Global Navigation Satellite System Positioning Research Articles

A Comprehensive Analysis of Factors Affecting GNSS Observation Noise

Observation noise is one of the most significant error sources in the Global Navigation Satellite System (GNSS). It can be influenced by various factors. Analyzing these factors is crucial for developing a stochastic model for GNSS navigation and positioning. This process ensures that the statistical properties of the observational data are accurately characterized, leading to more reliable and precise positioning results. Previous research has predominantly focused on code type and PPP techniques, often limited by the inability to separately assess observation types across different frequency bands due to ionospheric delay. If based on short baseline, these studies were generally constrained by limited experimental data. This study provides a detailed analysis of the affecting factor on observation noise, including elevation, SNR (signal-to-noise ratio), different receiver and antenna type, different GNSS system, and different frequency bands etc. In addition, environmental effects on observation noise are investigated by comparison between short baseline and zero baseline.

Machine learning-based modelling of zenith wet delay using terrestrial meteorological data in the Brazilian territory

Abstract. The Zenith Total Delay (ZTD) is one of the primary error sources derived from the neutral atmosphere associated with the GNSS (Global Navigation Satellite Systems) technique. Zenith Wet Delay (ZWD) is the smallest part of the ZTD, but the high variability is caused by spatial-temporal variation, making the modelling of this component a challenging task. Although ZWD is considered an error in GNSS positioning, it is also a variable composed mainly of water vapour and can, therefore, be used for atmospheric investigations, and assists in climate studies for precipitation events. In this work, a model was trained to estimate the delay wet component from surface atmospheric parameters. The training data comes from 29 radiosonde stations around Brazil, for a six-year period (2017 to 2022), with data collected at 12 h UTC (Universal Time Coordinated). The model was validated using the holdout technique, with 70% of the data used in training and 30% for validation (cross-validation analysis). The generated model achieved a RMSE (Root Mean Squared Error) of approximately 38 mm, with an 81% of determination coefficient.

A high precision 3-D tropospheric delay model over China using ERA5 data

The zenith tropospheric delay (ZTD) is an important error in Global Navigation Satellite System (GNSS) navigation and positioning. The current most empirical tropospheric delay models are two-dimensional with low spatial and temporal resolution and cannot capture high-frequent accurate ZTD variations in small areas and short periods, particularly in Mainland China with diverse climate changes and large terrain differences. In this paper, a high precision three-dimensional (3-D) tropospheric delay grid model (ZTD_3D) over China with a horizontal resolution of 0.25° × 0.25° and a time resolution of 1 hour was established with the piecewise function describing the height change of ZTD from 2016-2019 fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis data (ERA5). The performance of the proposed model is verified by using radiosonde data and ZTD products from the Crustal Movement Observation Network of China (CMONOC), as well as the global pressure and temperature models (GPT2, GPT3-1 and GPT3-5). Results show that the RMS of ZTD_3D model is 2.04 cm when compared to radiosonde observations, and the accuracy is 55.1 %, 54.7 % and 63.1 % higher than that of GPT3-1 model, GPT3-5 model and GPT2 model, respectively, while the RMS of ZTD_3D model is 3.66 cm when compared to GPS ZTD from CMONOC, and the accuracy is 1.6 % and 29.7 % higher than that of GPT3-5 mode and GPT2 model, respectively. The application of the ZTD_3D model in GNSS precise point positioning (PPP) has showed accuracy improvement in the vertical direction. The model proposed in this study can provide accurate ZTD information and a reliable tropospheric delay correction model for precise GNSS positioning.

Reduction of Multipath Effect in GNSS Positioning by Applying Pseudorange Acceleration as Weight.

