GNSS Measurement Technique in Aerial Navigation

Currently, the Global Navigation Satellite System (GNSS) plays a critical role in providing position information for UAVs. Traditional GNSS receivers typically employ the scalar-tracking (ST) method to track signals and extract observations. An advanced alternative to ST is the Vector Delay Lock Loop (VDLL), which enables more reliable navigation solution estimation for GNSS receivers. To enhance GNSS positioning performance for UAVs, this paper proposes a cooperative VDLL (CoVDLL) that incorporates ranging information. While single VDLL (S-VDLL) explores the inherent relationship between signal tracking parameters and navigation solutions, the CoVDLL leverages signal tracking parameters from multiple UAVs along with their ranging data. To optimize navigation solution estimation in the CoVDLL, a Factor Graph Optimization (FGO) algorithm is employed to realize the navigation solution’s optimal estimation. Experiments conducted under various settings demonstrate that the CoVDLL method reduces positioning errors by an average of approximately 30% compared to the single-VDLL approach. Full article

The multipath effect is a critical factor that prevents the Global Navigation Satellite System (GNSS) from achieving millimeter-level positioning accuracy. A multipath hemispherical map (MHM) is a popular approach to achieving real-time multipath error mitigation. The premise of the constructed MHM model is that the residuals in the grid only contain multipath errors and noise without any outliers. However, when there are numerous obvious outliers in each grid, the traditional quality control method is unable to detect them effectively. Therefore, we propose a multipath hemispherical map with strict quality control (MHM-S) to mitigate multipath errors. This method first uses the maximum phase delay to eliminate obvious outliers. Then, the 3-sigma rule and F-test are applied to remove the remaining few outliers in the grid. After applying the proposed MHM-S method, the experimental results show that when the PRN20 satellite is affected by outliers, the standard deviation (STD) reduction rate of the MHM-S residuals is 12.03% compared with the residual STDs of the MHM model. In addition, we evaluate the capabilities of MHM-S with carrier phase observation (MHM-SC) and carrier phase and pseudo-range observation (MHM-SCP) models in multipath error mitigation. Especially in the east direction, the positioning accuracy of the MHM-SCP model is improved by 48% compared with the MHM-SC model. Full article

High-precision DCBs are essential for effective multi-frequency and multi-constellation GNSS integration, especially in processing compatible signal observations. This study utilizes data from MGEX, iGMAS, and CORS stations to estimate and analyze long time series of BDS/GNSS DCBs, focusing on stability and influencing factors. Results indicate that DCBs for the same signal, but different channels exhibit similar ranges and trends. Among BDS DCBs, those from satellites with rubidium atomic clocks are more stable than those with hydrogen atomic clocks. An upgrade and maintenance of BDS in late 2022, reported by NABU, likely contributed to DCB jumps. BDS-compatible signal DCBs show weaker stability compared to GPS and Galileo. Variations in GNSS signal processing and receiver algorithms also impact DCB stability. Converting DCBs to OSBs and performing RMS statistics revealed that smaller differences between signals increase the susceptibility of observation equations to observation quality. Full article

The Global Navigation Satellite System (GNSS) can be utilized for long-distance and high-precision time transmission. With the ongoing development of low Earth orbit (LEO) satellites and the rapidly changing geometric relationships between them, the convergence rate of ambiguity parameters in Precise Point Positioning (PPP) algorithms has increased, enabling fast and reliable time transfer. In this paper, GPS is used as an experimental case, the LEO satellite constellation is designed, and simulated LEO observation data are generated. Then, using the GPS observation data provided by IGS, a LEO-enhanced PPP model is established. The LEO-augmented PPP model is employed to facilitate faster and more reliable high-precision time transfer. The application of the LEO-augmented PPP model to time transfer is examined and discussed through experimental examples. These examples show multiple types of time transfer links, and the experimental outcomes are uniform. GPS + LEO is compared with exclusive GPS time transfer schemes. The clock offset of the time transfer link for the GPS + LEO scheme converges more swiftly, meaning that the time required for the clock offset to reach a stable level is the briefest. In this paper, standard deviation is employed to assess stability, and Allan deviation is utilized to assess frequency stability. The results show that the clock offset stability and frequency stability achieved by the GPS + LEO scheme are superior within the convergence time range. Controlled experiments with different numbers of satellites for LEO enhancement indicate that time transfer performance can be improved by increasing the number of satellites. As a result, augmenting GPS tracking data with LEO observations enhances the time transfer service compared to GPS alone. Full article

The potential for the use of smartphones in GNSSs (Global Navigation Satellite Systems) positioning has increased in recent years due to the emergence of the ability of Android-based devices used to process raw satellite data. This paper presents the results of a study on the use of SBAS data transmitted by the EGNOS (European Geostationary Navigation Overlay Service) system in GNSS positioning using a Xiaomi Mi8 smartphone. Raw data recorded at a fixed point were used in post-processing calculations in GPS/EGNOS positioning by determining the coordinates for every second of a session of about 5 h and comparing the results to those obtained with a Septentrio AsteRx2 GNSS receiver operating at the same time at a distance of about 3 m. The calculations were performed using the assumptions of the GNSS/SBAS positioning algorithms, which were modified with carrier-phase smoothed code observations and the content of the corrections transmitted by EGNOS. Full article

Real-Time (RT) Precise Point Positioning (PPP) uses precise satellite orbits and clock corrections, and employs a separate receiver for positioning. With the growing demand, RT PPP is becoming an increasingly popular research topic. The ambiguity resolution (AR) can significantly improve the positioning accuracy and convergence time of PPP, so it is essential to study PPPAR in RT mode. In this paper, 37 MGEX stations from around the world are chosen, and the RT orbit, clock, and phase biases products broadcast by the Centre National d’Etudes Spatiales (CNES) are applied to PPPAR. Additionally, the residuals of the RT phase biases products, convergence time, and positioning accuracy are investigated. The results indicate that GPS products have the best quality of AR, with wide-lane (WL) and narrow-lane (NL) residuals of 98.9% and 95.3%, respectively, within ±0.25 cycles. Within ±0.25 cycles, the WL and NL residuals of the Galileo are 98.2% and 94.3%, respectively. Within ±0.25 cycles, the (Beidou Navigation Satellite System) BDS has a poor quality of AR, with WL and NL residuals of 97.3% and 73.1%, respectively. Due to the poor quality of the BDS AR, the convergence time of the BDS is not calculated in this paper. The convergence time of other systems is significantly reduced after AR processing, and the convergence time of the GPS/Galileo combination is the fastest, being 17.14 min in kinematic mode and only 11.85 min in static mode. The positioning accuracy of the GPS, Galileo, GPS/Galileo, and GPS/Galileo/BDS in the E and U directions is significantly improved after PPPAR. Full article

The fast and accurate solution of integer ambiguity is the key to achieve GNSS high-precision positioning. Based on the lattice theory of high-dimensional ambiguity solving, the reduction time consumption is much larger than the search time consumption, and it is especially important to improve the efficiency of the lattice basis reduction algorithm. The Householder QR decomposition with minimal column pivoting is utilized to pre-sort the basis vectors and reduce the number of basis vector exchanges during the reduction process by partial size reduction and relaxing the basis vector exchange condition to improve the reduction efficiency of the LLL algorithm. The improved algorithm is validated using simulated and measured data, respectively, and the performance advantages and disadvantages of the improved algorithm are evaluated from the perspectives of the extent of reduction basis orthogonality and the quality of reduction basis size reduction. The results show that the improved LLL algorithm can significantly reduce the number of basis vector exchanges and the reduction time consumption. The HSLLL and PSLLL algorithms with the Siegel condition as the basis vector exchange condition have a better reduction effect, but are slightly less stable. The PLLLR algorithm significantly improves the search ambiguity resolution efficiency, which is conducive to the rapid realization of ambiguity resolution. Full article

