Simulation Study of Multi-GNSS Positioning Systems in Urban Canyon Environments

Abstract

This study presents a comprehensive performance evaluation of hybrid global navigation satellite system (GNSS) configurations in urban canyon environments across South Korea, focusing on the integration of Global Positioning System (GPS) with the BeiDou, GLONASS, Galileo, Quasi Zenith Satellite System (QZSS), and Navigation with Indian Constellation (NavIC) constellations. Simulation scenarios representing pedestrian, vehicular, and unmanned aerial vehicle (UAV) movements are used to analyze the positioning accuracy and reliability of each hybrid system. The results indicate that GPS–BeiDou and GPS–QZSS combinations consistently provide superior accuracy and continuous satellite visibility, with GPS–BeiDou achieving centimeter-level precision in the UAV scenario. In contrast, GPS–GLONASS and GPS–NavIC systems exhibit higher error rates and less stable performance. These findings emphasize the critical role of satellite availability, receiver altitude, and signal compatibility in achieving robust positioning. Although the results are specific to South Korea, the proposed evaluation framework is broadly applicable and can help other countries assess hybrid GNSS performance to guide the design and optimization of their regional navigation satellite systems.

1. Introduction

Global navigation satellite systems (GNSSs) have become integral to daily life, underpinning an ever-expanding range of location-based services and technologies. As global demand for real-time, high-accuracy positioning continues to grow, GNSSs have emerged as the backbone of countless civil, commercial, and defense applications. From guiding autonomous vehicles and unmanned aerial systems to enabling smartphone navigation, precision agriculture, environmental monitoring, and disaster response, GNSSs supply the critical spatial and temporal data that modern infrastructure and intelligent systems require [1]. A function of GNSSs is their ability to deliver continuous, global, all-weather positioning and timing services autonomously and passively. It offers highly available, automated solutions that scale from mass-market devices to scientific and industrial platforms. GNSS signals are broadcast by medium Earth orbit (MEO) or/and geostationary Earth orbit (GEO) satellites, enabling users to determine their position anywhere on Earth using computing pseudo-range measurements to at least four satellites [2]. These signals support not only navigation and mapping but also highly synchronized time dissemination essential to power grids, financial transactions, and communication networks.

The global positioning system (GPS), maintained by the United States, remains the most widely used constellation in South Korea and much of the world. Its long-standing availability, global coverage, and robust supporting infrastructure have made it the default positioning reference for both consumer-grade and professional applications. Nevertheless, exclusive dependence on GPS introduces vulnerabilities, especially for safety- or time-critical services. A notable example occurred in early 2016 when the U.S. Air Force decommissioned several GPS satellites [3]. During the operation, incorrect timestamps, off by roughly 13 µs, were inadvertently uploaded to functional spacecraft, triggering disruptions that persisted for more than 12 h across multiple industries worldwide. The incident underscored the risks inherent in relying on a single constellation: GPS outages can interrupt accurate positioning, air traffic control, maritime navigation, telecommunications, and time synchronization services, including radio and television broadcasting [4]. Beyond isolated failures, single-constellation receivers suffer degraded performance in challenging environments, most notably urban canyons where skyscrapers and other infrastructure block or reflect satellite signals. In such settings, the number of visible satellites can fall below the minimum required for an accurate position fix, and the signals that do reach the receiver are often compromised by multipath effects. Together, these factors worsen satellite geometry, elevate dilution of precision (DOP), and increase positioning error, weaknesses to which single-constellation systems are particularly prone because they lack the satellite diversity and geometric redundancy offered by multi-constellation designs.

To address these limitations, using multiple constellations, commonly called multi-GNSSs, has become a critical strategy for improving positioning performance, availability, and reliability [5]. In addition to GPS, several global and regional systems, China’s BeiDou Navigation Satellite System (BDS), Russia’s Globalnaya Navigazionnaya Sputnikovaya Sistema (GLONASS), European Union’s Galileo, Japan’s Quasi-Zenith Satellite System (QZSS), and India’s Navigation with Indian Constellation (NavIC), broadcast complementary signals that enhance overall GNSS service quality. Integrating observations from multiple constellations yields a larger number of visible satellites, better satellite geometry, greater redundancy, and heightened resilience to localized interference or constellation-specific anomalies. The motivations for employing multi-GNSSs are manifold. First, increased satellite visibility lowers the risk of position outages in environments prone to signal blockages, such as urban canyons and dense forests. Second, the more favorable spatial distribution of satellites across different orbital planes reduces DOP, directly improving positioning accuracy. Third, multi-GNSS solutions offer superior fault tolerance: if one system fails or degrades, measurements from other constellations can sustain uninterrupted positioning. Finally, access to diverse signal structures and frequencies enables sophisticated error mitigation techniques, including multifrequency ionospheric corrections and more effective multipath suppression.

Several studies have examined the core positioning techniques used in multi-GNSSs, including single-point positioning (SPP), precise point positioning (PPP), and real-time kinematic (RTK) methods. Li et al. [6] developed and demonstrated a four-constellation model for real-time precise orbit determination, clock estimation, and positioning based on a unified parameter-estimation approach. Their results showed that integrating all four GNSS constellations improved positioning accuracy by ~25% and shortened convergence time by ~70% compared with GPS-only solutions, while maintaining centimeter-level precision and more than 99.5% availability even under high elevation cutoffs. N. Nadarajah et al. [7] evaluated the benefits of combining GPS, BeiDou, and Galileo for PPP-RTK using the Curtin PPP-RTK platform across large- and small-scale networks. Processing multi-GNSS data from several receiver types, including low-cost single-frequency units, reduced convergence time from 103 min with GPS-only observations to 15 min with multi-GNSSs and ambiguity resolution and to as little as 2 min for in-the-loop users. X. Li et al. [8] proposed a multi-frequency, multi-GNSS PPP-RTK technique that couples precise atmospheric corrections with a cascade ambiguity-fixing strategy, achieving centimeter-level accuracy and rapid ambiguity resolution in urban settings. Likewise, T. Liu et al. [9] introduced a multi-GNSS PPP model that jointly processes raw code and phase observations from GPS, GLONASS, BeiDou, and Galileo while rigorously modeling inter-system biases and GLONASS inter-frequency code biases. The results demonstrate high-precision positioning, i.e., mm to cm level accuracy, and reveal that inter-system biases vary daily due to clock datum differences, while GLONASS inter-frequency biases remain stable. J. Guo et al. [10] further assessed the feasibility of multi-GNSS PPP for precision agriculture through both static and kinematic experiments conducted under varied environmental conditions.