A novel approach is proposed to mitigate the multipath effect that is considered a major source of error in global navigation satellite system (GNSS) positioning in urban areas. We utilize code pseudorange acceleration measurements as a weight in a least squares estimation process. If GNSS signals are reflected off a surrounding surface, they cause large variations in the recorded pseudorange measurement. Accelerations computed at each epoch with three consecutive pseudoranges exhibit significant fluctuations in a multipath signal. As a result, positioning accuracy improved by 75% horizontally and 79% vertically compared to not applying any weight. Even when multipath errors exist, the range acceleration (RA) value is sometimes low at many epochs. When a threshold value for the signal-to-noise ratio was additionally applied besides RA, the positioning accuracy at two test sites (including a deep urban environment) improved by more than 80% in both horizontal and vertical directions.

An efficient improved singular spectrum analysis for processing GNSS position time series with missing data

Summary The improved SSA (ISSA) method is widely recognized for directly extracting signals from gappy time series without requiring prior interpolation. However, it is rather time consuming, particularly for long time series with large window sizes, such as Global Navigation Satellite System (GNSS) position time series. This study proposes an efficient ISSA method that yields equivalent results to the ISSA method while significantly reducing computation time. Both methods aim to minimize the quadratic norm of principal components, while our method has fewer unknown parameters in the principal component computation than those of the ISSA method. We evaluate the performance of the proposed method using real GNSS position time series from 27 permanent stations located in mainland China. Results show that the proposed method can effectively reduce computation time than the ISSA method and the improvement depends on the chosen window size, the time series length, and the percentage of missing data. This efficient approach can be naturally extended to principal component analysis (PCA) and multi-channel SSA (MSSA) for processing multiple incomplete time series, improving computational efficiencies compared to the modified PCA and the improved MSSA while maintaining unchanged results. We also compare the ISSA method with the modified SSA (SSAM) and the iterative SSA methods using both real and synthetic time series data. Results indicate that the ISSA method outperforms the SSAM method, and when conducted iteratively, also surpasses the iterative SSA method.

GNSS/IMU/LO integration with a new LO error model and lateral constraint for navigation in urban areas

The quest for reliable vehicle navigation in urban environments has led the integration of Light Detection and Ranging (LiDAR) Odometry (LO) with Global Navigation Satellite Systems (GNSS) and Inertial Measurement Units (IMU). However, the performance of the integrated system is limited by a lack of accurate LO error modeling. In this paper, we propose a weighted GNSS/IMU/LO integration-based navigation system with a novel LO error model. The Squared Exponential Gaussian Progress Regression (SE-GPR) based LO error model is developed by considering the vehicle velocity and number of point cloud features. Based on error prediction for GNSS positioning and LO, a weighting strategy is designed for integration in an Extended Kalman Filter (EKF). Furthermore, error accumulation of the navigation state, especially in GNSS-challenging scenarios, is restrained by the LiDAR-Aided Lateral Constraint (LALC) and Non-Holonomic Constraint (NHC). An experiment was conducted in a deep urban area to test the proposed algorithm. The results show that the proposed algorithm delivers horizontal and three-dimensional (3D) positioning Root Mean Square Errors (RMSEs) of 3.669 m and 5.216 m, respectively. The corresponding accuracy improvements are 35.9% and 50.0% compared to the basic EKF based GNSS/IMU/LO integration.

A Method for Assisting GNSS/INS Integrated Navigation System during GNSS Outage Based on CNN-GRU and Factor Graph

In complex urban road environments, vehicles inevitably experience frequent or sustained interruptions of the Global Navigation Satellite System (GNSS) signal when passing through overpasses, near tall buildings, and through tunnels. This results in the reduced accuracy and robustness of the GNSS/Inertial Navigation System (INS) integrated navigation systems. To improve the performance of GNSS and INS integrated navigation systems in complex environments, particularly during GNSS outages, we propose a convolutional neural network–gated recurrent unit (CNN-GRU)-assisted factor graph hybrid navigation method. This method effectively combines the spatial feature extraction capability of CNN, the temporal dynamic processing capability of GRU, and the data fusion strength of a factor graph, thereby better addressing the impact of GNSS outages on GNSS/INS integrated navigation. When GNSS signals are strong, the factor graph algorithm integrates GNSS/INS navigation information and trains the CNN-GRU assisted prediction model using INS velocity, acceleration, angular velocity, and GNSS position increment data. During GNSS outages, the trained CNN-GRU assisted prediction model forecasts pseudo GNSS observations, which are then integrated with INS calculations to achieve integrated navigation. To validate the performance and effectiveness of the proposed method, we conducted real road tests in environments with frequent and sustained GNSS interruptions. Experimental results demonstrate that the proposed method provides higher accuracy and continuous navigation outcomes in environments with frequent and sustained GNSS interruptions, compared to traditional GNSS/INS factor graph integrated navigation methods and long short-term memory (LSTM)-assisted GNSS/INS factor graph navigation methods.

