BeiDou, HAS, BDS-3 PPP-B2b	<5 min (fixed solution)	~2.5 cm	Vehicle testing
Multi-GNSS PPP (dynamic) [164]	MGEX products (GFZ), multi-constellation	GPS + GLONASS + Galileo + BeiDou	~10–15 min	Centimeter -decimeter level	Sea trials
PPP (dynamics, single constellation) [164]	GPS-only, standard PPP products	GPS	~20–30 min	0.3–0.5 m	Bathymetric mapping
GNSS in interference conditions [165]	Analysis of signal degradation in multipath and under foliage	GPS L2 vs. L2C, Galileo	-	Accuracy degradation	Stationary tests on construction equipment

3.4. Cloud and Edge Architectures

Cloud and edge architectures fundamentally change the paradigm of GNSS receiver system design by redistributing the computational load between resource-constrained terminals and remote computing resources. The concept of a “cloud receiver” involves transferring the most resource-intensive operations of code and phase correction, implementing PPP/RTK/PPP-RTK algorithms, and post-processing raw IF counts to centralized or peripheral servers, while the user device is limited to signal collection and preprocessing. Early works [45,166] showed that this approach significantly reduces the power consumption of mobile terminals and simplifies their architecture, while maintaining high positioning accuracy. Thus, in [45], a comparative analysis of energy consumption was carried out: it was shown that the GNSS module is one of the most energy-intensive components of an IoT device along with the RF interface, while moving processing to the cloud allows for reducing energy consumption with a comparable positioning accuracy.

Figure 4 shows the architecture of GNSS integration with cloud and edge computing, which redistributes the computational load between the user terminal and remote servers. The terminal receives and performs the initial processing of signals, extracting pseudorange, carrier phase, and Doppler measurements, which are transmitted to the server via a bidirectional TCP/IP connection. The cloud part of the architecture includes a synchronization and data conversion module to the RTCM3 format, as well as PPP/RTK/PPP-RTK computing units and IF count post-processing units that perform real-time coordinate refinement. This distributed structure improves the accuracy, reliability, and energy efficiency of GNSSs with limited user device resources.

The practical feasibility of cloud PPP has been confirmed by experimental research. In [167], a cloud architecture called NavCm was proposed that supports PPP with BDS PPP-B2b and Galileo corrections. Without additional services, a positioning quality of 0.06–0.08 m horizontally and ≈0.08–0.10 m vertically was achieved, and, when using PPP-B2b services, the accuracy reached 5 cm and 13 cm, respectively. In dynamic tests on vehicles, NavCm and PRIDE PPP-AR showed a comparable stability and accuracy (<4 cm in both coordinates), demonstrating the applicability of cloud PPP solutions for real-time navigation.

Cloud processing has also proven its effectiveness for smartphones and IoT terminals. Refs. [168,169] describe practical implementations of Android applications that collect raw GNSS observations and transmit them to cloud servers. The reverse solution returned to the device provides high-precision real-time positioning with significantly less load on computing resources and the battery.

The key limitation of centralized cloud solutions remains latency, which is especially critical for real-time tasks such as RTK and PPP-RTK for UAVs and autonomous vehicles. Ref. [170] analyzed latency sources from observation transmission to result return and showed that network conditions and server load are dominant contributors. In contrast, edge architectures mitigate this by placing part of the computation closer to the user at geographically distributed edge servers. For instance, [171] proposed offloading satellite selection and partial data preprocessing to edge servers, while retaining PPP/RTK corrections in the cloud. Tests on autonomous tractors under severe signal shadowing confirmed stable and low-latency performance.

Another important aspect of cloud architecture implementation is scalability and security. In [172], it is noted that cloud platforms have the advantages of redundancy, flexibility, and the ability to serve a large number of customers, but they face the risks of compromising location data and the possibility of attacks through correction substitution. Therefore, in critical infrastructure scenarios, authentication, integrity protection, and access control mechanisms are required at the cloud and edge node levels. Refs. [45,170,172] emphasize the need for hybrid schemes that include cryptographic channel protection, pre-filtering and compression of observations, and adaptive traffic management to improve fault tolerance.

The characteristics of cloud and edge architectures for GNSS receivers are shown in Table 7. Recent studies confirm that cloud and edge architectures provide the technological basis for the implementation of high-precision PPP/RTK/PPP-RTK algorithms in mass-market devices, including smartphones and IoT terminals. However, issues of latency, security, and cost-effectiveness remain unresolved, requiring the development of hybrid architectures that balance centralized cloud resources with distributed processing at the edge.

Table 7. Characteristics of cloud and edge architectures.