The accuracy of multi-GNSS positioning can be degraded by code- and phase-level inter-system inconsistencies, satellite hardware delays, and atmospheric effects. Håkansson et al. [11] provided a comprehensive review of hardware-induced code and phase biases, detailing their sources, their impacts on ambiguity resolution and ionospheric modeling, and practical strategies for mitigation, such as bias differencing and pre-estimation. Torre et al. [12] analyzed inter-system time biases among five GNSS constellations using multi-day data from European tracking stations equipped with different receiver types; they quantified discrepancies between broadcast and precise ephemerides and highlighted consistent system- and receiver-dependent offsets. O. Montenbruck et al. [13] established a harmonized framework for assessing signal-in-space range errors across multiple constellations by reconciling antenna offset, time reference, and group delay differences. Addressing atmospheric influences, Ren et al. [14] developed a global ionospheric model that assimilates observations from four constellations, showing that multi-GNSS data markedly improve modeling accuracy and spatial resolution compared with GPS-only or dual-system approaches.

High-precision applications also rely on accurate orbital information, and the choice between broadcast and precise ephemerides strongly affects attainable accuracy. In this context, Montenbruck et al. [15] presented a year-long evaluation of signal-in-space ranging errors for multiple constellations by comparing broadcast ephemeris data with precise IGS products, illustrating the performance differentials most relevant to multi-GNSS positioning.

The key contributions of this research can be summarized as follows:

• To demonstrate that dual constellation systems can achieve comparable urban canyon performance to full multi-GNSS setups in many scenarios, challenging the prevailing “more constellations are always better” assumption;
• To identify distinct advantages of specific regional systems, enabling cost-effective system design choices for developing nations;
• To provide the first systematic framework for evaluating dual constellation urban navigation performance, filling a critical gap between single GNSS and full multi-GNSS studies.

Recognizing these advantages, this study presents a detailed performance analysis of various hybrid GNSS combinations. Using comprehensive simulations, we examine the gains achieved by integrating multiple constellations over single constellation positioning, with a special focus on demanding operational environments. Because each constellation is distinguished by unique satellite geometry, orbital parameters, signal structure, and regional coverage, evaluating specific hybrids quantitatively is essential to clarify their benefits under different conditions. The remainder of the paper is organized as follows. Section 2 describes the methodology adopted in this study, including the simulation setup and system configurations. Section 3 presents and analyzes the simulation results, comparing the positioning performance of several hybrid combinations across representative environmental scenarios. Finally, Section 4 summarizes the key findings and offers recommendations for the future development and optimization of South Korea’s regional navigation satellite system (RNSS).

2. Methodology

This section presents the methodological framework used to evaluate the positioning performance of multi-GNSS constellations.

2.1. Satellite Visibility

Satellite visibility is defined as the number of satellites whose elevation angles exceed a prescribed mask angle at a given epoch. Only satellites with elevation angles above the mask angle are considered visible and used in the positioning computation. In other words, at any given moment, the UE counts the satellites that are above the mask angle, and only these satellites contribute to the positioning solution.

Under nominal conditions, GNSS constellations are designed to perform optimally in open-sky environments, where satellite signals reach the receiver along direct line-of-sight (LOS) paths. Under these circumstances, the receiver can acquire a sufficient number of strong, high-quality signals simultaneously, thereby ensuring accurate and reliable position estimation. GNSS performance, however, deteriorates markedly when signal reception is obstructed, as is often the case in urban canyons or indoor settings. Figure 1 illustrates four representative satellite signal propagation scenarios encountered in an urban canyon. Satellite A exemplifies a non-line-of-sight (NLOS) situation in which the signal arrives only after reflection. Satellite B enjoys an unobstructed LOS path and consequently contributes positively to positioning accuracy. Satellite C presents a mixed condition, combining LOS and reflected components and thus introducing multipath errors. Satellite D is completely blocked and therefore unavailable for positioning. These contrasting signal conditions underscore the need for precise modeling of satellite visibility in built-up areas.

To characterize that visibility, several models have been proposed in the literature. J. A. Del Peral-Rosado et al. [16] proposed a sophisticated approach, known as the generalized elevation mask model. This formulation defines the mask angle as an explicit function of the satellite’s azimuth angle and incorporates the fundamental physical characteristics of the urban canyon, i.e., street width and building height. By assuming symmetrical building facades on both sides of a street, the model computes a direction-dependent mask angle that reflects the street’s aspect ratio, thereby yielding a more realistic and azimuth-specific depiction of the obstructed sky view. Its principal limitation lies in the assumption that the GNSS receiver is located exactly on the street centerline, an idealized placement that only rarely matches real user trajectories or receiver installations.

Building on that framework, J. Li et al. [17] introduced an extended elevation mask model that determines the mask angle for a receiver situated at any lateral position within the street, rather than restricting it to the centerline. As illustrated in Figure 2, this enhancement accommodates diverse building heights, variable street widths, and arbitrary receiver placements, producing a more flexible and realistic representation of urban environments. By capturing these spatial dynamics, the model affords more accurate predictions of satellite visibility and signal obstruction, capabilities that are particularly critical for evaluating multi-GNSS performance in complex urban settings. In the present study, this refined elevation mask model is adopted to emulate urban signal conditions faithfully and to strengthen the reliability of the multi-GNSS performance analysis. The elevation mask angle, ${\alpha }_{mask}$, is defined as follows [17]:

$${\alpha }_{mask}=\left|{\tan }^{-1}\left[{\displaystyle \frac{h_b-h}{W_d}}·\cos \left({\phi }_{az}\right)\right]\right|$$

(1)

where $h_b$ denotes the building height, $h$ is the receiver altitude, $W_d$ represents the horizontal distance between the receiver and the building facade, and ${\phi }_{az}$ is the satellite azimuth angle.