Preliminary insights on fast GNSS signal capture using SFT and FFT frequency shift

Global Navigation Satellite Systems (GNSS) are the cornerstone of modern navigation and positioning technology. In this paper, we introduce an innovative approach to GNSS signal acquisition, specifically designed to enhance the performance and speed of the signal lock-on process with real-world applications in mind. Our proposed algorithm leverages advanced mathematical tools, including Fast Fourier Transform (FFT) and Inverse FFT, to streamline the acquisition process. Notably, it eliminates the need for an Intermediate Frequency (IF) down mixer, simplifying hardware and potentially reducing power consumption in GNSS receivers. One key breakthrough is using the FFT's "circle shift" to handle Doppler frequency offsets resulting from relative satellite-receiver motion. This method significantly reduces the computational burden during Doppler frequency search, ensuring a faster and more efficient lock-on to satellite signals. Furthermore, we exploit the sparse nature of GNSS signals in the reverse FFT calculation, utilizing a Sparse Fourier Transform (SFT) for efficient processing. This innovation allows quicker reverse FFT computations, pivotal in the acquisition process. Through extensive simulations, we demonstrate the superior performance of our improved algorithm. Its speed and reliability make it well-suited for many practical GNSS applications, such as vehicle navigation, precision agriculture, surveying, and geolocation services. By enhancing acquisition efficiency, our approach contributes to more accurate, responsive, and energy-efficient GNSS positioning, benefiting users in both civilian and industrial sectors.

A Hybrid Algorithm of LSTM and Factor Graph for Improving Combined GNSS/INS Positioning Accuracy during GNSS Interruptions.

In urban road environments, global navigation satellite system (GNSS) signals may be interrupted due to occlusion by buildings and obstacles, resulting in reduced accuracy and discontinuity of combined GNSS/inertial navigation system (INS) positioning. Improving the accuracy and robustness of combined GNSS/INS positioning systems for land vehicles in the presence of GNSS interruptions is a challenging task. The main objective of this paper is to develop a method for predicting GNSS information during GNSS outages based on a long short-term memory (LSTM) neural network to assist in factor graph-based combined GNSS/INS localization, which can provide a reliable combined localization solution during GNSS signal outages. In an environment with good GNSS signals, a factor graph fusion algorithm is used for data fusion of the combined positioning system, and an LSTM neural network prediction model is trained, and model parameters are determined using the INS velocity, inertial measurement unit (IMU) output, and GNSS position incremental data. In an environment with interrupted GNSS signals, the LSTM model is used to predict the GNSS positional increments and generate the pseudo-GNSS information and the solved results of INS for combined localization. In order to verify the performance and effectiveness of the proposed method, we conducted real-world road test experiments on land vehicles installed with GNSS receivers and inertial sensors. The experimental results show that, compared with the traditional combined GNSS/INS factor graph localization method, the proposed method can provide more accurate and robust localization results even in environments with frequent GNSS signal loss.

The Real-Time Detection of Vertical Displacements by Low-Cost GNSS Receivers Using Precise Point Positioning.