The ground-based augmentation system (GBAS) is a regional system supporting navigation and ensuring the integrity of aircraft near airports during precision approaches. Standardized at the international level, GBAS Approach Service Types (GASTs) C and D, which are defined for the GPS L1 signal, support CAT I and II/III precision approaches with decision heights of 200 and 50 ft, respectively. However, the future GBAS, GAST E, which utilizes dual-frequency and multi-constellation signals, and the GAST D1, defined for both GPS L1 and Galileo E1 signals, require the establishment of standards. To define the continuity requirement, the number of critical satellites must be considered. Currently, there is a lack of analysis on the number of critical satellites for various GBAS service types available to the public. This paper aims to evaluate the number of critical satellites for future GBAS service types, employing optimized GPS and Galileo constellations and assessing all potential protection levels worldwide. The methodology to model the difference of position solutions using the 30 s and 100 s smoothing filters is presented in detail to compute the protection level for GASTs D and D1. The resulting number of critical satellites can be used to define the continuity allocation of future GBAS. Full article

Fused LEO navigation systems have been proposed as a low-cost means of supplementing and backing up global navigation satellite system (GNSS) navigation services based on low-earth orbit (LEO) constellations, which means broadcasting navigation signals based on the spectrum and hardware of the currently planned communication constellation. In this paper, we introduce Doppler-aided positioning to fused LEO navigation systems, which can improve the positioning performance and availability of fused LEO navigation systems by addressing insufficient pseudorange measures caused by insufficient navigation resources or the early stages of system construction. Theoretical analysis and simulation results show that Doppler-aided positioning based on the weighted least squares (WLS) method can improve the positioning accuracy of pseudorange positioning and achieve 95% three-dimensional errors within 21 m, even if the number of pseudorange measurements is less than four. Therefore, Doppler-aided positioning can expand the application scenarios of independent navigation services for fused LEO navigation systems. Full article

Real-time GNSS PPP is commonly used for high-precision positioning, but its utility is constrained by factors that necessitate extended convergence periods for a dependable accuracy. Multipath, as an unmodeled error, significantly curtails PPP performance in time-constrained scenarios. Approximately 31 consecutive days of multi-GNSS data from the satellite positioning service of the German national survey (SAPOS) network were collected to evaluate the effectiveness of multipath correction for real-time PPP ambiguity resolution (AR). Using principal component analysis (PCA) to extract the common-mode error (CME) from observation residuals prior to multipath modeling, a multipath hemispherical map (MHM) and sidereal filtering (SF) approach were employed to alleviate the effects of multipath and assess the efficacy of multipath correction in real-time PPP-AR. The average RMS reductions of the carrier-phase and pseudorange residual of multi-GNSS were 25.5% and 20.1% with MHM ${}_{0.5}$, while being 24.4% and 18.3% using SF. With MHM ${}_{0.5}$ correction, the TTFF reductions were approximately 7.0%, 17.7%, 37.5%, and 23.7% for G/GE/GC/GEC kinematic PPP-AR, respectively; and the convergence times for G/GE/GC PPP-AR were reduced to 18.2, 11.7, and 8.6 min, while GEC achieved an average convergence time of 7.1 min; a remarkable improvement compared to the multipath-uncorrected result (18 min). Moreover, 80% of the stations achieved convergence within 10 min, while 40% achieved convergence within 5 min. The kinematic positioning accuracy for the GEC solution improved from 0.97, 0.88, and 2.07 cm, to 0.94, 0.70, and 1.72 cm. In the static results, the TTFF shortened by 30.1%, 19.1%, and 20.1% for G/GE/GC, and the GEC decreased from 10.5 to 9.7 min; the average convergence time for G/GE/GC shortened to 13.0, 10.0, and 11.3 min, and for GEC shortened from 12.5 to 8.3 min. For the GPS-only solution, 78.3% of stations achieved convergence within 15 min. Similarly, for the GE scheme, the convergence time was primarily concentrated within 10 min, and for GC and GEC, with the application of enhanced multipath error correction, some of the stations even achieved convergence of PPP-AR within 5 min. The static positioning accuracy for GEC PPP was 0.50, 0.30, and 0.71 cm for the east, north, and up components. Full article

Multipath error is an important factor restricting the relative positioning accuracy of the Beidou Navigation Satellite System (BDS). Because of the complexity of the reflection environment, the mathematical modeling of multipath errors is quite difficult. The sidereal filtering algorithm corrects multipath errors by using the feature of period repetition, which can greatly reduce its influence and improve the accuracy of positioning and attitude measurement. In view of the constellation heterogeneity of BDS, it is more complicated to apply sideral filtering. Based on the reconstructed single-difference residual of the carrier phase, the multipath repetition time of the Beidou satellite is estimated using the idea of segmentation. The Tikhonov regularization method and the classical wavelet method are used to extract the multipath of the single-difference residual of the carrier phase, and the “clean” sequence of the single-difference residual is obtained. The experimental results show that it is feasible to extract the multipath error correctly by Tikhonov regularization, and the multipath error is smoother than the original residual measurement. Furthermore, the estimation method of the regularization parameter is further optimized. After using the optimized Tikhonov regularization method with sidereal filtering, the mean RMS improvements of GEO, IGSO, and MEO satellites are 45.9%, 38.2%, and 37.5%, respectively. The positioning accuracy on E, N, and U components is improved by 24.8%, 26.3%, and 42.7%, respectively. The attitude resolution accuracy is improved by 22.9% in the yaw angle and 12.6% in the pitch angle. The proposed method can be an alternative BDS multipath error modeling and mitigation approach. Full article

Cycle slip detection and repair is a prerequisite to obtain high-precision positioning based on a carrier phase. Traditional triple-frequency pseudorange and phase combination algorithm are highly sensitive to the pseudorange observation accuracy. To solve the problem, a cycle slip detection and repair algorithm based on inertial aiding for a BeiDou navigation satellite system (BDS) triple-frequency signal is proposed. To enhance the robustness, the INS-aided cycle slip detection model with double-differenced observations is derived. Then, the geometry-free phase combination is united to detect the insensitive cycle slip, and the optimal coefficient combination is selected. Furthermore, the L2-norm minimum principle is used to search and confirm the cycle slip repair value. To correct the INS error accumulated over time, the extended Kalman filter based on the BDS/INS tightly coupled system is established. The vehicular experiment is conducted to evaluate the performance of the proposed algorithm from a few aspects. The results indicate that the proposed algorithm can reliably detect and repair all cycle slips that occur in one cycle, including the small and insensitive cycle slips as well as the intensive and continuous cycle slips. Additionally, in signal-challenged environments, the cycle slips occurring 14 s after a satellite signal outage can be correctly detected and repaired. Full article

To guarantee the integrity of a global navigation satellite system (GNSS) for safety-critical users, a satellite-based augmentation system (SBAS) makes use of the integrity monitoring architecture, of which the signal quality monitor (SQM) is an important component to address the potential risks caused by satellite-induced signal anomalies. Due to the introduction of dual-frequency multi-constellation (DFMC) techniques in 2025, the ranging uncertainty will be reduced by the elimination of first-order ionospheric delay, but the biases measured in each individual signal will be inflated by the ionosphere-free combinations. Moreover, multiple modulations of DFMC signals might introduce applicability uncertainty of a traditional SQM method that has been protecting GPS L1C/A signal only. Thus, higher requirements are put forward for future SQM methods in detection sensitivity and modulation independence. This paper first proposes a design methodology for the SQM algorithm for BDS B1C/B2a signals, which could be easily extended to the DF combinations of other GNSS core constellations. Then, by comparing the performances of SQM baseline algorithms based on traditional multi-correlator and emerging chip domain observables (CDOs), respectively, the superiority of CDO-based SQM is declared. Detailed design iterations are further discussed, including the algorithm practicalization with optimizing code-phase bin length and lowering sampling frequency, as well as the metric simplification, to promote the overall performance while preserving a lower implementation complexity. Ultimately, a CDO-based SQM algorithm for BDS B1C/B2a signals is reached, which would be considered as an effective candidate in new generation DFMC SBASs. Full article