Type of Solution	Correction Methods/Features	Examples of Configurations/Services	Convergence Time	Positioning Accuracy	Experimental Conditions
Cloud-PPP (NavCm) [167]	PPP with using global ephemerides; support for BDS and Galileo	NavCm	Minutes (typical for PPP)	Without services: 0.06–0.08 m (horizontal), 0.08–0.10 m (vertical); with PPP-B2b: 5 cm (horizontal) and 13 cm (vertical)	Static tests, dynamic tests on vehicles
Cloud-PPP (PRIDE PPP- AR) [167]	PPP-AR (ambiguity resolution) in the cloud	PRIDE PPP-AR	Minutes	<4 cm (horizontal and vertical accuracy)	Dynamic tests on transport
Cloud-PPP for smartphones and IoT [168]	Transmission of “raw” observations to the server	Android application	Depends on the service	Sub-decimeter accuracy (2 cm horizontally and 5 cm vertically)	Mobile devices
Centralized cloud [170]	Full processing on cloud server	-	Depends on network and load	1–2 cm in static, when moving, positioning error is determined by network latency: from <1 m	Mobile devices
Edge architecture [171]	Transfer of computations to edge servers; the cloud performs the final calculation	Edge servers + cloud	Less latency than in a centralized cloud	Centimeter accuracy (PPP/RTK) is maintained	Tractor movement under shading conditions

Table 7. Characteristics of cloud and edge architectures.

Type of Solution	Correction Methods/Features	Examples of Configurations/Services	Convergence Time	Positioning Accuracy	Experimental Conditions
Cloud-PPP (NavCm) [167]	PPP with using global ephemerides; support for BDS and Galileo	NavCm	Minutes (typical for PPP)	Without services: 0.06–0.08 m (horizontal), 0.08–0.10 m (vertical); with PPP-B2b: 5 cm (horizontal) and 13 cm (vertical)	Static tests, dynamic tests on vehicles
Cloud-PPP (PRIDE PPP- AR) [167]	PPP-AR (ambiguity resolution) in the cloud	PRIDE PPP-AR	Minutes	<4 cm (horizontal and vertical accuracy)	Dynamic tests on transport
Cloud-PPP for smartphones and IoT [168]	Transmission of “raw” observations to the server	Android application	Depends on the service	Sub-decimeter accuracy (2 cm horizontally and 5 cm vertically)	Mobile devices
Centralized cloud [170]	Full processing on cloud server	-	Depends on network and load	1–2 cm in static, when moving, positioning error is determined by network latency: from <1 m	Mobile devices
Edge architecture [171]	Transfer of computations to edge servers; the cloud performs the final calculation	Edge servers + cloud	Less latency than in a centralized cloud	Centimeter accuracy (PPP/RTK) is maintained	Tractor movement under shading conditions

3.5. Integrated GNSS/INS/LiDAR Architectures

Integrated architectures combining GNSS with inertial measurement units (INS) and additional sensors (primarily LiDAR and cameras) are one of the most effective practical solutions for improving navigation accuracy and stability in challenging urban environments and in the presence of multipath. This position is confirmed both by review papers on GNSS/INS integration and by numerous experimental studies demonstrating a significant reduction in navigation errors when combining absolute (GNSS) and relative (IMU, LiDAR, vision) measurements [27,91,98,173,174]. Work [173] also presents typical INS/GNSS integration architectures: loosely coupled integration, tightly coupled integration, and deeply coupled integration.

Architectural integration models range from loosely coupled schemes to tightly and deeply coupled solutions; the choice of a specific scheme is determined by the requirements for GNSS loss resilience, computational load, and target application (automobile, UAV, surveying equipment). A review of the current methods emphasizes that tightly coupled and deeply coupled approaches better maintain accuracy during short-term and long-term GNSS outages by directly using carrier phase measurements and inertial increments [173,174]. In contrast, loosely coupled models are simpler to implement but exhibit a larger drift accumulation, especially in long-term outages.

Practical experiments show that adding LiDAR to GNSS/INS significantly improves navigation stability and accuracy. In [175], GNSS/INS/LiDAR-SLAM integration was implemented through factor graph optimization, and a reduction in errors during GNSS outage simulation was demonstrated: the root mean square errors in the north/east directions decreased by approximately 82.2% and 79.6%, respectively, compared to GNSS/INS integration. All other things being equal, vertical and angular accuracies also improved significantly, and the relative error during the GNSS downtime period decreased to 0.26% of the distance traveled, which is critical for mobile mapping and geodesy. These results emphasize that LiDAR compensates for INS drift and GNSS calibration errors in urban environments.

Similarly, field experiments confirm that LiDAR-based augmentation improves robustness: in prolonged GNSS outages, the horizontal and vertical RMSE decreased by 51% and 78%, respectively, compared to GNSS/INS-only configurations. In complex urban areas, tightly coupled GNSS/IMU/LiDAR systems consistently achieve sub-meter accuracy and show a 60–75% better performance over conventional methods [176,177,178]. This improvement illustrates that LiDAR complements INS dynamics with dense geometric features, enabling a stable pose estimation even without GNSS.

For UAVs and geodetic platforms, these integrations are particularly advantageous. LiDAR provides dense 3D scene geometry, while the fusion of high-frequency INS data and periodic GNSS updates ensures an accurate state estimation. Work [176] demonstrates that, when the GNSS receiver fails, an integration with LiDAR allows the UAV trajectory to be restored with a significant reduction in RMSE, making the solution promising for unmanned aviation and autonomous robotic platforms.