Vertical displacements are traditionally measured with precise levelling, which is inherently time consuming. Rapid or even real-time height determination can be achieved by the Global Navigation Satellite System (GNSS). Nevertheless, the accuracy of real-time GNSS positioning is limited, and the deployment of a network of continuously operating GNSS receivers is not cost effective unless low-cost GNSS receivers are considered. In this study, we examined the use of geodetic-grade and low-cost GNSS receivers for static and real-time GNSS levelling, respectively. The results of static GNSS levelling were processed in four different software programs or services. The largest differences for ellipsoidal/normal heights reached 0.054 m/0.055 m, 0.046 m/0.047 m, and 0.058 m/0.058 m for points WRO1, BM_ROOF, and BM_CP, respectively. In addition, the values depended on the software used and the location of the point. However, the multistage experiment was designed to analyze various strategies for GNSS data processing and to define a method for detecting vertical displacement in a time series of receiver coordinates. The developed method combined time differentiation of coordinates estimated for a single GNSS receiver using the Precise Point Positioning (PPP) technique and Butterworth filtering. It demonstrated the capability of real-time detection of six out of eight displacements in the range between 20 and 55 mm at the three-sigma level. The study showed the potential of low-cost GNSS receivers for real-time displacement detection, thereby suggesting their applicability to structural health monitoring, positioning, or early warning systems.

An improved Gaussian process for filling the missing data in GNSS position time series considering the influence of adjacent stations

Due to various unavoidable reasons or gross error elimination, missing data inevitably exist in global navigation satellite system (GNSS) position time series, which may result in many analysis methods not being applicable. Typically, interpolating the missing data is a crucial preprocessing step before analyzing the time series. The conventional methods for filling missing data do not consider the influence of adjacent stations. In this work, an improved Gaussian process (GP) approach is developed to fill the missing data of GNSS time series, in which the time series of adjacent stations are applied to construct impact factors, together with a comparison of the conventional GP and the commonly used cubic spline methods. For the simulation experiments, the root mean square error (RMSE), mean absolute error (MAE) and correlation coefficient (R) are adopted to evaluate the performance of the improved GP. The results show that the filled missing data of the improved GP are closer to the true values than those of the conventional GP and cubic spline methods, regardless of the missing percentages ranging from 5 to 30%, with an interval of 5%. Specifically, the mean relative RMSE and MAE improvements for the improved GP with respect to the conventional GP are 21.2%, 21.3% and 8.3% and 12.7%, 16.2% and 11.01% for the North (N), East (E) and Up (U) components, respectively. In the real experiment, eight GNSS stations are analyzed using improved GP, together with conventional GP and a cubic spline. The results indicate that the first three principal components (PCs) of the improved GP can perverse 98.3%, 99.8% and 77.0% of the total variance for the N, E and U components, respectively. This value is obviously higher than those of the conventional GP and cubic spline. Therefore, we can conclude that the improved GP can better fill in the missing data in GNSS position time series than the conventional GP and cubic spline because of the impacts of adjacent stations.

A Low-Cost GNSS/INS integration method aided by Cascade-LSTM Pseudo-Velocity measurement for bridging GNSS outages

Global Navigation Satellite System (GNSS) and Inertial Navigation System (INS) together overcome their individual shortcomings, providing accurate navigation results in GNSS/INS integrated systems. However, the entire system’s positioning accuracy deteriorates over time during GNSS outages. In this paper, a pseudo-velocity measurement predicted by a Cascade-LSTM is introduced to GNSS/INS integration to bridge GNSS outages. Specifically, the Cascade-LSTM neural network, which is sensitive to angular features and suitable for processing multi-scale time series data, is proposed to predict GNSS position increments. A pseudo-velocity measurement update model for Kalman Filter (KF) is then established to incorporate these predictions into GNSS/INS integration during GNSS outages. GNSS-prohibited situation was simulated on road field data collected using a low-cost GNSS/INS integrated system to evaluate the proposed method. The comparison results demonstrate that the proposed method outperforms KF-only and the conventional pseudo-position measurement aided KF, especially in situations involving long GNSS outages and significant vehicle dynamics.