The surrounding environment of a GNSS observation station is changed during a flood, and this results in a more serious multipath than in a normal environment. Considering that the multipath error is largely related to the pseudo-range multipath and CNR (Carrier-to-noise ratio) of the GNSS signal, the influence of floods on a pseudo-range multipath and CNR is analyzed in theory and through experiment. To ensure the accuracy of the analysis results, the ground track repeat period of GPS, GLONASS, and BDS satellites is investigated from the perspective of theory and skyplots. Two real cases study collected in Zhengzhou and Xinxiang, China, in 2021, are used to demonstrate the influence of floods on a pseudo-range multipath and CNR in detail. Experimental results show that the pseudo-range multipath of a GPS satellite performs more seriously during a flood. The maximum RMS increase rate is approximately 17.85%, and the average of all other satellites with a whole arc is approximately 6.55%. In addition, the CNR of three GNSS systems performs a decrease during a flood. For GPS and GLONASS satellites, the decrease performs more seriously at a high elevation angle than that at a low elevation angle. The maximum decrease is approximately 5 dB-Hz for the GPS satellite and approximately 7 dB-Hz for the GLONASS satellite. In terms of the BDS system, the CNR of all three orbital type satellites decreases during a flood. The average decrease is approximately 2 dB-Hz for BDS MEO and GEO satellites, and about 1 dB-Hz for the BDS IGSO satellite. Full article

In global navigation satellite systems (GNSSs)-based positioning, user receiver clock jump is a common phenomenon on the low-cost receiver clocks and can break the continuity of observation time tag, carrier phase and pseudo range. The discontinuity may affect precise point positioning-related parameter estimation, including receiver clock error, position, troposphere and ionosphere parameters. It is important to note that these parameters can be used for timing, positioning, atmospheric inversion and so on. In response to this problem, the receiver clock jumps are divided into two types. The first one can be expressed by the carrier phase and pseudo range having the same scale jump, and the second one is that they are having different scale jumps. For the first type, if a small priori variance of receiver clock error is provided, it can affect the accuracy of ionospheric delay estimation both in static and kinematic mode, while in the latter mode, it also affects position estimation. However, if large process noise is provided, numerical problems may arise since other parameters’ process noises are usually small, it is proposed to use the single point positioning with pseudo ranges to provide a priori value of receiver clock error, and an empiric value is assigned to its prior variance, this handle can avoid the above problems. For the second type, instead of compensating so many raw observations in the traditional methods, it is proposed to compensate the ambiguities at the clock jump epochs only in a new method. The new method corrects the Melbourne–Wubbena (MW) combination firstly in order to avoid the misjudging of cycle slips for current epoch, and the second step is to compensate the corresponding ambiguities, then, after Kalman filtering, the MW and its mean should be corrected back in order to avoid the misjudging of cycle slips at the next epoch. This approach has the advantage of handling the clock jump epoch-wise and can avoid correcting the rest of the observations as the traditional methods used to. With the numerical validation examples both in static and kinematic modes, it shows the new method is simple but efficient for real time precise point positioning (PPP). Full article

The global navigation satellite system (GNSS) real-time kinematic (RTK) technique is used to achieve relative positioning centimeter levels among multiple agents on the move. A typical GNSS RTK estimates the relative positions of multiple rover receivers with respect to a single-base receiver. In a fleet of rover GNSS receivers, this approach is inefficient because each rover receiver only uses GNSS measurements of its own and those sent from a single-base receiver. In this study, we propose a novel GNSS RTK framework that facilitates the precise positioning of a swarm of moving vehicles through the GNSS measurements of multiple receivers and broadcasts fixed-integer ambiguities of GNSS carrier phases. The proposed framework not only provides efficient RTK positioning but also reliable performance with a limited number of GNSS satellites in view. Our experimental flight tests with six GNSS receivers showed that the systematic procedure of the proposed framework could maintain lower than 6 cm of 3D RMS positioning errors, whereas the conventional RTK failed to resolve the correct integer ambiguities of double difference carrier phase measurements more than 13% in five out of nine total baselines. Full article

The Global Navigation Satellite System (GNSS) time series non-constructive deformation shows significant seasonal variations, and the study of its periodic term components and possible physical mechanisms has important theoretical significance and application value for the accurate use of the data and more in-depth analysis. In this paper, wavelet transform (WT) is used to extract the seasonal terms of 24 GNSS continuous station time series, Gravity Recovery and Climate Experiment (GRACE) displacement time series and precipitation data in the Sichuan–Yunnan area, and the three data sets are compared and analyzed in terms of amplitude, phase and cross-correlation coefficient (CC), and the results show that the seasonal deformation in the area is strongly related to the precipitation variation. GNSS and GRACE have good consistency in the vertical component, and the seasonal variation is mainly related to the hydrological load; the difference in the horizontal component is obvious, and the amplitude of the seasonal term of GNSS is larger than that of GRACE, indicating that the resolution of GRACE in the horizontal component is lower than that of the vertical component, and the overall estimation accuracy is lower than that of GNSS. There are significant seasonal terms of annual and semi-annual cycles for the three GNSS components, and the vertical component mainly shows the seasonal deformation of the annual cycle with the strongest seasonality; the horizontal component mainly shows the deformation of the semi-annual cycle, and the seasonality of the N component is stronger than that of the E component, and they are negatively correlated with a coefficient of −0.90. Full article

The global navigation satellite system has achieved great success in the civil and military fields and is an important resource for space-time information services. However, spoof interference has always been one of the main threats to the application security of satellite navigation receivers. In order to further improve the application security of satellite navigation receivers, this paper focuses on the application scenarios where narrowband and spoofing interference exist at the same time, studies the problem of spoofing interference detection under mixed interference conditions, then proposes a spoofing interference detection method based on the tracking loop identification curve. This method can effectively deal with the detection of spoofing interference under the conditions of narrowband interference and, at the same time, it can effectively detect the spoofing interference of gradual deviation. Simulation experiments verify the effectiveness of the spoofing interference detection method, based on the tracking loop discrimination curve. In typical jamming and spoofing scenarios, when the spoofing signal is about 7.5 m away from the real signal, the method used in this paper can achieve effective detection. The proposed detection method is of great significance for improving the anti-spoofing capability of satellite navigation receivers. Full article

With the increase in satellites in the medium Earth orbit (MEO) region, there should be a focus on orbit safety in the MEO region. A safe orbit disposal strategy is necessary to maintain the sustainability of the MEO region. This paper focuses on long-term evolution modeling, safety analysis of MEO objects, and different disposal techniques for end-of-life BDS-2 MEO satellites. On the one hand, a long-term numerical evolution model is established, and mean equinoctial elements are adopted to propagate a long-term orbit. Long-term evolution for the MEO region over 100 years is carried out, including the Galileo, BDS, GPS, and GLONASS constellations. The earliest orbit intersection time with other global navigation satellite system (GNSS) constellations is put forward. On the other hand, a dynamic model and an optimization model for disposal orbit are established, which minimize the eccentricity growth within 200 years and the fuel consumption for maneuvering to the disposal orbit. The bounds for the disposal region of BDS MEO satellites are also proposed, which consider the measurement and control error of BDS MEO satellites and the eccentricity bounds for end-of-life BDS MEO satellites. A genetic algorithm is adopted to optimize the orbital elements for end-of-life BDS MEO satellites. In addition, two disposal cases, namely, upraising and reducing the orbit, for end-of-life BDS MEO satellites are simulated. The long-term evolutions for the disposal of orbital elements within 200 years are implemented, and the fuel consumption is calculated. The results show that the current MEO region is relatively safe and that the eccentricity is the most important factor that influences the long-term evolution of safety analysis for BDS MEO disposal orbits. Upraising the orbit is safe for end-of-life BDS MEO satellites. This investigation provides the theoretical foundation for investigating the long-term evolutionary mechanisms of the MEO region and references disposal strategy analysis for decommissioned navigation satellites, and the spent upper stages for other GNSS constellations. Full article