There are also cost-effective approaches to improving the accuracy of integrated systems. For example, the use of several inexpensive receivers in a single integrated GNSS/SINS system with cascaded and centralized filters has been shown to be a way to significantly improve accuracy without significantly increasing the cost of the platform [179]. Machine learning methods such as cascaded LSTM networks are employed to predict pseudovelocities and stabilize navigation during extended GNSS outages [180]. These approaches demonstrate that algorithmic advances can partially offset hardware limitations.

Methodologically advantageous are closely/deeply coupled filters and factor graph optimization, which use carrier-phase and lidar point measurements for joint state estimation—hybrid schemes combining local preprocessing and distributed post-processing.

Despite its obvious advantages, GNSS/INS/LiDAR integration places increased demands on the synchronization of measurement time stamps, accurate sensor calibration, and computing resources. Budget IMUs have stronger drift, which requires advanced error models, calibration, and adaptive filtering (MVC-EKF, H_∞, etc.) [181,182]. Practical implementation on UAVs imposes strict requirements on weight, power consumption, and latency, which makes the development of lightweight factor graph optimization algorithms relevant [175,177,183].

The characteristics of integrated GNSS/INS/LiDAR architectures are shown in Table 8. Recent research and field tests clearly show that GNSS/INS/LiDAR integration represents a budget-friendly and technologically mature direction capable of improving positioning accuracy and navigation stability in difficult conditions. For geodesy, mapping, and UAV navigation, the combination of GNSS, INS, and LiDAR measurements is a promising area with a high potential for practical applications and use in modern methods: factor graph optimization, adaptive filters, and machine learning to compensate for prolonged absence GNSS measurements.

Table 8. Characteristics of integrated GNSS/INS/LiDAR architectures.

Type of Solution	Correction Methods/Features	Examples of Configurations/Services	Convergence Time	Positioning Accuracy	Experimental Conditions
GNSS/INS/LiDAR-SLAM + factor graph optimization [175]	Joint optimization by carrier phase and LiDAR points; INS drift compensation	Mobile mapping, geodesy	Stable convergence, even during GNSS interruptions	RMSE reduction: N ≈ 82%, E ≈ 79%; relative error at simple GNSS −0.26% distance traveled	Tests with modeling of losses GNSS, urbanized conditions
GNSS/INS/LiDAR (close integration) [176,177,178]	Use of carrier GNSS and LiDAR phases in filters; hybrid schemes	UAV for mapping, autonomous vehicles	Convergence is maintained during GNSS interruptions	Improved accuracy 60–75% compared to GNSS/INS; support for sub-meter accuracy	Field tests under conditions of partial/complete GNSS loss
GNSS/SINS Systems [179]	Use of several inexpensive receivers + cascaded/centralized filters	Low-cost integrated platforms	Rapid recovery in failures	-	Laboratory and field tests
GNSS/INS + ML (Cascade LSTM) [180]	The ML model predicts pseudovelocities for filtering in the absence of GNSS	Autonomous platforms	Stability is maintained during prolonged losses	Improved accuracy during prolonged downtime; reduction in INS drift	Tests on long GNSS outages

Table 8. Characteristics of integrated GNSS/INS/LiDAR architectures.

Type of Solution	Correction Methods/Features	Examples of Configurations/Services	Convergence Time	Positioning Accuracy	Experimental Conditions
GNSS/INS/LiDAR-SLAM + factor graph optimization [175]	Joint optimization by carrier phase and LiDAR points; INS drift compensation	Mobile mapping, geodesy	Stable convergence, even during GNSS interruptions	RMSE reduction: N ≈ 82%, E ≈ 79%; relative error at simple GNSS −0.26% distance traveled	Tests with modeling of losses GNSS, urbanized conditions
GNSS/INS/LiDAR (close integration) [176,177,178]	Use of carrier GNSS and LiDAR phases in filters; hybrid schemes	UAV for mapping, autonomous vehicles	Convergence is maintained during GNSS interruptions	Improved accuracy 60–75% compared to GNSS/INS; support for sub-meter accuracy	Field tests under conditions of partial/complete GNSS loss
GNSS/SINS Systems [179]	Use of several inexpensive receivers + cascaded/centralized filters	Low-cost integrated platforms	Rapid recovery in failures	-	Laboratory and field tests
GNSS/INS + ML (Cascade LSTM) [180]	The ML model predicts pseudovelocities for filtering in the absence of GNSS	Autonomous platforms	Stability is maintained during prolonged losses	Improved accuracy during prolonged downtime; reduction in INS drift	Tests on long GNSS outages

3.6. Integrated GNSS/IoT Architectures

Architectures combining GNSS and Internet of Things (IoT) devices are forming a new field of application that combines the mass availability of inexpensive equipment with the capabilities of cloud/edge processing. For example, [184] presents a specialized GNSS chip for IoT that supports energy-saving operating modes. Comparative tests with the NovAtel GNSS/INS reference solution show that, even in scenarios with unfavorable reception conditions (NLOS, multipath, low temperatures), the chip provides stable reception, and the use of ultra-low power modes allows it to operate in conditions of limited energy balance, which is critically important for IoT terminals. The architecture diagram of the integrated GNSS/IoT system is shown in Figure 5, which shows the main functional blocks of the device, interaction with GNSS signals, and data transmission between the IoT device, service provider (SP), and location data aggregator (LA).