Multipath mitigation for GPS/Galileo/BDS-3 precise point positioning with overlap-frequency signals

The multipath effect is a major Global Navigation Satellite System (GNSS) error source due to its environment-dependent characteristic, which complicates its mitigation process for the high-rate determination of displacements. For instance, Sidereal Filtering (SF) and Multipath Hemispherical Map (MHM) require the observations spanning at least one full cycle of satellite orbit repeat period (e.g., ten days for Galileo navigation satellite system (Galileo) to reproduce the satellite geometry against ground stations. As a consequence, the practicability of SF and MHM is limited due to potential station-surrounding changes over a long period. In this study, we used the overlap-frequency signals on Global Positioning System (GPS) L1/L5, Galileo E1/E5a, and BeiDou-3 Navigation Satellite System (BDS-3) B1C/B2a to construct an interoperable MHM (i.e., MHM_GEC) across constellations to mitigate multipath more efficiently. We thus used 31 days of 1-Hz GPS/Galileo/BDS-3 data at 21 stations in Europe to compare this overlap-frequency MHM with those GNSS-specific MHMs (i.e., MHM_G for GPS, MHM_E for Galileo, and MHM_C for BDS-3), as well as SF. It is confirmed that the multipath effects on overlap-frequency signals are of a high spatial consistency across all GNSS. The mean reduction rate of applying MHM_GEC to GPS, Galileo, and BDS-3 carrier-phase residuals is 25%, 31%, and 28.5%, respectively, which are up to 25 percentage points higher than those of MHM_G, MHM_E, and MHM _C. Furthermore, the MHM_GEC constructed using 5 to 6 days of data can improve the positioning precision by 40%, outperforming the MHM_E, MHM_C, and SF using 10 days of data. Therefore, the interoperable MHM_GEC is more efficient in mitigating multipath effects for high-precision GNSS positioning.

Investigation of the Contribution of Five Broadcast Ionospheric Models (GPSK, NTCMG, NEQG, BDGIM, and BDSK) and IRTG to GNSS Positioning During Different Solar Activities in Solar Cycle 25

AbstractAdditional ionospheric information is essential for mitigating errors in single‐frequency (SF) Global Navigation Satellite Systems (GNSS) positioning. The increasing number of low‐cost dual‐frequency (DF) receiver users faces limitations in tracking DF observables compared to traditional geodetic receivers. Consequently, ionospheric correction algorithms (ICAs) are also essential for low‐cost DF devices in hybrid‐frequency positioning. To evaluate the performance of commonly used ICAs during solar cycle 25, our study presents a global statistical investigation of the contribution of five broadcast ionospheric models (BIMs) and the International GNSS Service (IGS) combined real‐time global ionospheric maps (IRTG) to the positioning domain, covering both quiet and perturbed ionospheric conditions. The BIMs investigated include the GPS Klobuchar (GPSK), Galileo NequickG (NEQG), NTCM‐GlAzpar (NTCMG), BDS‐2 Klobuchar (BDSK), and BeiDou Global Ionospheric delay correction Model (BDGIM). Experimental results from standard point positioning indicate that IRTG demonstrates superior overall accuracy compared to all BIMs, with a mean 3D root mean squared (RMS) of 2.76 m during perturbed period. Specifically, GPSK, NTCMG, NEQG, BDGIM, and BDSK exhibit RMS values of 2.03, 1.67, 1.72, 1.62, and 2.36 m during quiet conditions, and 4.02, 3.17, 2.86, 3.14, and 4.44 m during perturbed conditions, respectively. Among the BIMs, NEQG demonstrates superior performance at middle and high latitudes but exhibits lower accuracy than NTCMG and BDGIM at low latitudes during daytime under quiet conditions. BDGIM performs slightly better than NTCMG at low latitudes but slightly worse at high latitudes. BDSK shows notable improvement for high‐ and mid‐latitude regions since 3 June 2020.