The satellite visibility of various GNSS constellations was evaluated over eight days at Gangnam Underground Station, South Korea, and the results are illustrated in Figure 3. Following the findings of Li et al. [17], which demonstrate that GNSS satellite visibility decreases as the elevation mask angle increases, a mask angle of 40° was employed to replicate typical urban canyon conditions in which surrounding buildings obstruct low-elevation signals. The goal is to assess and compare the visibility performance of each constellation under the constrained environments commonly encountered in dense South Korean urban areas. GPS and BeiDou exhibit the greatest average satellite visibility, with mean satellite counts of 3.8874 and 3.9610, maximum counts of 7 and 8, and minimum counts of 2 and 1, respectively. This strong performance can be attributed to the global coverage and relatively dense constellations of these systems, which currently operate 32 and 36 satellites in orbit, respectively. Interestingly, GLONASS shows constant satellite visibility throughout the entire observation period, consistently maintaining visibility of three satellites. This behavior results from the particular orbital configuration and satellite geometry of the GLONASS constellation. Unlike GPS and BeiDou, which employ staggered orbital planes with varying inclinations, GLONASS satellites are deployed in three orbital planes inclined at 64.8°, with evenly spaced satellites designed to provide continuous coverage at high latitudes [18]. In regions such as South Korea, which lies at mid-latitudes outside GLONASS’s optimal service area, satellite visibility remains limited yet stable. Notably, although both GLONASS and Galileo operate with 24 satellites, the minimum number of visible Galileo satellites observed is 0. This is due to the orbital configuration of the Galileo system, which employs three orbital planes at a higher altitude and a lower inclination angle of 56°. Although this design favors coverage over Europe and equatorial regions, it leads to suboptimal satellite visibility in East Asia. Consequently, there are periods during which all Galileo satellites are either near the horizon or positioned on the opposite side of the Earth relative to the user, resulting in instances of zero visibility. Among the RNSS, QZSS demonstrates better satellite visibility than NavIC, with a mean number of visible satellites of 2.7305 compared with 1.0817 for NavIC. This difference arises primarily from the design objectives of the two systems: QZSS was developed to augment GNSS performance in the Asia-Pacific region, including Japan and neighboring countries, whereas NavIC is optimized for regional coverage over the Indian subcontinent. As a result, NavIC offers limited satellite visibility outside its designed service area.

2.2. Pseudo-Range Measurement

GNSS positioning relies on trilateration, whereby the receiver’s location is obtained by determining its distance from multiple satellites. With range measurements to at least three satellites, the receiver’s position can be resolved as the intersection of three spheres, each centered on a known satellite position and having a radius equal to the satellite-to-receiver distance. This distance is inferred by measuring the signal’s propagation time and multiplying it by the speed of light. In practice, however, satellite and receiver clocks are not perfectly synchronized, introducing an unknown clock bias. Therefore, the measured range represents an apparent rather than the true geometric distance and is referred to as a pseudo-range. To estimate the signal travel time, the receiver processes the incoming GNSS signal through correlation techniques, which generally involve three sequential stages, namely, acquisition, tracking, and demodulation. The core concept is to de-spread the received signal by multiplying it with two locally generated replicas: the satellite’s pseudorandom-noise (PRN) code and a synchronized carrier. The de-spread signal is then integrated over a selected time interval to improve the output signal-to-noise ratio (SNR). This integration acts as a low-pass filter, and the coherent integration time is usually chosen as an integer multiple of the PRN code duration. When the locally generated replica is correctly aligned with the incoming signal, a distinct peak appears in the correlator output, revealing the code phase delay that corresponds to the transmission time offset. The correlation coefficient is expressed as follows [19]:

$$R\left(\tau \right)={\int }_0^{T_1}r\left(t\right)·r_c\left(t-\tau \right)·\cos \left(2\pi f_{c}t+\phi \right)dt$$

(2)

where $r\left(t\right)$ is the received signal, $r_c\left(t\right)$ is the time-shifted local PRN code replica, $f_c$ is the carrier frequency, $\phi$ is the code phase offset, and $T_1$ is the coherent integration time.

The output of the correlation process typically exhibits a pronounced peak when the locally generated replica is precisely aligned with the incoming GNSS signal. This peak corresponds to the estimated code delay and is used to determine the signal’s time of arrival (TOA). As illustrated in Figure 4, the correlation output reaches its maximum at the point of alignment, indicating the time shift required to synchronize the receiver with the transmitted signal. The resulting pseudo-range between the ith GNSS satellite and the receiver is therefore expressed as follows:

$${\rho }_i=c·{\tau }_i$$

(3)

where $c$ is the speed of light, and ${\tau }_i$ is the estimated TOA.

Because Equation (3) omits several error sources and the observation model is nonlinear, a nonlinear least squares technique is commonly used to estimate the receiver’s position. This approach minimizes the sum of squared discrepancies between measured and predicted pseudo-ranges, thereby accounting for measurement noise, satellite geometry, and other perturbations. The state vector to be estimated at iteration k is expressed as follows:

$$L_r^k={\left[x_r^k,y_r^k,z_r^k,{\delta }_r^k\right]}^T$$

(4)

where ${\left(x_r,y_r,z_r\right)}^T$ is the receiver’s unknown location, and ${\delta }_r$ is the receiver clock bias.

In GNSS positioning, the pseudo-range is the observed distance between the UE and a satellite, which includes the true geometric distance, the receiver clock bias, and other measurement errors. The modeled Euclidean distance to the ith satellite at the ith iteration of the Gauss–Newton algorithm is expressed as follows:

$$d_i^k=\sqrt{{\left(x_{sat,i}-x_r^k\right)}^2+{\left(y_{sat,i}-y_r^k\right)}^2+{\left(z_{sat,i}-z_r^k\right)}^2}$$

(5)

where ${\left(x_{sat,i},y_{sat,i},z_{sat,i}\right)}^T$ is the known satellite position.

Because Equation (5) contains square root terms, the relationship between observations and unknown parameters is inherently nonlinear. In this study, we solve the positioning problem with the Gauss–Newton iterative algorithm [20], which treats the task as a nonlinear regression problem. The observed pseudo-range measurement received from the ith satellite can be expressed as follows:

$${\rho }_i=d_i^k+e_m+{\delta }_r^k·c$$

(6)

where $e_m$ is an aggregate error term, including all unmodelled error sources, e.g., the ionospheric, tropospheric delays, multipath effects, etc.