The use of hybrid GNSS/IoT technology allows for the use of corrections that are downloaded via an IP connection to the service. In [57], an IoT device with PPP-RTK support is presented, developed on the basis of a low-budget GNSS module u-blox ZED-F9P, which is integrated with a controller that provides network interaction. Kinematic tests have shown decimeter accuracy in urban environments, and the device can transmit positioning solutions via IoT Internet interfaces, confirming the technology’s potential for mass application. Compared with traditional receivers, such IoT-based solutions trade real-time performance for scalability and energy efficiency, making them more suitable for large distributed networks than for time-critical applications.

The integration of GNSS and IoT demonstrates a high applied value in the monitoring of natural and civil objects. For example, [185] implements a multi-sensor GNSS-IoT system for measuring water surface elevation (WSE), including a GNSS receiver, ultrasonic sensors, and an accelerometer. In field tests at the Hugong Reservoir (Australia) over a period of four months, an accuracy of 7 mm was achieved for 6-hour averaged solutions and 28 mm for single epoch measurements without averaging. The system retained more than 90% of solutions meeting quality standards, even during moderate storms, confirming the applicability of GNSS-IoT for long-term autonomous monitoring and the verification of satellite missions such as SWOT.

For infrastructure monitoring tasks, [46] developed an IoT platform with a dual-band GNSS receiver (L1/L2) supporting RTK corrections. Long-term testing (15 days) demonstrated an accuracy comparable to that of a high-precision receiver. Moreover, by reducing the sampling rate to 60 measurements per hour, the system maintained stability, confirming the feasibility of continuous, cost-effective monitoring. This balance between energy efficiency and precision shows the advantage of IoT-based systems for large-scale structural health monitoring compared with classical geodetic receivers that require constant power and maintenance.

Moving heavy computing tasks to the cloud significantly improves the scalability and efficiency of systems. In [186], a cloud-based GNSS architecture for monitoring the state of the ionosphere is proposed, where total electron concentration (TEC) data collected by IoT nodes is aggregated in the cloud and used to build real-time maps of the ionosphere. Experimental results showed an accuracy of 98.23%, sensitivity of 97.87%, responsiveness of 95.32%, and throughput of 98.35%, which exceeds the traditional methods of obtaining ionospheric parameters from navigation messages, IGS, or regional GNSS networks. This confirms that distributed IoT sensing combined with centralized GNSS data fusion can achieve both a high precision and system-wide responsiveness.

However, GNSS-based IoT architectures still have limitations. First, the dependence on network connectivity and cloud processing creates latency risks, which are especially critical for applications with strict timing requirements, such as UAV control. Second, centralized data aggregation increases vulnerability to security and privacy threats. Ref. [46] notes the need to protect communication channels and data authentication.

Machine learning (ML/DL) methods are increasingly applied to optimize GNSS/IoT performance. Ref. [187] reviews the application of ML/DL to process GNSS data arrays and combat major problems such as multipath, signal shadowing, and urban interference using classification methods (LOS determination, NLOS, failures/outliers), prediction or restoration of missing measurements, improvement of positioning accuracy, and adaptive/contextual models. It has been shown that neural network models can improve positioning reliability in dense urban environments and reduce energy consumption through the adaptive control of receiver operating modes.

The characteristics of integrated GNSS/IoT architectures are shown in Table 9. Recent studies show that the GNSS/IoT architecture combines low hardware costs, the high scalability of sensor networks, and the capabilities of cloud/edge processing. This allows for millimeter-level accuracy in observations of the dynamics of natural objects [185], decimeter-level accuracy in kinematic urban scenarios [57], and a high efficiency in ionospheric monitoring [186]. The challenges of reducing latency, protecting data, and ensuring energy efficiency remain unresolved, requiring the implementation of hybrid architectures, multi-sensor integration, and ML/DL methods to improve robustness.

Table 9. Characteristics of integrated GNSS/IoT architectures.

Type of Solution	Correction Methods/Features	Examples of Configurations/Services	Convergence Time	Positioning Accuracy	Experimental Conditions
Specialized GNSS chip for IoT [184]	Support for ultra-low power consumption, NLOS operation and multipath	Proprietary chip, comparison with the NovAtel GNSS/INS reference	-	-	Multipath
IoT device with PPP-RTK [57]	Integration of u-blox ZED-F9P with IoT controller, transmission of corrections via IP	u-blox ZED-F9P + network controller	Minutes (typical for PPP-RTK)	Decimeter accuracy in urban conditions	Kinematic tests, data transmission via IoT
GNSS-IoT for monitoring water surface (WSE) [185]	GNSS + ultrasonic sensors + accelerometer; long-term monitoring	Multi-sensor GNSS-IoT system	6-hour averaging	7 mm (averaged over 6 h), 28 mm (epochal values)	Field tests, Hugong Reservoir (Australia)
IoT platform for infrastructure [46]	Dual-band GNSS (L1/L2) + RTK; simulation of reduced number of measurements	Low-cost receivers + IoT platform	-	About 0.5 cm CEP, maximum—up to 2.5 cm	Infrastructure monitoring
GNSS/IoT + ML/DL [187]	Classification LOS/NLOS, prediction of missing measurements, adaptive models	ML/DL models integrated with GNSS-IoT	Depends on the algorithm	Decimeters or centimeters (under optimal conditions) for RTK	Urban environment

Table 9. Characteristics of integrated GNSS/IoT architectures.