Open Access GNSS Data for Studies of the Lithosphere

AbstractVarious types of Global Navigation Satellite System (GNSS) data are used for a wide range of applications. When modeled correctly, millimeter precision daily GNSS position time‐series yield velocities and other derived products that can be used for investigations of lithospheric processes and properties. In this review paper, we describe the specific types of GNSS data and data products that are valuable for studies of the lithosphere, such as coseismic offsets, post‐seismic decay in time‐series, seasonal signals, secular velocities, and strain rates, and how those data are derived. We also discuss the applications of several types of GNSS data and data products. We provide open access resources for precision GNSS daily position time‐series, quality secular velocity solutions, and daily GNSS RINEX files for researchers interested in processing their own data.

A survey of machine learning techniques for improving Global Navigation Satellite Systems

Global Navigation Satellite Systems (GNSS)-based positioning plays a crucial role in various applications, including navigation, transportation, logistics, mapping, and emergency services. Traditional GNSS positioning methods are model-based, utilizing satellite geometry and the known properties of satellite signals. However, model-based methods have limitations in challenging environments and often lack adaptability to uncertain noise models. This paper highlights recent advances in machine learning (ML) and its potential to address these limitations. It covers a broad range of ML methods, including supervised learning, unsupervised learning, deep learning, and hybrid approaches. The survey provides insights into positioning applications related to GNSS, such as signal analysis, anomaly detection, multi-sensor integration, prediction, and accuracy enhancement using ML. It discusses the strengths, limitations, and challenges of current ML-based approaches for GNSS positioning, providing a comprehensive overview of the field.

GNSS spoofing detection for UAVs using Doppler frequency and Carrier-to-Noise Density Ratio

Unmanned Aerial Vehicles (UAVs) are typical real-time embedded systems, which require precise locations for completing flight missions. The Global Navigation Satellite System (GNSS) plays a crucial role in navigation and positioning for UAVs. However, GNSS spoofing attacks pose an increasing threat to GNSS-dependent UAVs. Existing spoofing detection methods primarily rely on simulated data, perception data from multiple UAVs, or various control parameters. This paper proposes SigFeaDet, a signal feature-based GNSS spoofing detection approach for UAVs utilizing machine learning techniques. The core concept revolves around identifying anomalies in signal features arising from differences between authentic and spoofing signals. Key signal features, including Carrier-to-Noise Density Ratio (CN0) and Doppler frequency crucial for GNSS positioning, are employed to discern spoofing signals. Various machine learning algorithms are leveraged to train on GNSS signal data, determining the most effective classifier. TEXBAT GNSS dataset is processed to extract spoofing signal data, and flight experiments are conducted to gather GNSS data, augmenting the authentic GNSS signal dataset. The detection accuracy exceeds 95%. Equal Error Rate (EER) is approximately 5%. We evaluate various impact factors on SigFeaDet to show its robustness, including differences in velocities, altitudes, and experimental locations (10 kilometers apart), and the accuracy consistently surpasses 99%.

Comparing Discrete and Empirical Troposphere Delay Models: A Global IGS‐Based Evaluation

AbstractZenith tropospheric delay (ZTD) is an important atmospheric parameter in radio‐space‐geodetic techniques such as Global Navigation Satellite System (GNSS), which is pivotal for GNSS positioning, navigation and meteorology. The Vienna Mapping Function (VMF) data server is a widely utilized source for implementing ZTD, offering two types of models, that is, the empirical one and the discrete one with Grid‐wise and Site‐wise models. Therefore, to evaluate the accuracy of these models becomes the focus of this article. Specifically, this study investigates their performances in terms of calculation of ZTD, using the hourly values derived from the International GNSS Service data as references. The results show that the root mean square err (RMSE) of the Site‐wise, Grid‐wise and global pressure and temperature 3 model are 11.71/13.03/38.56 mm, respectively, indicating the discrete model performs generally better than the empirical model, and the Site‐wise model is the better of the two discrete models. From the perspective of spatial resolution, the performance of these three models in ZTD calculation shows obvious influences of latitude changes and elevation differences. From the temporal analysis, the accuracy of the discrete model shows differences over different UTC epochs, while the empirical model can only express the seasonal ZTD characteristics with the average RMSE at different epochs being similar, the specifically values are 39.67, 39.26, 39.38 and 39.18 mm at UTC 0:00, 6:00, 12:00 and 18:00, respectively. The histogram and boxplot well indicate the accuracy differences of the three models in different seasons. Additionally, the time series of three models at different latitudes were also explored in this research. These explorations are conducive to the selection of appropriate models for calculating ZTD based on specific requirements.