The Gauss–Newton algorithm is used in this study to iteratively minimize the residuals between the observed and predicted pseudo-ranges, ultimately refining the UE’s estimated position and clock bias. The residual quantifies the discrepancy between the observed and modelled distances. Minimizing the sum of squared residuals over all visible satellites ensures convergence toward the optimal solution. The residual for each observation can be expressed as follows:

$${\eta }_i^k={\rho }_i-d_i^k$$

(7)

These residuals are stacked into a vector, which can be expressed as follows:

$${\eta }^k=\left[\begin{array}{c}{\eta }_1^k\\ {\eta }_2^k\\ ⋮\\ {\eta }_N^k\end{array}\right]$$

(8)

The Gauss–Newton algorithm iteratively updates the estimation of $L_r$ to minimize the sum of squared residuals. At each iteration $k$, the update rule is given by the following:

$$L_r^{k+1}=L_r^k+{\left(J^{T}J\right)}^{-1}{J}^T{\eta }^k$$

(9)

Here, $J$ is the Jacobian matrix containing the first-order partial derivatives of the residuals with respect to the unknown parameters:

$$J=\left[\begin{array}{cccc}{\displaystyle \frac{\mathsf{\partial }\left(x_{sat,1}-x_r\right)}{\mathsf{\partial }{\rho }_1}}& {\displaystyle \frac{\mathsf{\partial }\left(y_{sat,1}-y_r\right)}{\mathsf{\partial }{\rho }_1}}& {\displaystyle \frac{\mathsf{\partial }\left(z_{sat,1}-z_r\right)}{\mathsf{\partial }{\rho }_1}}& c\\ {\displaystyle \frac{\mathsf{\partial }\left(x_{sat,2}-x_r\right)}{\mathsf{\partial }{\rho }_2}}& {\displaystyle \frac{\mathsf{\partial }\left(y_{sat,2}-y_r\right)}{\mathsf{\partial }{\rho }_2}}& {\displaystyle \frac{\mathsf{\partial }\left(z_{sat,2}-z_r\right)}{\mathsf{\partial }{\rho }_2}}& c\\ ⋮& ⋮& ⋮& ⋮\\ {\displaystyle \frac{\mathsf{\partial }\left(x_{sat,N}-x_r\right)}{\mathsf{\partial }{\rho }_N}}& {\displaystyle \frac{\mathsf{\partial }\left(y_{sat,N}-y_r\right)}{\mathsf{\partial }{\rho }_N}}& {\displaystyle \frac{\mathsf{\partial }\left(z_{sat,N}-z_r\right)}{\mathsf{\partial }{\rho }_N}}& c\end{array}\right]$$

(10)

The weighted cost function can be modeled as follows:

$$V={\displaystyle \frac{1}{2}}{\eta }^{T}W\eta$$

(11)

where $W$ is a positive definite diagonal matrix used to weigh the contribution of each residual in the cost function. The weight matrix $W$ is constructed from the inverse of the measurement noise covariance, which can be expressed as follows:

$$W=R^{-1}$$

(12)

Here, $R$ denotes the covariance matrix of the measurement noise, expressed as follows [21]:

$$R=\left[\begin{array}{cccc}{\displaystyle \frac{1}{{e_m}^2}}& 0& 0& 0\\ 0& {\displaystyle \frac{1}{{e_m}^2}}& 0& 0\\ ⋮& ⋮& \ddots & ⋮\\ 0& 0& 0& {\displaystyle \frac{1}{{e_m}^2}}\end{array}\right]$$

(13)

Equations (11)–(13) ensure that residuals from measurements with higher uncertainty, i.e., larger variance, are assigned lower weights, while those from more reliable measurements contribute more significantly to the cost function.

Finally, the positioning error can be calculated as follows:

$$Err=\sqrt{{\left\{R_{ear}·{\cos }^{-1}\left[\sin \left(y_{tr}\right)\sin \left(y_{est}\right)+\cos \left(y_{tr}\right)\cos \left(y_{est}\right)\cos \left(x_{tr}-x_{est}\right)\right]\right\}}^2+{\left(h_{tr}-h_{est}\right)}^2}$$

(14)

where ${\left(x_{tr},y_{tr},h_{tr}\right)}^T$ denotes the true UE position, ${\left(x_{est},y_{est},h_{est}\right)}^T$ represents the estimated UE location, and $R_{ear}$ is the radius of the Earth.

2.3. Inter-System Bias

In multi-GNSS positioning, signals from several constellations are combined to improve accuracy, availability, and robustness. Because each constellation maintains its own system time, clock offsets arise between systems; these inter-system biases (ISBs) must be modeled and estimated to maintain consistency in the integrated solution. In this study, GPS time is adopted as the common reference because South Korea’s navigation infrastructure relies primarily on GPS, making GPS time both practical and locally relevant. To synchronize observations, ISBs are introduced into the measurement equations to compensate for temporal discrepancies between each constellation’s clock and GPS time. Following [22], the ionosphere-free pseudo-range equations are expressed as follows:

$$P^{GPS}\left(t\right)=r^{GPS}\left(t\right)+{\delta }_r^{GPS}\left(t\right)·c-{\delta }_t^{GPS}\left(t\right)·c+e_m\left(t\right)$$

(15)

$$P^{BeiDou}\left(t\right)=r^{BeiDou}\left(t\right)+{\delta }_r^{GPS}\left(t\right)·c-{\delta }_t^{BeiDou}\left(t\right)·c+{ISB}_{GPS}^{BeiDou}+e_m\left(t\right)$$

(16)

$$P^{GLONASS}\left(t\right)=r^{GLONASS}\left(t\right)+{\delta }_r^{GPS}\left(t\right)·c-{\delta }_t^{GLONASS}\left(t\right)·c+{ISB}_{GPS}^{GLONASS}+e_m\left(t\right)$$

(17)

$$P^{Galileo}\left(t\right)=r^{Galileo}\left(t\right)+{\delta }_r^{GPS}\left(t\right)·c-{\delta }_t^{Galileo}\left(t\right)·c+{ISB}_{GPS}^{Galileo}+e_m\left(t\right)$$

(18)

$$P^{NavIC}\left(t\right)=r^{NavIC}\left(t\right)+{\delta }_r^{GPS}\left(t\right)·c-{\delta }_t^{NavIC}\left(t\right)·c+{ISB}_{GPS}^{NavIC}+e_m\left(t\right)$$