Type of Solution	Correction Methods/Features	Examples of Configurations/Services	Convergence Time	Positioning Accuracy	Experimental Conditions
Specialized GNSS chip for IoT [184]	Support for ultra-low power consumption, NLOS operation and multipath	Proprietary chip, comparison with the NovAtel GNSS/INS reference	-	-	Multipath
IoT device with PPP-RTK [57]	Integration of u-blox ZED-F9P with IoT controller, transmission of corrections via IP	u-blox ZED-F9P + network controller	Minutes (typical for PPP-RTK)	Decimeter accuracy in urban conditions	Kinematic tests, data transmission via IoT
GNSS-IoT for monitoring water surface (WSE) [185]	GNSS + ultrasonic sensors + accelerometer; long-term monitoring	Multi-sensor GNSS-IoT system	6-hour averaging	7 mm (averaged over 6 h), 28 mm (epochal values)	Field tests, Hugong Reservoir (Australia)
IoT platform for infrastructure [46]	Dual-band GNSS (L1/L2) + RTK; simulation of reduced number of measurements	Low-cost receivers + IoT platform	-	About 0.5 cm CEP, maximum—up to 2.5 cm	Infrastructure monitoring
GNSS/IoT + ML/DL [187]	Classification LOS/NLOS, prediction of missing measurements, adaptive models	ML/DL models integrated with GNSS-IoT	Depends on the algorithm	Decimeters or centimeters (under optimal conditions) for RTK	Urban environment

4. Discussion About Research Challenges and Open Problems

Having considered in Section 2 the current methods of combating the main factors affecting the accuracy of GNSS positioning, a number of issues have been identified that are still of scientific interest.

Atmospheric errors. For single-frequency receivers, ionospheric errors remain critical (up to 10–15 m), and global models such as Klobuchar provide only a partial compensation [22,24]. More accurate methods used in phase receivers for PPP, such as GIMs, DMD forecasts, and TEC [65], are relatively stable in disturbed ionospheric conditions, but do not yet provide stability during solar flares and coronal mass ejections [188]. The use of ML and DL models to improve GIM and TEC maps [66] yields the smallest errors for short forecast horizons [189].

In the context of RTK positioning, the distance between the base and the GNSS receiver is significant. The longer the distance, the worse it affects the accuracy and reliability of ambiguity resolution. RTK positioning is also sensitive to ionospheric disturbances [68]. Ionosphere prediction models, including those obtained using machine learning, can potentially improve positioning [190].

Tropospheric delay (especially ZWD) is highly variable and poorly modeled by global empirical functions (GPT2, UNB3). Even when using VMF3 or Numerical Weather Prediction (NWP), residual errors may occur. Tropospheric delays not only affect the accuracy but also slow down the convergence of PPP solutions. The most favorable solutions are obtained using regional polynomial or grid models of the troposphere, which allow for centimeter accuracy of up to 3 cm horizontally and reduce the convergence time by 30–65% [127], but the density of regional networks is important. The use of machine learning and neural networks, trained on global models (e.g., ERA5) and used to build short-term troposphere forecast models from which ZHD and ZWD are extracted, allows for NWP-level accuracy [129].

At short baselines, RTK is not very dependent on the troposphere. NWP is effective for correcting tropospheric errors in RTK solutions at long baselines, providing centimeter accuracy [133]. When using network corrections for RTK positioning, it is important to choose the interpolation method for spatial delay prediction. Kriging shows the best stable results in different weather conditions [132].

Orbit and clock errors. For SPP solutions, the accuracy is limited to 3–15 m, as broadcast ephemerides are used [22]. Accurate IGS products allow centimeter errors in PPP to be achieved, but with a long convergence time (tens of minutes) [75]. SSR corrections improve the PPP-RTK solution and reduce the time to resolve ambiguities to seconds [79], but require a global infrastructure. For RTK solutions on long bases > 50–100 km, residual ephemeris and clock errors are compensated successfully by network corrections [78].

Multipath. Multipath is a local error for which there are no models with ready-made corrections. The task of eliminating errors due to the multipath effect is solved in two ways: hardware improvements (antimultipath antennas, new correlators) and algorithmic improvements (filtering, ML, integration with INS/LiDAR).