Continuity of GNSS as a critical attribute for safety applications in land transport

The Global Navigation Satellite System (GNSS) is widely used for air traffic management—more than 150,000 aircraft and 5000 airports worldwide are equipped with SBAS (Satellite-based augmentation system) technology, which contributes to safer and more efficient air operations. The next challenge is to extend GNSS positioning to maritime, autonomous cars and railway control systems preserving their safety requirements. The main parameter is the integrity of the GNSS positioning, although the time for which the integrity is guaranteed, defined by continuity, the most demanding requirement for aviation applications, has not been sufficiently investigated for land transportation. The aim of this paper is to close this gap by clarifying: (1) where the requirement for GNSS continuity comes from, (2) why GNSS continuity is needed in land transport, and (3) how GNSS-based applications can be made more reliable when needed. Using a comparative analysis, the continuity requirements in aviation, rail, maritime, and road transport have been investigated showing their importance for railways and automotive control, paving the way to eventually update the current EN 50126 (RAMS) and ISO/TR 4804 standards respectively for railways and automated cars. One of the main findings, through Markov modeling, is the improvement of the Mean Time to System Failure (MTTFsys) that for the railway safety-of-life applications can be significantly increased from about 521 h up to 5 × 105 h. These results can contribute to accelerating the adoption of GNSS positioning for automated land transportation, by exploiting the extensive experience brought by the aviation sector where GNSS was introduced 20 years ago.

LEO-Enhanced GNSS/INS Tightly Coupled Integration Based on Factor Graph Optimization in the Urban Environment

Precision point positioning (PPP) utilizing the Global Navigation Satellite System (GNSS) is a traditional and widely employed technology. Its performance is susceptible to observation discontinuities and unfavorable geometric configurations. Consequently, the integration of the Inertial Navigation System (INS) and GNSS makes full use of their respective advantages and effectively mitigates the limitations of GNSS positioning. However, the GNSS/INS integration faces significant challenges in complex and harsh urban environments. In recent years, the geometry between the user and the satellite has been effectively improved with the advent of lower-orbits and faster-speed Low Earth Orbit (LEO) satellites. This enhancement provides more observation data, opening up new possibilities and opportunities for high-precision positioning. Meanwhile, in contrast to the traditional extended Kalman filter (EKF) approach, the performance of the LEO-enhanced GNSS/INS tightly coupled integration (TCI) can be significantly improved by employing the factor graph optimization (FGO) method with multiple iterations to achieve stable estimation. In this study, LEO data and the FGO method were employed to enhance the GNSS/INS TCI. To validate the effectiveness of the method, vehicle data and simulated LEO observations were subjected to thorough analysis. The results suggest that the integration of LEO data significantly enhances the positioning accuracy and convergence speed of the GNSS/INS TCI. In contrast to the FGO GNSS/INS TCI without LEO enhancement, the average enhancement effect of the LEO is 22.16%, 7.58%, and 10.13% in the north, east, and vertical directions, respectively. Furthermore, the average root mean square error (RMSE) of the LEO-enhanced FGO GNSS/INS TCI is 0.63 m, 1.21 m, and 0.85 m in the north, east, and vertical directions, respectively, representing an average improvement of 41.91%, 13.66%, and 2.52% over the traditional EKF method. Meanwhile, the simulation results demonstrate that LEO data and the FGO method effectively enhance the positioning and convergence performance of GNSS/INS TCI in GNSS-challenged environments (tall buildings, viaducts, underground tunnels, and wooded areas).