(19)

where $P^{sys}\left(t\right)$ is the ionosphere-free pseudo-range for constellation sys, $r^{sys}\left(t\right)$ is the geometric distance between satellite and receiver antenna phase centers, ${\delta }_r^{GPS}\left(t\right)$ is the receiver clock bias relative to GPS time, ${\delta }_t^{sys}\left(t\right)$ is the satellite clock bias, and ${ISB}_{GPS}^{sys}$ is the inter-system bias between GPS and the specified constellation. This inter-system bias term captures the combined effects of (i) time reference differences among GNSS constellations, (ii) inconsistencies in clock datums distributed by different analysis center products, and (iii) receiver-specific hardware delays that arise when signals from multiple systems are processed simultaneously. Such biases are particularly significant in multi-GNSS positioning, where measurements from constellations such as GPS, BeiDou, GLONASS, and Galileo are integrated into a common solution. Although GLONASS employs a frequency division multiple access (FDMA) scheme, unlike the code division multiple access (CDMA) techniques used by most other GNSS, which introduces an additional inter-frequency bias in pseudo-range measurements, this specific effect is not modeled here because the present work is confined to simulation-based analysis. It is also noteworthy that QZSS is excluded from explicit inter-system bias modeling owing to its interoperability with GPS and its use of the same time reference. Consequently, no additional inter-system time offset is required when QZSS measurements are incorporated into a multi-GNSS solution, and its pseudo-ranges can be used directly alongside those from GPS without separate bias compensation.

2.4. 3D Urban Canyon Environment Modelling

To evaluate multi-GNSS positioning under realistic and challenging conditions, we constructed a simulated three-dimensional (3D) urban canyon environment. The test area is located near Gangnam Underground Station in Seoul, South Korea, specifically along the narrow streets of Secho-daero-gil. This district, characterized by densely built infrastructure, typifies an urban canyon. Specifically, high-rise buildings and confined roadways frequently block signals and generate severe multipath, both of which degrade GNSS performance. Building geometries were extracted from OpenStreetMap, which provides public geospatial data on footprints, estimated heights, usage types, and, where available, building materials. These data were parsed and processed to create a structured representation of the urban layout. Figure 5a shows the distribution of building heights in the study zone, offering a clear picture of urban density and elevation variability. To capture local changes in ground height, terrain data from the GMTED2010 global elevation model were incorporated. By combining building and terrain information, we rendered a high-fidelity 3D urban canyon model (Figure 5b). This model accurately reproduces potential signal blockages and propagation effects. A user equipment (UE) route was then designed to traverse streets with dense building coverage, enabling a comprehensive assessment of multi-GNSS positioning under degraded signal conditions.

3. Numerical Results

This section presents simulation results that evaluate the positioning performance of multi-GNSSs in a realistic urban canyon environment. A dedicated simulator was developed to emulate signal propagation characteristics, specifically LOS, NLOS, and signal blockages, as experienced by a UE device navigating through a densely built-up area. Figure 6 illustrates both the simulation environment and the system state during operation. The left panel of Figure 6 shows a top-down view of the simulated 3D urban canyon model introduced in Section 2.4 and depicted earlier in Figure 5b. The predefined UE trajectory appears as a blue dashed line, and the UE’s current location is marked by a blue dot. This visualization facilitates assessment of the UE’s movement relative to surrounding structures and helps evaluate signal availability along the route. The right panel of Figure 6 displays the real-time visibility status of GPS satellites: satellites with a direct LOS to the receiver are shown in green, those affected by multipath propagation appear in red, and satellites obstructed by buildings are rendered in grey. This dynamic visibility model enables the simulator to account for urban-induced signal degradation with high fidelity.

The UE’s position is estimated at a temporal resolution of 1 ms, enabling fine-grained analysis of positioning performance throughout the entire movement trajectory. To comprehensively evaluate the effectiveness of different GNSS and RNSS configurations, the simulator assesses five hybrid systems: GPS combined individually with BeiDou, GLONASS, Galileo, QZSS, and NavIC. This study deliberately limits the analysis to dual constellation pairings, GPS plus one additional GNSS or RNSS, rather than integrating multiple systems simultaneously. This decision is motivated by both practical and strategic considerations. Although incorporating more than two constellations can enhance positioning accuracy and availability, it also introduces substantial challenges, including increased inter-system biases, greater receiver complexity, higher power consumption, and a heavier computational burden. These constraints are particularly relevant for low-power or size-constrained applications, such as pedestrian or UAV platforms. Moreover, in environments characterized by severe signal obstruction, excessive redundancy may yield diminishing returns. This analysis also anticipates the future deployment of the Korean Positioning System (KPS). As South Korea advances toward establishing its own RNSS, understanding the benefits and limitations of current hybrid configurations is essential for guiding KPS design and operational integration. By isolating the performance of GPS in combination with individual constellations, the study provides a clear reference framework for evaluating how KPS could contribute to improved positioning robustness and whether dual system integration remains a viable, efficient strategy for national deployment objectives.

The five hybrid configurations are evaluated across three representative use case scenarios designed to reflect practical deployment conditions relevant to urban mobility applications:

• Scenario 1 (Pedestrian): UE speed = 3 km/h; receiver height = 1.5 m, simulating handheld or wearable device usage.
• Scenario 2 (Vehicle): UE speed = 60 km/h; receiver height = 3 m, representative of typical ground transportation platforms.
• Scenario 3 (UAV): UE speed = 60 km/h; receiver height = 60 m, capturing the operational characteristics of low-altitude aerial platforms commonly employed in urban environments.

Evaluating each hybrid configuration under these scenarios allows a comprehensive assessment of positioning performance across a broad spectrum of realistic urban mobility conditions.

3.1. Performance Analysis of Scenario 1

Six hybrid GNSS positioning systems were evaluated, and their results are displayed in Figure 7. The trace for GPS + BeiDou appears in blue, GPS + GLONASS in orange, GPS + Galileo in yellow, GPS + QZSS in purple, GPS + NavIC in green, and the GPS-only baseline in brick-red. Red asterisks mark epochs when a position fix was impossible because fewer than four satellites were visible. On the horizontal axis, time stamps correspond to the UE’s progress along its route, while the vertical axis reports the instantaneous positioning error in meters.