From the point of view of hardware improvements using antennas for code receivers, it is important for the antenna to be able to receive signals from a large number of satellites, including low-angle ones, in order to improve the geometry (GDOP). For phase receivers, it is important to be able to stabilize the phase center and suppress reflected waves, which is critical for resolving ambiguities. The use of advanced correlators, such as multi-correlators [87], is one of the key hardware methods for mitigating multipath, allowing errors to be reduced by an order of magnitude (from 10 m to 1 m). The use of improved correlators is also applicable to phase receivers. However, at the level of phase observations, the multipath effect still remains, and algorithmic methods are required to correct it.

The accuracy of SPP solutions in multipath conditions without correction can degrade to tens of meters. To level out multipath errors in SPP solutions, RAIM-based methods for rejecting suspicious signals are widely used, which improve horizontal accuracy to 13–17 m [81], as well as methods for rejecting poor-quality data by C/N₀ and elevation angle, improving the accuracy to 22 m [88]. The next class of algorithms are NLOS signal clustering algorithms [83], which provide an accuracy up to 2.4 m. ML models (SVR, RF, GBDT, MLP) allow NLOS recognition and reduce errors to 2.5–5 m [89].

Another widely used method is integration with other sensors. In particular, an integration with LiDAR [91] reduces SPP errors in urban environments to 2–3 m. That is, ML-based algorithms are more promising, but accuracy still remains at the meter level.

Multipath is especially critical for phase observations. In this regard, many software and algorithmic solutions have been developed for PPP modes, such as sidereal filtering, Multipath Hemispherical Map, wavelet analysis, etc. Sidereal filtering (SF, ASF, MSF) and the Multipath Hemispherical Map (MHM) use the repeatability of multipath errors for each satellite and allow accuracy to be improved to millimeters [93,95]. The ML classification of NLOS improves weight models in EKF and reduces RMSE in PPP by 30–40% [96]. The multi-constellation and multi-frequency solutions used to build the Multipath Hemispherical Map even more efficiently provide an even higher accuracy < 1 cm [97]. Thus, multi-frequency and multi-constellation solutions allow for the faster and denser coverage of the sky to refine the MHM, but this requires the use of multi-day satellite data. Integrating PPP with INS/LiDAR reduces errors in dense urban areas to the meter level [98].

To improve the accuracy of RTK solutions in multipath conditions, robust filters (RIF, GM-KF, V-KF) are used, which increase the stability of RTK in severe noise conditions, showing an accuracy of up to 15 mm horizontally [104]. Adapted RAIM algorithms [102] also provide millimeter accuracy. Integrating GNSS with 3D LiDAR and IMU through factor graph optimization increases the probability of successful ambiguity resolution and improves accuracy to the sub-meter level [27]. ML classifiers improve 3D accuracy by more than 30% to the millimeter level [101]. In other words, the best solution for mitigating multipath in RTK solutions is robust filters and ML.

Receiver noise. Budget GNSS modules suffer from high noise levels, which makes them difficult to use in mass-market devices. There are two main approaches to noise reduction: algorithmic methods of filtering and observation weighting (Kalman, robust/adaptive filtering, wavelet, C/N₀ weighting) and hardware methods (improved antennas, integration with other sensors).

For code receivers, robust and adaptive EKFs (e.g., the Robust Adaptive Extended Kalman Filter) allow for noise variability and outliers to be taken into account. Sub-meter accuracy is achieved [135]. Wavelet decomposition effectively isolates high-frequency noise [136], while C/N₀ and elevation weighting allow the weight of “dangerous” observations to be dynamically reduced, which reduces the average horizontal error to a few meters [138]. Thus, filtering and weighting models improve accuracy but do not reduce errors below the meter level in conditions of strong noise and multipath.

PPP algorithms are sensitive to noise and outliers, as they rely on filtering in EKF. In this regard, improved robust adaptive filters (χ² criterion, equivalent weighting functions) are being developed that provide centimeter RMS values compared to classical filters [139]. Smoothing and incremental smoothing reduce errors in dynamics to the submeter level [143]. C/N₀ and elevation weighting improve horizontal accuracy. Experiments using different antennas for low-cost receivers operating in PPP-RTK mode have shown submeter accuracy when selecting a specific type of antenna [55]. Integration with external sensors (INS, Vision) in a tightly coupled architecture improves the stability of the solution, but not its accuracy in high noise conditions [146]. In other words, robust and adaptive filters show the best performance for PPP solutions. Robust filtering on budget receivers operating in RTK mode improves the result but is not stable under strong dynamics [103].

Having reviewed modern GNSS receiver architectures aimed at providing high-precision and reliable positioning in Section 3, we compared six GNSS architectures: hardware-based, software-based, multi-frequency and multi-constellation, cloud/edge, integrated GNSS/INS/LiDAR, and integrated GNSS/IoT (Table 10).