In emergency response and disaster rescue, unmanned aerial vehicles (UAVs) onboard thermal infrared (TIR) sensors are an essential means of acquiring ground information in the nighttime working environment. To enable field personnel to make better decisions based on TIR video streams returned from a UAV, the geographic information enhancement of TIR video streams is required. At present, it is difficult for low-cost UAVs to carry high-precision attitude sensors and thus obtain high-precision camera attitude information to meet the enhanced processing requirements of UAV TIR video streams. To this end, this paper proposes an improved Kalman filter algorithm to improve the geographic registration (geo-registration) accuracy by fusing the positioning and heading data from the dual-antenna real-time kinematic global positioning system (RTK-GPS) with onboard internal measurement unit (IMU) data. This method can yield high-precision position and attitude data in real time based on low-cost UAV hardware, based on which high-precision geo-registration results can be obtained. The computational complexity can be reduced compared with video stream feature tracking algorithms. Furthermore, the problem of unstable matching due to the low resolution and texture level of TIR video streams can be avoided. The experimental results prove that the proposed method can reduce the registration error by 66.15%, and significantly improve the geo-registration accuracy of UAV TIR video streams. Thus, it can strongly support the popularization and practicality of the application of augmented reality (AR) technology to low-cost UAV platforms. Full article

High-output-rate relative positions are required for high-speed safety-critical kinematic-to-kinematic applications such as pre-crash sensing and shipboard landing. We propose a real-time, high-output-rate relative positioning method based on the integration of a real time kinematic (RTK) differential global navigation satellite systems (DGNSS) relative positioning algorithm, carrier-phase-based tightly coupled GNSS/Inertial navigation system (TC-GNSS/INS) integration algorithm and polynomial prediction algorithm for position increment. We focus on the rarely studied issue that data broadcast rates and sampling rates have effects on the integrated relative positioning accuracy under different motion states of a moving base. A vehicle-to-vehicle field test with a frequently turning base demonstrates the advantages of the proposed method, such as low bit rate of broadcast data, high output rate of position solutions and excellent real-time tolerance of latency. The results show that compared with the 10-Hz output of sole RTK DGNSS relative positioning, the proposed method can provide centimeter-level-accuracy relative positions at an output rate of 125 Hz with a sampling rate of 1 Hz, and the bit rate can be reduced by 83.12%. A UAV-to-boat field test with straight-line-motion moving base is then carried out to validate the applicability of the proposed system for aircraft applications. The results show that the broadcast rate of position increments of the moving base can be further reduced. Full article

Frequency-domain anti-jamming technology is a common anti-jamming method for satellite navigation receivers. 1/2 overlapping windowing can effectively solve the spectrum leakage in the frequency domain conversion process, but the traditional window function will cause the loss of signal energy. This paper proposes a window function design method with no loss of signal energy, which can effectively solve the signal energy loss caused by the window function. The feasibility of the proposed method is theoretically deduced, and the effectiveness of the proposed method is verified by simulation and measured data. Compared with the traditional window function, the signal-to-noise ratio improvement of the method proposed in this paper is better than 0.5 dB. The frequency domain anti-jamming processing is optimized, the signal-to-noise ratio loss caused by the anti-jamming processing is reduced, and the anti-jamming performance is indirectly improved. This plays an important role in the performance optimization of satellite navigation system links. Full article

A satellite navigation system makes it simple to find and navigate to a specific position. Although a carrier measurement is required to establish a precise position due to the characteristics of the carrier observation, it is difficult to determine a robust position in a poor signal reception environment such as urban areas. Various studies are being carried out to overcome this problem, with cycle slips being the most important factor. With only a single frequency, it is very challenging to detect cycle slips in multiple satellite channels at the same time. A geometry-based technique is proposed in this study as a technical solution for detecting simultaneous cycle slips for multiple channels utilizing only a single-frequency receiver. The method could detect a half-wavelength size of cycle slip for each channel through the geometry information. Full article

The main purpose of this article is to evaluate the comprehensive performance of two inter-frequency code bias (IFCB) models using undifferenced and uncombined observations. These two IFCB models estimate IFCB parameters for each GLONASS satellite (EG model) and IFCB parameters using a quadratic function of frequency channels K (K = −7…6) (QF model). The data sampled in 30 s from 140 stations of the IGS network on 1–7 September 2021, are used for this study. We analyze all the combinations, including the GLONASS data, from the perspective of positioning accuracy, convergence time, and data utilization. The results show that the positioning accuracy of these two IFCB models for the same combination is comparable in three directions in both static and kinematic modes under long-term observation; the positioning accuracies of each IFCB model for all the combinations are almost the same in three directions in static mode, and the positioning accuracy of the combinations including the GPS data in three directions is better than that of the combinations not including the GPS data for kinematic mode. For some combinations, such as GLONSS-only and GPS/GLONASS, the convergence time of the EG model is better than that of the QF model, but the improvement rate does not exceed 22%. However, for other combinations, such as GLONASS/BDS and GLONASS/BDS/GALILEO, the convergence time of the QF model is better than that of the EG model, and the improvement rate in some directions is more than 50%. For the combinations including GPS data, the data utilization of the EG and QF models are almost the same for both static and kinematic modes; however, for combinations without GPS data, the data utilization of the QF model is better than that of the EG model. For these two IFCB models (EG and QF models), all combinations can achieve the set accuracy thresholds in three directions, but the EG model has more parameters to estimate than the QF model. From the perspectives of positioning accuracy, solution convergence time, data utilization, and the number of estimated parameters for each IFCB model, we suggest that the IFCB should be estimated using the QF model when performing combined PPP for different combinations. Full article

When performing area coverage tasks in some special scenarios, fixed-wing aircraft conventionally adopt the scan-type of path planning, where the distance between two adjacent tracks is usually less than the minimum turning radius of the aircraft. This results in increased energy consumption during turning between adjacent tracks, which means a reduced task execution efficiency. To address this problem, the current paper proposes an area coverage path planning method for a fixed-wing unmanned aerial vehicle (UAV) based on an improved genetic algorithm. The algorithm improves the primary population generation of the traditional genetic algorithm, with the help of better crossover operator and mutation operator for the genetic operation. More specifically, the good point set algorithm (GPSA) is first used to generate a primary population that has a more uniform distribution than that of the random algorithm. Then, the heuristic crossover operator and the random interval inverse mutation operator are employed to reduce the risk of local optimization. The proposed algorithm is verified in tasks with different numbers of paths. A comparison with the conventional genetic algorithm (GA) shows that our algorithm can converge to a better solution. Full article

The integrated navigation system consisting of an inertial navigation system (INS) and Global Navigation Satellite System (GNSS) provides continuous high-accuracy positioning whereas the navigation accuracy during a GNSS outage inevitably degrades owing to INS error divergence. To reduce such degradation, a gated recurrent unit (GRU) and adaptive Kalman filter (AKF)-based hybrid algorithm is proposed. The GRU network, which has advantages of high accuracy and efficiency, is constructed to predict the position variations during GNSS outage. Furthermore, this paper takes the GRU-predicted error accumulation into consideration, and introduces AKF as a supplementary methodology to improve the navigation performance. The proposed hybrid algorithm is trained and tested by practical road datasets and compared with four algorithms, including the standard KF, Multi-Layer Perceptron (MLP)-aided KF, Long Short Time Memory (LSTM) aided KF, and GRU-aided KF. Periods of 180 and 120 s GNSS outage are employed to test the performance of the proposed algorithm in different time scales. The comparison result between the standard KF and neural network-aided KF indicates that the neural network is an effective methodology for bridging GNSS outages. The performance comparison between three kinds of neural networks demonstrate that both recurrent neural networks surpass the MLP in prediction position variation, and the GRU transcends the LSTM in prediction accuracy and training efficiency. Furthermore, it is concluded that the adaptive estimation theory is an effective complement to neural network-aided navigation, as the GRU-aided AKF reduced the horizontal error of GRU-aided KF by 31.71% and 16.12% after 180 and 120 s of GNSS outage, respectively. Full article