According to the findings reported in [17], the GPS-only configuration yields mean, maximum, and minimum positioning errors of 28.3626, 32.4029, and 25.5252 m, respectively. The percentage of NaN values, which indicate instances where the UE cannot determine its location due to receiving fewer than four satellite signals, is 50.62%.

As illustrated in Figure 7, the hybrid configuration that combines GPS with BeiDou demonstrates the best overall performance. This configuration achieves a mean positioning error of 13.5387 m, a maximum error of 38.0805 m, and a minimum error of 1.0022 m. Notably, it also registers a 0% occurrence of NaN values. This outcome indicates that the GPS–BeiDou combination provides continuous and reliable positioning availability throughout the pedestrian trajectory. The superior performance of the GPS–BeiDou configuration can be attributed to several key factors, including the large number of operational BeiDou satellites, their favorable geometric distribution, and robust sky coverage over East Asia. The consistent visibility of at least four satellites ensures the avoidance of any positioning outages. This capability is particularly advantageous in complex urban environments, where satellite signal blockage and multipath effects are frequent. Interestingly, although the GPS–QZSS configuration involves fewer satellites than the GPS–BeiDou setup, it delivers comparable performance in Scenario 1. This scenario simulates a pedestrian use case in a dense urban setting characterized by severe signal obstruction caused by high-rise buildings and narrow street corridors.

The GPS–QZSS configuration yields a mean positioning error of 15.1288 m, maximum error of 44.9057 m, and minimum error of 1.0044 m, also with a 0% NaN rate. The strong performance of GPS–QZSS is largely due to the unique orbital characteristics of QZSS satellites, which operate in quasi-zenith orbits. These orbits are specifically designed to ensure that at least two QZSS satellites maintain high elevation angles over Japan and nearby regions, including South Korea. Signals from satellites at high elevation angles are less likely to be obstructed by surrounding infrastructure and are less affected by multipath propagation. As a result, the QZSS system offers more stable and reliable LOS signal reception in urban settings compared to signals from low-elevation satellites. Another contributing factor to the performance of GPS–QZSS is the high degree of interoperability between the two systems. QZSS adopts the same time reference and frequency bands (L1, L2, and L5) as GPS, eliminating the need to estimate inter-system time biases. This compatibility facilitates seamless integration into GPS-based receivers, allowing for efficient signal fusion and reduced positioning uncertainty, even in challenging urban environments.

The GPS–GLONASS and GPS–Galileo hybrid configurations show moderate performance improvements over the GPS-only baseline in Scenario 1. The percentage of epochs in which the UE fails to obtain a position fix is 0.11% for the GPS–GLONASS configuration and 6% for the GPS–Galileo configuration. The corresponding mean positioning errors are 22.9200 and 27.3505 m, respectively. In terms of positioning continuity and overall accuracy, GPS–GLONASS outperforms GPS–Galileo. This performance disparity can be primarily attributed to better satellite visibility in the GLONASS constellation when operating in urban environments. As discussed in Section 2.1, setting an elevation mask angle of 40° simulates urban signal blockage. Under these conditions, GLONASS maintains visibility of at least three satellites, whereas Galileo occasionally experiences complete satellite outages, reducing visibility to zero. These outages significantly degrade positioning performance. However, when comparing the maximum and minimum errors, GPS–Galileo demonstrates better precision than GPS–GLONASS. The maximum error for GPS–GLONASS reaches 101.0056 m, while GPS–Galileo records a significantly lower maximum of 72.9044 m. Similarly, the minimum error achieved by GPS–Galileo is 3.0983 m, marginally better than the 4.0009 m minimum for GPS–GLONASS. These results suggest that when Galileo satellites are visible, GPS–Galileo can deliver more accurate positioning than GPS–GLONASS. This advantage is due to the Galileo system’s advanced signal structure, which employs modernized CDMA signals featuring enhanced multipath mitigation and higher chipping rates. These features improve measurement precision under reflective and obstructed conditions. In contrast, GLONASS uses an FDMA-based scheme, which introduces inter-frequency biases that are more difficult to calibrate, especially in mixed constellation processing scenarios. This limitation can negatively impact the accuracy of hybrid GPS–GLONASS positioning systems.

Finally, the GPS–NavIC configuration exhibits the weakest performance among all evaluated hybrid systems. It produces a mean positioning error of 22.3996 m, a maximum error of 106.7822 m, and a minimum error of 4.0002 m. Furthermore, the percentage of epochs with failed location estimation is 34.31%, highlighting frequent positioning outages throughout the simulation. The primary cause of this degraded performance is the limited number of satellites and regional coverage area of the NavIC system, which is optimized for India and nearby regions. Over South Korea, satellite visibility is insufficient to provide meaningful support for GPS in maintaining consistent and accurate position fixes. During periods when GPS satellites alone are insufficient and no NavIC satellites are visible, the receiver is unable to compute a position fix, resulting in a high rate of unavailability. A comprehensive summary of the positioning performance across all hybrid GNSS configurations is presented in

Table 1. Positioning error comparison for Scenario 1.

System	Mean (m)	Max (m)	Min (m)	NaN (%)
GPS-Only [17]	28.3626	32.4029	25.5252	50.62
GPS + GLONASS	22.9200	101.0056	4.0009	0.11
GPS + BeiDou	13.5387	38.0805	1.0022	0
GPS + Galileo	27.3505	72.9044	3.0983	6
GPS + NavIC	22.3996	106.7822	4.0001	34.31
GPS + QZSS	15.1288	44.9057	1.0044	0

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3.2. Performance Analysis of Scenario 2

According to the results reported in [17], the GPS-only system exhibits a mean positioning error of 45.3706 m, a maximum error of 711.924 m, and a minimum error of 24.1395 m, with a NaN percentage of 47.5%. Compared to Scenario 1, the significantly higher maximum positioning error in Scenario 2 indicates a substantial degradation in performance. This decline is primarily due to the increased receiver velocity in the vehicular scenario, which amplifies the Doppler effect. As the receiver moves rapidly, the relative velocity between it and the satellites changes more dynamically, leading to frequent Doppler shifts that must be precisely tracked. Failure to compensate for these shifts can result in signal loss or degraded tracking accuracy. Additionally, high-speed movement intensifies the variability of the multipath environment. As the receiver’s surroundings change more quickly, due to moving reflective surfaces and shifting LOS conditions, the GNSS signals are more susceptible to errors. These rapidly changing conditions contribute to increased signal tracking failures and reduced pseudo-range measurement accuracy.