The analysis shows that the hardware-based architecture remains relevant due to its standardization and low cost, but is limited in terms of accuracy and security in difficult reception conditions. Software-defined solutions provide the highest flexibility and allow for the implementation of the latest processing and protection algorithms, while requiring significant computing power. Multi-frequency and multi-constellation receivers demonstrate significant accuracy improvements (centimeter level in PPP-RTK and millimeter level in triple-frequency PPP models), increase fault tolerance, and reduce convergence time, making them promising for unmanned systems and geodesy. Cloud and edge architectures reduce terminal power consumption and enable the scaling of high-precision services (PPP-B2b, Galileo HAS), but they are vulnerable to network attacks and have limitations in terms of data transmission latency. The integration of GNSS with INS and LiDAR significantly improves navigation robustness and reliability, providing sub-meter accuracy even during prolonged shadowing or signal loss and compensating for multipath effects, but such systems are costly and computationally complex. Finally, the integration of GNSS with IoT demonstrates the potential for large-scale and cost-effective applications with minimal power consumption and low cost; decimeter and even centimeter accuracy is achieved in PPP-RTK, opening up opportunities for infrastructure monitoring, hydrology, agriculture, and transportation. Thus, the trend in GNSS navigation development is towards the hybridization of architectures and combining the advantages of accuracy, energy efficiency, and security depending on the target application area.

Table 10. Systematic comparison of six modern GNSS architectures.

Architecture	Accuracy	Disadvantages	Positive Aspects	Applicability
Hardware-based receivers	SF-LC: 0.2–1 m in open sky, 0.5–3 m in the city [150,154]; DF-LC: up to 2–5 cm in RTK at short bases < 10 km [151]; Aviation: 1–3 m with SBAS/GB AS [148]	Low resistance to spoofing and jamming; reliability limited by multipath; moderate energy consumption (80–150 mW [153], up to 1 W [148])	High predictability of operation; certified solutions; low cost of mass-produced chips	Aviation, automotive navigation, agriculture, smartphones
SD-based receivers	Comparable to geodetic receivers: tracking at C/N0 > 28 dB-Hz [152]; RTK: 1–2 cm [191]	High computational and energy load (1–2 W [156]); integration difficulty; vulnerability to overload [157]	Versatility, signal reproduction, support for new systems (GPS, Galileo, BeiDou) [155,191]	Scientific research, ionosphere monitoring [191], anti-spoofing [157], RFI direction finding [158]
Multifrequency and multi-constellation receiver	PPP: 7–12 mm static (2 freq.) [163]; 4.9–12.1 mm (3 freq.) [163]; PPP-RTK: 2.5 cm [134]	Sensitive to multipath; moderate energy (100–250 mW [57]); antenna cost; partial susceptibility to signal degradation [165]	Centimeter accuracy even on inexpensive equipment; high fault tolerance [134]	Geodesy, unmanned vehicles, UAVs, maritime navigation [161,164]
Cloud and edge architectures	Cloud-PPP: 6–8 hor., 8–10 cm vert. [167]; PPP-B2b: 5–13 cm [167]; Edge-CB-GNSS: 2–4 cm [171]	Risk of data compromise [172]; network latency (2–5 s [170]); reliance on connectivity; low terminal energy (20–50 mW [45])	Scalability [57], energy efficiency, high accuracy with inexpensive terminals [45]	Smartphones, IoT terminals, autonomous transport, agricultural monitoring [45,168,171]
GNSS/INS/LiDAR integrated	Improved accuracy: reduction in RMSE to 82.2% and 79.6% [175]; sub-meter accuracy in the city [178]; with GNSS turned off, RMSE reduction by 51–78% [176]	High energy (15–20 W [175]); calibration complexity; costly sensors [181]; high computational load	High robustness; ability to navigate without GNSS [176]	Geodesy, mobile mapping, UAVs, autonomous machines [174,179]
GNSS/IoT integrated	PPP-RTK on a low-cost receiver: decimeter level in the city [57]; hydrology: 7 mm [185]	Medium-low security (vulnerable comm. channels [46]); network dependency; low energy (20–80 mW [184]); transmission delay	Low cost, mass production, integration with ML/DL for reducing energy consumption [187]	Hydrology [185], ionospheric maps [186], transport and agriculture [57]

Table 10. Systematic comparison of six modern GNSS architectures.