The main aim of this paper is to present the results of research on the application of a modified mathematical model to determine the quality parameters of SBAS (Satellite Based Augmentation System) satellite positioning in aviation. The authors developed a new calculation strategy to determine the resultant values of the parameters of accuracy, continuity, availability and integrity of SBAS positioning. To achieve it, a weighted mean model was used for the purposes of developing a mathematical algorithm to determine the resultant values of SBAS positioning. The created algorithm was implemented for two SBAS supporting systems, i.e., EGNOS (European Geostationary Navigation Overlay Service) and SDCM (System of Differential Correction and Monitoring). The algorithm was tested in a flight test conducted with a Diamond DA 20-C airplane in north-eastern Poland in 2020. The conducted research revealed that the resultant error of the position in 3D space determined with use of the proposed weighted mean model improved by, respectively, 1–7% in comparison to the standard arithmetic mean model and by 1–37% in comparison to a single SBAS/EGNOS solution. Moreover, the application of the Multi-SBAS positioning algorithm results in an increase in the nominal results of continuity and availability by 50% in comparison to the arithmetic mean model. Apart from that, the values of the integrity parameters determined with use of the proposed weighted mean model improved by 62–63% in comparison to the standard arithmetic mean model. Full article

The accuracy of time synchronization can be significantly increased by enhancing the performance of atomic clocks. Future-generation time-frequency loads will be equipped with the latest ultrahigh-precision atomic clocks (with a day stability better than 10⁻¹⁷) and will leverage advantages of the space environment such as microgravity and low interference to operate a new generation of high-performance time-frequency payloads on low-orbit spacecraft. Moreover, using the high-precision time-frequency system of ground stations, low-time-delay high-performance time-frequency transmission networks, which have the potential to achieve ultrahigh-precision time synchronization, will be constructed. By considering full link error terms above the picosecond level, this paper proposes a new space-to-ground microwave two-way time synchronization method for scenarios involving low-orbit spacecraft and ground stations. Using the theoretical principles and practical application scenarios related to this method, a theoretical and simulation verification platform was developed to research the impact of the attitude, phase center calibration, and orbit determination errors on the single-frequency two-way time synchronization method. The effectiveness of this new method was verified. The results showed that when the attitude error is less than 72 arc seconds (0.02°), the phase center calibration error is less than 1 mm, and the precision orbit determination (POD) error is less than 10 cm (three-axis). After disregarding nonlink error terms such as equipment noise, this method can attain a space-to-ground time synchronization accuracy of better than 1.5 ps, and the time deviation (TDEV) of the transfer link is better than 0.7 ps @ 100 s, which results in ultrahigh-precision space-to-ground time synchronization. Full article

Positioning of spacecraft (e.g., geostationary orbit (GEO), high elliptical orbit (HEO), and lunar trajectory) is crucial for mission completion. Instead of using ground control systems, global navigation satellite system (GNSS) can be an effective approach to provide positioning, navigation and timing service for spacecraft. In 2020, China finished the construction of the third generation of BeiDou navigation satellite system (BDS-3); this global coverage system will contribute better sidelobe signal visibility for spacecraft. Meanwhile, with more than 100 GNSS satellites, multi-GNSS navigation performance on the spacecraft is worth studying. In this paper, instead of using signal-in-space ranging errors, we simulate pseudorange observations with measurement noises varying with received signal powers. Navigation performances of BDS-3 and its combinations with other systems were conducted. Results showed that, owing to GEO and inclined geosynchronous orbit (IGSO) satellites, all three types (GEO, HEO, and lunar trajectory) of spacecraft received more signals from BDS-3 than from other navigation systems. Single point positioning (SPP) accuracy of the GEO and HEO spacecraft was 17.7 and 23.1 m, respectively, with BDS-3 data alone. Including the other three systems, i.e., GPS, Galileo, and GLONASS, improved the SPP accuracy by 36.2% and 19.9% for GEO and HEO, respectively. Navigation performance of the lunar probe was significantly improved when receiver sensitivity increased from 20 dB-Hz to 15 dB-Hz. Only dual- (BDS-3/GPS) or multi-GNSS (BDS-3, GPS, Galileo, GLONASS) could provide continuous navigation solutions with a receiver threshold of 15 dB-Hz. Full article

Aiming at the problem of high-precision positioning of mass-pedestrians with low-cost sensors, a robust single-antenna Global Navigation Satellite System (GNSS)/Pedestrian Dead Reckoning (PDR) integration scheme is proposed with Gate Recurrent Unit (GRU)-based zero-velocity detector. Based on the foot-mounted pedestrian navigation system, the error state extended Kalman filter (EKF) framework is used to fuse GNSS position, zero-velocity state, barometer elevation, and other information. The main algorithms include improved carrier phase smoothing pseudo-range GNSS single-point positioning, GRU-based zero-velocity detection, and adaptive fusion algorithm of GNSS and PDR. Finally, the scheme was tested. The root mean square error (RMSE) of the horizontal error in the open and complex environments is lower than 1 m and 1.5 m respectively. In the indoor elevation experiment where the elevation difference of upstairs and downstairs exceeds 25 m, the elevation error is lower than 1 m. This result can provide technical reference for the accurate and continuous acquisition of public pedestrian location information. Full article

Due to different designs of receiver correlators and front ends, receiver-related pseudorange biases, called signal distortion biases (SDBs), exist. Ignoring SDBs that can reach up to 0.66 cycles and 10 ns in Melbourne-Wübbena (MW) and ionosphere-free (IF) combinations can negatively affect phase bias estimation. In this contribution, we investigate the SDBs and evaluate the impacts on wide-lane (WL) and narrow-lane (NL) phase bias estimations, and further propose an approach to eliminating these SDBs to improve phase bias estimation. Based on a large data set of 302 multi-global navigation satellite system (GNSS) experiment (MGEX) stations, including 5 receiver brands, we analyze the characteristics of these SDBs The SDB characteristics of different receiver types for different GNSS systems differ from each other. Compared to the global positioning system (GPS) and BeiDou navigation satellite system (BDS), SDBs of Galileo are not significant; those of BDS-3 are significantly superior to BDS-2; Septentrio (SEPT) receivers show the most excellent consistency among all receiver types. Then, we apply the corresponding corrections to phase bias estimation for GPS, Galileo and BDS. The experimental results reveal that the calibration can greatly improve the performance of phase bias estimation. For WL phase biases estimation, the consistencies of WL phase biases among different networks for GPS, Galileo, BDS-2 and BDS-3 improve by 89%, 77%, 76% and 78%, respectively. There are scarcely any improvements of the fixing rates for Galileo due to its significantly small SDBs, while for GPS, BDS-2 and BDS-3, the WL ambiguity fixing rates can improve greatly by 13%, 27% and 14% after SDB calibrations with improvements of WL ambiguity fixing rates, the corresponding NL ambiguity fixing rates can further increase greatly, which can reach approximately 16%, 27% and 22%, respectively. Additionally, after the calibration, both WL and NL phase bias series become more stable. The standard deviations (STDs) of WL phase bias series for GPS and BDS can improve by more than 46%, while those of NL phase bias series can yield improvements of more than 13%. Ultimately, the calibration can make more WL and NL ambiguity residuals concentrated in ranges within ±0.02 cycles. All these results demonstrate that SDBs for phase bias estimation cannot be ignored and must be considered when inhomogeneous receivers are used. Full article