As shown by the red box in Figure 8, the GPS-only trajectory displays a distinctive sawtooth-like error pattern, characterized by a gradual accumulation of error followed by a sharp correction. Specifically, the positioning error increases steadily over approximately 0.3-s intervals and then drops abruptly every 0.4 s, resulting in a repeating zigzag waveform. This pattern primarily stems from the GPS data update rate used in the simulation, which is set to one update every 0.4 s. Between updates, the receiver estimates its position by extrapolating from the last known value, causing error to build up over time. When a new update becomes available at the 0.4-s mark, the receiver corrects its position using fresh satellite measurements, leading to a sudden reduction in accumulated error. This recurring cycle produces the periodic sawtooth error profile observed. In contrast, the hybrid GNSSs do not exhibit this cyclic sawtooth behavior. These systems benefit from the integration of multiple satellite constellations, which improve both temporal resolution and signal redundancy. Because different GNSSs may transmit updates at staggered intervals, the combined data stream allows for more frequent updates or smoother interpolation between them. This improved temporal granularity enhances positioning continuity and suppresses the cyclic error pattern observed in the GPS-only configuration.

As illustrated in Figure 8, the GPS–BeiDou hybrid system continues to deliver the best overall positioning performance among all evaluated configurations. It attains a mean positioning error of 12.6153 m, a maximum error of 32.3916 m, and a minimum error of 0.9063 m. Notably, the NaN percentage remains 0%, indicating uninterrupted satellite visibility along the entire vehicular trajectory. The GPS–QZSS system also performs strongly, yielding a mean error of 12.7094 m, a maximum error of 34.9568 m, and a minimum error of 0.8606 m, likewise with 0% NaN epochs. These results confirm the effectiveness of QZSS in enhancing GPS-based positioning accuracy under dynamic urban conditions. Moreover, GPS–QZSS and GPS–BeiDou exhibit consistently similar performance in both Scenario 1 and Scenario 2, each achieving sub-meter minimum errors in the vehicular scenario. This consistency reflects QZSS’s design mandate to bolster GPS performance in obstructed environments across Japan and neighboring East-Asian regions. Because QZSS signals occupy the same frequency bands (L1, L2, and L5) and share the GPS time scale, they integrate seamlessly without inter-system bias correction. The similar satellite elevation profiles of QZSS and GPS also improve geometric diversity and lower DOP, an advantage in urban canyons where LOS visibility is frequently compromised.

Similar to Scenario 1, the GPS–GLONASS hybrid shows moderate accuracy in the vehicular test. It posts a mean error of 19.5688 m, a maximum error of 101.5908 m, and a minimum error of 3.2387 m, with the NaN percentage reduced to 0%. Compared with its pedestrian scenario performance, this configuration achieves a modest decrease in mean error and eliminates outages; however, the persistently large maximum error signals a continuing vulnerability to accuracy degradation, likely rooted in GLONASS’s FDMA signal structure. Inter-frequency biases inherent to FDMA complicate calibration and can undermine accuracy when multipath or rapid Doppler shifts are present. Even so, the GLONASS constellation’s stable satellite visibility enables continuous position estimation throughout the vehicular route. The GPS–Galileo hybrid records a mean positioning error of 17.6252 m, a maximum error of 66.5682 m, and a minimum error of 2.8246 m. Despite favorable accuracy metrics, it experiences a sharp rise in positioning outages. The NaN percentage climbs to 18.75% in Scenario 2, compared with 6% in Scenario 1. This degradation in continuity is primarily attributable to the higher velocity of the UE in the vehicular scenario. At elevated speeds, Doppler shifts in the received satellite signals become more pronounced. Although modern receivers employ tracking loops that dynamically estimate and compensate for Doppler frequency variations, rapid fluctuations can still challenge the robustness of their signal-tracking algorithms, particularly when dealing with weaker or marginal Galileo signals that already operate near the receiver’s sensitivity threshold. Consequently, the receiver may intermittently lose lock on individual satellites, reducing the number of usable signals for position computation. Whenever fewer than four satellites are tracked simultaneously, the receiver cannot determine a position fix, producing NaN epochs. Additionally, as noted in Section 2.1, the Galileo constellation often provides limited visibility in the dense urban environments of South Korea relative to other GNSSs. The higher speed of the UE causes it to traverse complex urban geometries more quickly, leading to frequent and abrupt changes in propagation conditions, including sudden losses of line-of-sight and increased multipath interference, which further exacerbate signal outages. Because fewer Galileo satellites are visible and their geometry is less favorable than that of other constellations in East Asian urban corridors, any obstruction more readily translates into positioning failure. Thus, although GPS–Galileo can achieve high precision under optimal signal conditions, its susceptibility to signal loss in high-dynamics, obstructed settings curtails overall reliability.

Finally, the GPS–NavIC hybrid achieves a mean positioning error of 12.7094 m, a maximum error of 55.4447 m, and a minimum error of 4.0003 m. The share of epochs without a fix drops to 28.75%, an improvement over Scenario 1 yet still indicative of limited continuity. This outcome reflects the constrained satellite visibility of NavIC outside its core service region. Designed for India and its immediate surroundings, NavIC employs a mix of geostationary and inclined geosynchronous satellites whose geometry over East Asia is sparse. Although NavIC signals can enhance accuracy when available, their intermittent presence and limited geometric diversity in South Korea restrict overall system reliability. During intervals when GPS satellites alone are insufficient and no NavIC satellites are visible, the receiver cannot compute a fix, elevating the rate of unavailable epochs. A comprehensive statistical summary of positioning performance for all hybrid GNSS configurations in Scenario 2 is provided in

Table 2. Positioning error comparison for Scenario 2.