Architecture	Accuracy	Disadvantages	Positive Aspects	Applicability
Hardware-based receivers	SF-LC: 0.2–1 m in open sky, 0.5–3 m in the city [150,154]; DF-LC: up to 2–5 cm in RTK at short bases < 10 km [151]; Aviation: 1–3 m with SBAS/GB AS [148]	Low resistance to spoofing and jamming; reliability limited by multipath; moderate energy consumption (80–150 mW [153], up to 1 W [148])	High predictability of operation; certified solutions; low cost of mass-produced chips	Aviation, automotive navigation, agriculture, smartphones
SD-based receivers	Comparable to geodetic receivers: tracking at C/N0 > 28 dB-Hz [152]; RTK: 1–2 cm [191]	High computational and energy load (1–2 W [156]); integration difficulty; vulnerability to overload [157]	Versatility, signal reproduction, support for new systems (GPS, Galileo, BeiDou) [155,191]	Scientific research, ionosphere monitoring [191], anti-spoofing [157], RFI direction finding [158]
Multifrequency and multi-constellation receiver	PPP: 7–12 mm static (2 freq.) [163]; 4.9–12.1 mm (3 freq.) [163]; PPP-RTK: 2.5 cm [134]	Sensitive to multipath; moderate energy (100–250 mW [57]); antenna cost; partial susceptibility to signal degradation [165]	Centimeter accuracy even on inexpensive equipment; high fault tolerance [134]	Geodesy, unmanned vehicles, UAVs, maritime navigation [161,164]
Cloud and edge architectures	Cloud-PPP: 6–8 hor., 8–10 cm vert. [167]; PPP-B2b: 5–13 cm [167]; Edge-CB-GNSS: 2–4 cm [171]	Risk of data compromise [172]; network latency (2–5 s [170]); reliance on connectivity; low terminal energy (20–50 mW [45])	Scalability [57], energy efficiency, high accuracy with inexpensive terminals [45]	Smartphones, IoT terminals, autonomous transport, agricultural monitoring [45,168,171]
GNSS/INS/LiDAR integrated	Improved accuracy: reduction in RMSE to 82.2% and 79.6% [175]; sub-meter accuracy in the city [178]; with GNSS turned off, RMSE reduction by 51–78% [176]	High energy (15–20 W [175]); calibration complexity; costly sensors [181]; high computational load	High robustness; ability to navigate without GNSS [176]	Geodesy, mobile mapping, UAVs, autonomous machines [174,179]
GNSS/IoT integrated	PPP-RTK on a low-cost receiver: decimeter level in the city [57]; hydrology: 7 mm [185]	Medium-low security (vulnerable comm. channels [46]); network dependency; low energy (20–80 mW [184]); transmission delay	Low cost, mass production, integration with ML/DL for reducing energy consumption [187]	Hydrology [185], ionospheric maps [186], transport and agriculture [57]

5. Conclusions and Future Directions

This review provides a detailed review of state-of-the-art GNSS correction techniques and receiver architectures aimed at achieving high-precision and reliable positioning.

The study identifies persistent open challenges across multiple domains.

Ionospheric errors remain critical for single-frequency GNSS receivers, and global models (Klobuchar, NeQuick) provide only a partial compensation. More accurate methods used on phase receivers (GIM, DMD, ML TEC forecasts) show promising results but are unstable during solar flares and in a disturbed ionosphere. In RTK positioning, the key limitations remain the baseline length and sensitivity to ionospheric disturbances. ML-based prediction models can improve the solution, but the integration of such forecasts into RTK network methods remains an open question. For the troposphere, global empirical models (GPT2, UNB3) are not accurate enough, and even VMF3/NWP retains residual errors. The best results are obtained with regional grid models and short-term forecasts based on ML/NWP. The use of accurate IGS products to correct atmospheric and ephemeris–time errors allows for centimeter accuracy to be achieved in PPP solutions, but requires a long convergence time (tens of minutes).

In multipath mitigation, methods such as ARAIM, MHM, robust filters (GM-KF, V-KF), and ML-based LOS/NLOS classifiers have reached millimeter-level accuracy for PPP and RTK solutions; however, their robustness in dynamic or obstructed conditions is still limited. Data fusion approaches based on factor graph optimization and adaptive filtering demonstrate significant improvements in navigation stability compared with traditional GNSS/INS integration, but their accuracy remains comparable to other modern hybrid methods and depends strongly on calibration quality and synchronization between sensors (GNSS, INS, LiDAR, camera).

In receiver noise correction, robust adaptive Kalman filters and hybrid visual–inertial integration markedly improve the accuracy for low-cost devices. Yet the systematic calibration and error modeling of mass-market GNSS sensors remain an open issue. Thus, a priority for future work is to develop open calibration frameworks and adaptive error-mapping algorithms suitable for mass production and network-aided operation.

The evolution of GNSS receiver architectures demonstrates a shift from rigid hardware-based systems toward intelligent, multi-sensor, cloud-connected, and edge-assisted architectures. Software-defined and cloud-based designs provide flexibility, while edge computing reduces latency, crucial for UAVs and autonomous vehicles.

The integration of GNSS with INS, LiDAR, and IoT sensors is the most promising direction for achieving sub-decimeter precision in complex environments. However, further research is needed on optimal data fusion frameworks and the calibration of heterogeneous sensors to ensure consistent accuracy and reliability.

In our opinion, the most promising future directions may include the following:

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Real-time data fusion frameworks for GNSS/INS/LiDAR/vision integration;

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Calibration standards and adaptive noise models for low-cost multi-frequency receivers;

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Unified open-source platforms for testing and benchmarking hybrid GNSS architectures;

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The development of ML-based troposphere and ionosphere forecasting integrated directly into PPP-RTK services;

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The integration of GNSS with IoT, cloud-edge, and ML-based processing for real-time PPP-RTK solutions.

This review suggests that the future of high-precision GNSS navigation equipment lies in its transformation into network-integrated, multi-sensor, and intelligent systems that can operate reliably, even in environments with limited satellite visibility.