At present, the design and manufacturing technology of mechanically dithered ring laser gyroscope (MDRLG) have matured, the strapdown inertial navigation systems (SINS) with MDRLG have been widely used in military and business scope. When the MDRLG is working, high-frequency dithering is introduced, which will cause the size effect error of the accelerometer. The accelerometer signal has a time delay relative to the system, which will cause the accelerometer time delay error. In this article, in order to solve the above-mentioned problem: (1) we model the size effect error of the mechanically dithering of the MDRLG and perform an error analysis for the size effect error of the mechanically dithering of the MDRLG; (2) we model the time delay error of accelerometer and perform an error analysis for the time delay error of accelerometer; (3) we derive a continuous linear 43-D SINS error model considering the above-mentioned two error parameters and expand the temperature coefficients of accelerometers, inner lever arm error, outer lever arm error parameters to achieve high-precision calibration of SINS. We use the piecewise linear constant system (PWCS) method during the calibration process to prove that all calibration parameters are observable. Finally, the SINS with MDRLG is used in laboratory conditions to test the validity of the calibration method. Full article

Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) is an attractive positioning technology due to its high precision and flexibility. However, the vulnerability of PPP brings a safety risk to its application in the field of life safety, which must be evaluated quantitatively to provide integrity for PPP users. Generally, PPP solutions are processed recursively based on the extended Kalman filter (EKF) estimator, utilizing both the previous and current measurements. Therefore, the integrity risk should be qualified considering the effects of all the potential observation faults in history. However, this will cause the calculation load to explode over time, which is impractical for long-time missions. This study used the innovations in a time window to detect the faults in the measurements, quantifying the integrity risk by traversing the fault modes in the window to maintain a stable computation cost. A non-zero bias was conservatively introduced to encapsulate the effect of the faults before the window. Coping with the multiple simultaneous faults, the worst-case integrity risk was calculated to overbound the real risk in the multiple fault modes. In order to verify the proposed method, simulation and experimental tests were carried out in this study. The results showed that the fixed and hold mode adopted for ambiguity resolution is critical to an integrity risk evaluation, which can improve the observation redundancy and remove the influence of the biased predicted ambiguities on the integrity risk. Increasing the length of the window can weaken the impact of the conservative assumption on the integrity risk due to the smoothing effect of the EKF estimator. In addition, improving the accuracy of observations can also reduce the integrity risk, which indicates that establishing a refined PPP random model can improve the integrity performance. Full article

Adaptive filtering algorithms can be used on the time-domain processing of navigation receivers to suppress interference and maintain the navigation and positioning function. The filter length can affect the interference suppression performance and hardware utilization simultaneously. In practical engineering, the filter length is usually set to a large number to guarantee anti-jamming performance, which means a high-performance receiver requires a high-complexity anti-jamming filter. The study aims at solving the problem by presenting a design method for the optimal filter order in the time-domain anti-jamming receiver, with no need for detailed interference information. According to interference bandwidth and jam-to-signal ratio (JSR), the approach designed a band-stop filter by Kaiser window for calculating the optimal filter order to meet interference suppression requirements. The experimental results show that the time-domain filtering processing has achieved good interference suppression performance for engineering requirements with optimal filter order in satellite navigation receivers. Full article

To satisfy the demands of civil aviation organizations and other users of satellite navigation systems for high-precision and high-integrity service performance, many countries and regions have established satellite-based augmentation systems (SBAS) referring to the Radio Technical Commission for Aeronautics (RTCA) service standards and agreements. The BeiDou SBAS (BDSBAS) provides both single-frequency service, which augments Global Positioning System (GPS) L1 C/A signal, and dual-frequency multi-constellation (DFMC) service, which augments BeiDou Navigation Satellite System (BDS) B1C and B2a dual frequency signals presently, meeting the requirements of the RTCA DO-229D protocol and the SBAS L5 DFMC protocol requirements, respectively. As one of the main error sources, the pseudorange bias errors of BDSBAS monitoring receivers were estimated and their effect on the performance of the BDSBAS service was analyzed. Based on the user algorithms of SBAS differential corrections and integrity information, the service accuracy, integrity, and availability of the BDSBAS were evaluated using real observation data. The results show that the maximum of monitoring receiver pseudorange bias errors between L1P and L1P/L2P can reach 1.57 m, which become the most important errors affecting the performance of the BDSBAS service. In addition, the results show that the pseudorange bias of GPS BlockIII is the smallest, while that of GPS BlockIIR is the largest. Compared with the positioning accuracy of the open service of the core constellation, the positioning accuracy of the BDSBAS service can be improved by approximately 47% and 36% for the RTCA service and DFMC service, respectively. For RTCA services, the protection limit (PL) calculated with the integrity information can 100% envelop the positioning error (PE) and no integrity risk event is detected. The service availability of BDSBAS for APV-I approach is approximately 98.8%, which is mainly affected by the availability of ionospheric grid corrections in the service marginal area. For DFMC service, the integrity risk is not detected either. The service availability for CAT-I approach is 100%. Improving the availability of ionospheric grid corrections is one of the important factors to improve service performance of BDSBAS RTCA service. Full article

With the rapid development and gradual perfection of GNSS in recent years, improving the real-time service performance of GNSS has become a research hotspot. In GNSS single-point positioning, broadcast ephemeris is used to provide a space–time reference. However, the orbit parameters of broadcast ephemeris have meter-level errors, and no mathematical model can simulate the variation of this, which restricts the real-time positioning accuracy of GNSS. Based on this research background, this paper uses a BP (Back Propagation) neural network and a PSO (Particle Swarm Optimization)–BP neural network to model the variation in the orbit error of GPS and BDS broadcast ephemeris to improve the accuracy of broadcast ephemeris. The experimental results showed that the two neural network models in GPS can model the broadcast ephemeris orbit errors, and the results of the two models were roughly the same. The one-day and three-day improvement rates of RMS(3D) were 30–50%, but the PSO–BP neural network model was better able to model the trend of errors and effectively improve the broadcast ephemeris orbit accuracy. In BDS, both of the neural network models were able to model the broadcast ephemeris orbit errors; however, the PSO–BP neural network model results were better than those of the BP neural network. In the GEO satellite outcome of the PSO–BP neural network, the STD and RMS of the orbit error in three directions were reduced by 20–70%, with a 20–30% improvement over the BP neural network results. The IGSO satellite results showed that the PSO–BP neural network model output accuracy of the along- and radial-track directions experienced a 70–80% improvement in one and three days. The one- and three-day RMS(3D) of the MEO satellites showed that the PSO–BP neural network has a greater ability to resist gross errors than that of the BP neural network for modeling the changing trend of the broadcast ephemeris orbit errors. These results demonstrate that using neural networks to model the orbit error of broadcast ephemeris is of great significance to improving the orbit accuracy of broadcast ephemeris. Full article

Global Positioning System (GPS) is a global navigation satellite system and the most common satellite system used in navigation and tracking devices. The phenomenon of week number rollover happened recently—a year ago—due to a design limitation in the week number variable that counting weeks which causes vast losses. As many fleet management systems depend on GPS raw data, such systems stopped working due to inaccurate data provided by GPS receivers. In this paper, we propose a technical and mathematical analysis for the GPS week number rollover phenomenon and suggest a solution to avoid the resulting damage to other subsystems that depend on the GPS device’s raw data. In addition, this paper seeks to provide precautionary measures to deal with the problem proactively. The Open Systems Interconnection model (OSI) and transport layer level solution that has been suggested depends on a TCP packet reforming tool that re-formats the value of the week number according to a mathematical model based on a timestamp complement. At the level of the database, a solution is also suggested which uses triggers. A hardware-level solution is suggested by applying a timestamp complement over the GPS internal controller. Complete testing is applied for all suggested solutions using actual data provided by Traklink—a leading company in navigation and fleet management solutions. After testing, it is evident that the transport layer level solution was the most effective in terms of speed, efficiency, accuracy, cost, and complexity. Applying a transport layer level complement mathematical model can fix the consequences of GPS week number rollover and provide stability to all subsystems that used GPS data from infected devices. Full article