System	Mean (m)	Max (m)	Min (m)	NaN (%)
GPS-Only [17]	45.3706	711.9240	24.1395	47.50
GPS + GLONASS	19.5688	101.5908	3.2387	0
GPS + BeiDou	12.6153	32.3916	0.9063	0
GPS + Galileo	17.6252	66.5682	2.8246	18.75
GPS + NavIC	11.5528	55.4447	4.0003	28.75
GPS + QZSS	12.7094	34.9568	0.8606	0

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3.3. Performance Analysis of Scenario 3

As reported in [17], the GPS-only system yields a mean positioning error of 27.5489 m, maximum error of 29.3575 m, and minimum error of 24.0641 m, with a NaN percentage of 27.5%. A comparative analysis across Scenarios 1, 2, and 3 reveals a consistent trend: as the receiver’s altitude increases, the NaN percentage decreases significantly. This trend indicates that higher altitudes enhance satellite visibility and signal strength, thereby reducing the likelihood of positioning outages. Improved LOS conditions at elevated positions mitigate the impact of urban obstructions, resulting in more stable and reliable GPS performance. It is particularly noteworthy that all hybrid GNSS configurations achieve a 0% NaN percentage in Scenario 3. This means the receiver can compute its position at every epoch during the UAV’s flight. This improvement is primarily attributed to the UAV’s high-altitude operation, which greatly reduces signal blockage by buildings and other ground-level structures. At these altitudes, LOS paths to multiple satellites from various constellations are consistently maintained, ensuring uninterrupted satellite visibility and robust positioning continuity.

Consistently across scenarios, the GPS–BeiDou hybrid system delivers the strongest overall positioning performance in Scenario 3, as illustrated in Figure 9. It records the lowest mean, maximum, and minimum errors of 5.4751, 14.4933, and 0.0306 m, respectively. Remarkably, the GPS–BeiDou configuration attains centimeter-level accuracy, underscoring its exceptional capability at typical UAV altitudes. This precision arises from BeiDou’s dense satellite availability and favorable constellation geometry, which together provide strong, consistent signal reception at higher elevations. Within the geographical context of South Korea, BeiDou satellites greatly enhance satellite visibility and geometric diversity when combined with GPS, enabling both precise and reliable UAV positioning. In contrast, the GPS–QZSS system no longer matches GPS–BeiDou’s performance. It yields a mean error of 5.8097 m, a maximum of 20.5042 m, and a minimum of 0.1128 m. The gap stems from the small number of operational QZSS satellites, typically four, which limits spatial geometry. Consequently, QZSS cannot offer the same geometric diversity at higher altitudes as the much denser, globally distributed BeiDou constellation.

The GPS–Galileo hybrid shows performance comparable to GPS–QZSS in Scenario 3, with a mean error of 5.7910 m, a maximum of 18.5891 m, and a minimum of 0.3254 m. The GPS–NavIC system does not perform as accurately as the three hybrids noted above. It records a mean error of 10.5251 m, a maximum error of 28.5407 m, and a minimum error of 0.4404 m. This comparatively lower accuracy reflects NavIC’s regional design. Optimized for the Indian subcontinent, it offers fewer visible satellites and less favorable geometry over East Asia, thereby limiting its contribution to the hybrid solution. Interestingly, the GPS–GLONASS pairing exhibits the weakest performance among all hybrids in Scenario 3, posting a mean error of 15.7780 m, a maximum of 49.2561 m, and a minimum of 0.9069 m. This decline is attributable to GLONASS’s FDMA signal structure; because each satellite broadcasts on a distinct frequency, the system is more vulnerable to frequency-dependent errors, especially under high-speed, high-dynamic, and multipath-rich conditions. Greater Doppler shifts and signal reflections amplify inter-frequency biases, complicating error mitigation and ultimately degrading accuracy. A comprehensive summary of positioning performance for all hybrid GNSS configurations in Scenario 3 is provided in

Table 3. Positioning error comparison for Scenario 3.

System	Mean (m)	Max (m)	Min (m)	NaN (%)
GPS-Only [17]	27.5489	29.3575	24.0641	27.50
GPS + GLONASS	15.7780	49.2561	0.9069	0
GPS + BeiDou	5.4751	14.4933	0.0306	0
GPS + Galileo	5.7910	18.5891	0.3254	0
GPS + NavIC	10.5251	28.5407	0.4404	0
GPS + QZSS	5.8097	20.5042	0.1128	0

.

In summary, increasing the receiver height results in improved overall positioning accuracy and a significant reduction in the percentage of NaN epochs. Notably, all hybrid GNSS configurations consistently outperform the standalone GPS-only system across all evaluated scenarios, exhibiting lower positioning errors and substantially enhanced positioning availability. Among the hybrid systems, the GPS–BeiDou combination consistently provides the highest accuracy across all three scenarios. In particular, it achieves centimeter-level precision in the UAV scenario, highlighting its robustness and suitability for high-altitude applications.

4. Conclusions

This study presented a comprehensive performance evaluation of hybrid GNSS positioning systems, specifically, GPS combined with BeiDou, GLONASS, Galileo, QZSS, and NavIC, across three distinct mobility scenarios, namely, pedestrian, vehicular, and UAV. The evaluation was conducted within a realistically rendered 3D urban canyon environment based on South Korean urban landscapes. Each configuration was assessed in terms of mean, maximum, and minimum positioning errors, as well as the percentage of epochs with unavailable position fixes (NaN percentage). The results offer valuable insights into the relative accuracy and reliability of different hybrid GNSSs under diverse and challenging urban conditions.

The analysis shows that the GPS–BeiDou hybrid consistently outperforms all other configurations across all scenarios. Notably, in the UAV scenario, it achieves centimeter-level accuracy, with a mean positioning error of just 5.4751 m and no positioning outages. This exceptional performance is primarily attributed to the high satellite density and favorable geometric configuration of the BeiDou constellation, which enhance signal strength and spatial diversity at higher altitudes. The GPS–QZSS system also demonstrates strong performance, particularly in the pedestrian and vehicular scenarios. Despite comprising only four operational satellites, QZSS is specifically designed for urban environments in East Asia and maintains high interoperability with GPS through similar frequency bands and modulation schemes, allowing for effective measurement fusion and robust performance.

Overall, this study highlights the critical role of satellite geometry, regional constellation design, and system compatibility in determining hybrid GNSS positioning performance. While the findings are specific to the urban conditions of South Korea, the evaluation methodology is broadly applicable. The insights derived from this analysis may inform the design and deployment of RNSS in other countries, particularly for addressing the challenges of urban navigation and ensuring seamless integration with global GNSS infrastructures.