Paving thickness and evenness are two key factors that affect the paving operation quality of earth-rock dams. However, in the recent study, both of the key factors characterising the paving quality were measured using finite point random sampling, which resulted in subjectivity in the detection and a lag in the feedback control. At the same time, the on-site control of the paving operation quality based on experience results in a poor and unreliable paving quality. To address the above issues, in this study, a novel assessment and feedback control framework for the paving operation quality based on the observe–orient–decide–act (OODA) loop is presented. First, in the observation module, a cellular automaton is used to convert the location of the bulldozer obtained by monitoring devices into the paving thickness of the levelling layer. Second, in the orient module, the learning automaton is used to update the state of the corresponding and surrounding cells. Third, in the decision module, an overall path planning method is developed to realise feedback control of the paving thickness and evenness. Finally, in the act module, the paving thickness and evenness of the entire work unit are calculated and compared to their control thresholds to determine whether to proceed with the next OODA loop. The experiments show that the proposed method can maintain the paving thickness less than the designed standard value and effectively prevent the occurrence of ultra-thick or ultra-thin phenomena. Furthermore, the paving evenness is improved by 21.5% as compared to that obtained with the conventional paving quality control method. The framework of the paving quality assessment and feedback control proposed in this paper has extensive popularisation and application value for the same paving construction scene. Full article

Aircraft flying the trans-arctic routes usually apply inertial navigation mechanization in two different navigation frames, e.g., the local geographic frame and the grid frame. However, this change of navigation frame will cause filter overshoot and error discontinuity. To solve this problem, taking the inertial navigation system/global navigation satellite system (INS/GNSS) integrated navigation system as an example, an integrated navigation method based on covariance transformation is proposed. The relationship of the system error state between different navigation frames is deduced as a means to accurately convert the Kalman filter’s covariance matrix. The experiment and semi-physical simulation results show that the presented covariance transformation algorithm can effectively solve the filter overshoot and error discontinuity caused by the change of navigation frame. Compared with non-covariance transformation, the system state error is thereby reduced significantly. Full article

For the tracking of high-dynamic satellite navigation signals, the conventional scalar tracking loop (STL) is vulnerable. Frequent signal-tracking interruption affects the continuity of navigation. The vector tracking loop (VTL) can overcome this disadvantage. However, there are some difficulties in implementing existing vector tracking methods on a real-time hardware receiver, such as the synchronization problem and computation load. This paper proposes an implementation framework of VTL based on a partial open-loop numerically controlled oscillator (NCO) control mode that can be implemented with minor modifications on an existing receiver platform. The structure of VTL, the design of the navigation filter, and the key points of hardware implementation are introduced in detail. Lastly, the VTL performance was verified by a GPS simulator test. The results show that the proposed VTL can run in real-time and be significantly improved in the tracking continuity of high-dynamic signals, tracking sensitivity, positioning accuracy, and recovery time for interrupted signals compared with those of STL. Full article

Suffering from hardware phase biases originating from satellites and the receiver, precise point positioning (PPP) requires a long convergence time to reach centimeter coordinate accuracy, which is a major drawback of this technique and limits its application in time-critical applications. Ambiguity resolution (AR) is the key to a fast convergence time and a high-precision solution for PPP technology and PPP AR products are critical to implement PPP AR. Nowadays, various institutions provide PPP AR products in different forms with different strategies, which allow to enable PPP AR for Global Positioning System (GPS) and Galileo or BeiDou Navigation System (BDS). To give a full evaluation of PPP AR performance with various products, this work comprehensively investigates the positioning performance of GPS-only and multi-GNSS (Global Navigation Satellite System) combination PPP AR with the precise products from CNES, SGG, CODE, and PRIDE Lab using our in-house software. The positioning performance in terms of positioning accuracy, convergence time and fixing rate (FR) as well as time to first fix (TTFF), was assessed by static and kinematic PPP AR models. For GPS-only, combined GPS and Galileo PPP AR with different products, the positioning performances were all comparable with each other. Concretely, the static positioning errors can be reduced by 21.0% (to 0.46 cm), 52.5% (to 0.45 cm), 10.0% (to 1.33 cm) and 21.7% (to 0.33 cm), 47.4% (to 0.34 cm), 9.5% (to 1.16 cm) for GPS-only and GE combination in north, east, up component, respectively, while the reductions are 20.8% (to 1.13 cm), 42.9% (to 1.15 cm), 19.9% (to 3.4 cm) and 20.4% (to 0.72 cm), 44.1% (to 0.66 cm), 10.1% (to 2.44 cm) for kinematic PPP AR. Overall, the positioning performance with CODE products was superior to the others. Furthermore, multi-GNSS observations had significant improvements in PPP performance with float solutions and the TTFF as well as the FR of GPS PPP AR could be improved by adding observations from other GNSS. Additionally, we have released the source code for multi-GNSS PPP AR, anyone can freely access the code and example data from GitHub. Full article

Data collected from a moving lidar sensor can produce an accurate digital representation of the physical environment that is scanned, provided the time-dependent positions and orientations of the lidar sensor can be determined. The most widely used approach to determining these positions and orientations is to collect data with a GNSS/INS sensor. The use of dual-antenna GNSS/INS sensors within commercial UAS-lidar systems is uncommon due to the higher cost and more complex installation of the GNSS antennas. This study investigates the impacts of using a single-antenna and dual-antenna GNSS/INS MEMS-based sensor on the positional precision of a UAS-lidar generated point cloud, with an emphasis on the different heading determination techniques employed by each type of GNSS/INS sensor. Specifically, the impacts that sensor velocity and acceleration (single-antenna), and a GNSS compass (dual-antenna) have on heading precision are investigated. Results indicate that at the slower flying speeds often used by UAS (≤5 m/s), a dual-antenna GNSS/INS sensor can improve heading precision by up to a factor of five relative to a single-antenna GNSS/INS sensor, and that a point of diminishing returns for the improvement of heading precision exists at a flying speed of approximately 15 m/s for single-antenna GNSS/INS sensors. Additionally, a simple estimator for the expected heading precision of a single-antenna GNSS/INS sensor based on flying speed is presented. Utilizing UAS-lidar mapping systems with dual-antenna GNSS/INS sensors provides reliable, robust, and higher precision heading estimates, resulting in point clouds with higher accuracy and precision. Full article

Aiming to improve the positioning accuracy of an unmanned aerial vehicle (UAV) swarm under different scenarios, a two-case navigation scheme is proposed and simulated. First, when the Global Navigation Satellite System (GNSS) is available, the inertial navigation system (INS)/GNSS-integrated system based on the Kalman Filter (KF) plays a key role for each UAV in accurate navigation. Considering that Kalman filter’s process noise covariance matrix Q and observation noise covariance matrix R affect the navigation accuracy, this paper proposes a dynamic adaptive Kalman filter (DAKF) which introduces ensemble empirical mode decomposition (EEMD) to determine R and adjust Q adaptively, avoiding the degradation and divergence caused by an unknown or inaccurate noise model. Second, a network navigation algorithm (NNA) is employed when GNSS outages happen and the INS/GNSS-integrated system is not available. Distance information among all UAVs in the swarm is adopted to compensate the INS position errors. Finally, simulations are conducted to validate the effectiveness of the proposed method, results showing that DAKF improves the positioning accuracy of a single UAV by 30–50%, and NNA increases the positioning accuracy of a swarm by 93%. Full article

In this paper a new mathematical algorithm is proposed to improve the accuracy of DGPS (Differential GPS) positioning using several GNSS (Global Navigation Satellites System) reference stations. The new mathematical algorithm is based on a weighting scheme for the following three criteria: weighting in function of baseline (vector) length, weighting in function of vector length error and weighting in function of the number of tracked GPS (Global Positioning System) satellites for a single baseline. The algorithm of the test method takes into account the linear combination of the weighting coefficients and relates the position errors determined for single baselines. The calculation uses a weighting scheme for three independent baselines denoted as $\left(1A,2A,3A\right)$. The proposed research method makes it possible to determine the resultant position errors for ellipsoidal BLh coordinates of the aircraft and significantly improves the accuracy of DGPS positioning. The analysis and evaluation of the new research methodology was checked for data from two flight experiments carried out in Mielec and Dęblin. Based on the calculations performed, it was found that in the flight experiment in Mielec, due to the application of the new research methodology, DGPS positioning accuracy improved from 55 to 94% for all the BLh components. In turn, in the flight experiment in Dęblin, the accuracy of DGPS positioning improved by 63–91%. The study shows that the highest DGPS positioning accuracy is seen when using weighting criterion II, the inverse of the square of the vector length error. Full article

Compared to the BeiDou regional navigation satellite system (BDS-2), the BeiDou global navigation satellite system (BDS-3) carried out a brand new integrity concept design and construction work, which defines and achieves the integrity functions for major civil open services (OS) signals such as B1C, B2a, and B1I. The integrity definition and calculation method of BDS-3 are introduced. The fault tree model for satellite signal-in-space (SIS) is used, to decompose and obtain the integrity risk bottom events. In response to the weakness in the space and ground segments of the system, a variety of integrity monitoring measures have been taken. On this basis, the design values for the new B1C/B2a signal and the original B1I signal are proposed, which are 0.9 × 10⁻⁵ and 0.8 × 10⁻⁵, respectively. The hybrid alarming mechanism of BDS-3, which has both the ground alarming approach and the satellite alarming approach, is explained. At last, an integrity risk analysis and verification work were carried out using the operating data of the system in 2019. The results show that the actual operation of the system is consistent with the conceptual design, which satisfies the integrity performance promised by BDS-3 in the ICAO SAPRs. Full article

There are two problems with using global navigation satellite system-interferometric reflectometry (GNSS-IR) to retrieve the soil moisture content (SMC) from single-satellite data: the difference between the reflection regions, and the difficulty in circumventing the impact of seasonal vegetation growth on reflected microwave signals. This study presents a multivariate adaptive regression spline (MARS) SMC retrieval model based on integrated multi-satellite data on the impact of the vegetation moisture content (VMC). The normalized microwave reflection index (NMRI) calculated with the multipath effect is mapped to the normalized difference vegetation index (NDVI) to estimate and eliminate the impact of VMC. A MARS model for retrieving the SMC from multi-satellite data is established based on the phase shift. To examine its reliability, the MARS model was compared with a multiple linear regression (MLR) model, a backpropagation neural network (BPNN) model, and a support vector regression (SVR) model in terms of the retrieval accuracy with time-series observation data collected at a typical station. The MARS model proposed in this study effectively retrieved the SMC, with a correlation coefficient (R²) of 0.916 and a root-mean-square error (RMSE) of 0.021 cm³/cm³. The elimination of the vegetation impact led to 3.7%, 13.9%, 11.7%, and 16.6% increases in R² and 31.3%, 79.7%, 49.0%, and 90.5% decreases in the RMSE for the SMC retrieved by the MLR, BPNN, SVR, and MARS model, respectively. The results demonstrated the feasibility of correcting the vegetation changes based on the multipath effect and the reliability of the MARS model in retrieving the SMC. Full article

The vector tracking loop (VTL) has high tracking accuracy and a superior ability to track weak signals in GNSS. However, traditional VTL architecture is established on continuous Code Division Multiple Access (CDMA) signal and is incompatible with pseudolite positioning systems (PLPS) because PLPS generally adopts a pseudo-random pulsing CDMA signal structure to mitigate the near-far effect. Therefore, this paper proposes an optimized VTL architecture for pseudo-random pulsing CDMA signals. To avoid estimation biases in PLPS, the proposed VTL adopts irregular update periods (IUP) pre-filters which adjust the update cycles according to the active timeslot intervals. Meanwhile, as the active timeslots of different pseudolites do not overlap, the sampling time of the navigation filter inputs is inconsistent and time-varying, causing jitter degradation. Thus, the proposed VTL predicts the measurements so that they can be sampled at the same time, which improves tracking accuracy. Simulation is carried out to evaluate the performance of the proposed VTL. The results suggest that the proposed VTL outperforms the traditional pre-filter-based VTL and IUP pre-filter-based VTL. Full article

Most UAVs rely on GPS for localization in an outdoor environment. However, in GPS-denied environment, other sources of localization are required for UAVs to conduct feedback control and navigation. LiDAR has been used for indoor localization, but the sampling rate is usually too low for feedback control of UAVs. To compensate this drawback, IMU sensors are usually fused to generate high-frequency odometry, with only few extra computation resources. To achieve this goal, a real-time LiDAR inertial odometer system (RTLIO) is developed in this work to generate high-precision and high-frequency odometry for the feedback control of UAVs in an indoor environment, and this is achieved by solving cost functions that consist of the LiDAR and IMU residuals. Compared to the traditional LIO approach, the initialization process of the developed RTLIO can be achieved, even when the device is stationary. To further reduce the accumulated pose errors, loop closure and pose-graph optimization are also developed in RTLIO. To demonstrate the efficacy of the developed RTLIO, experiments with long-range trajectory are conducted, and the results indicate that the RTLIO can outperform LIO with a smaller drift. Experiments with odometry benchmark dataset (i.e., KITTI) are also conducted to compare the performance with other methods, and the results show that the RTLIO can outperform ALOAM and LOAM in terms of exhibiting a smaller time delay and greater position accuracy. Full article

This paper designs a cascading vector tracking loop based on the Unscented Kalman Filter (UKF) for high dynamic environment. Constant improvement in dynamic performance is an enormous challenge to the traditional receiver. Due to the doppler effect, the satellite signals received by these vehicles contain fast changing doppler frequency shifts and the first and second derivatives of doppler frequency, which will directly cause a negative impact on the receiver’s stable tracking of the signals. In order to guarantee the dynamic performance and the tracking accuracy, this paper designs a vector carrier structure to estimate the doppler component of a signal. Firstly, after the coherence integral, the IQ values are reorganized into new observations. Secondly, the phase error and frequency of the carrier are estimated through the pre-filter. Then, the pseudorange and carrier frequency are used as the observations of the main filter to estimate the motion state of the aircraft. Finally, the current state is fed back to the carrier Numerical Controlled Oscillator (NCO) as a complete closed loop. In the whole structure, the cascading vector loop replaces the original carrier tracking loop, and the stable signal tracking of code loop is guaranteed by carrier assisted pseudo-code method. In this paper, with the high dynamic signals generated by the GNSS signal simulator, this designed algorithm is validated by a software receiver. The results show that this loop has a wider dynamic tracking range and lower tracking error than the second-order frequency locked loop assisted third-order phase locked loop in high dynamic circumstances. When the acceleration of carrier is 100 g, the convergence time of vector structure is about 100 ms, and the carrier phase error is lower than 0.6 mm. Full article

It has been proven that to solve the problems that arise in the combinatorial modeling of the prospects for the development of regional renewable energy, an algorithmically simple general combinatorial approach is the most appropriate option. The conceptual express method and corresponding mechanisms of the economic estimation of the efficiency of variants of the formation of regional systems of renewable energy have been suggested. These variants take into account the inflationary factors which serve as a basis of the analysis of investment and innovative projects of renewable energy sources by means of combinatorial modeling methods. To qualitatively analyze the effectiveness of the compared options, the system of existing indicators of the economic efficiency of renewable energy sources at the meso-level has been studied. The system was supplemented by informal and environmental indicators, the need for which is due to the fact that they have a significant impact on renewable energy in the region. Factors that significantly determine the effectiveness of the investment and innovation project for the introduction of renewable energy sources into the regional economy have been substantiated. Full article