3D Mapping Aided GNSS-Based Cooperative Positioning Using Factor Graph Optimization

Global navigation satellite systems (GNSSs) applied to intelligent transport systems in urban areas suffer from multipath and non-line-of-sight (NLOS) effects due to the signal reflections from high-rise buildings, which seriously degrade the accuracy and reliability of vehicles in real-time applications. Accordingly, the integration between GNSS and inertial navigation systems (INSs) could be utilized to improve positioning performance. However, the fixed GNSS solution uncertainty of the conventional integration method cannot determine the fluctuating GNSS reliability in fast-changing urban environments. This weakness becomes solvable using a deep learning model for sensing the ambient environment intelligently, and it can be further mitigated using factor graph optimization (FGO), which is capable of generating robust solutions based on historical data. This paper mainly develops the adaptive GNSS/INS loosely coupled system on FGO, along with the fixed-gain Kalman filter (KF) and adaptive KF (AKF) being taken as comparisons. The adaptation is aided by a convolutional neural network (CNN), and the feasibility is verified using data from different grades of receivers. Compared with the integration using fixed-gain KF, the proposed adaptive FGO (AFGO) maintains the 100% positioning availability and reduces the overall 2D positioning error by up to 70% in the aspects of both root mean square error (RMSE) and standard deviation (STD).

This study evaluates the suitability of compact, lowcost Global Navigation Satellite System (GNSS) receiver module in estimating the effects of tropospheric delay on accuracy of GNSS position solution at GNSS laboratory, the University of Burdwan, West Bengal, India with geographical coordinate of 23.2545°N, 87.8467°E, −11.402 m, using compact, low-cost uBlox F9P GNSS module and high cost Leica GR 50 geodetic receiver in March 2023. GNSS observation data were logged by the two receivers for 24 hours at 1Hz dual-frequency and converted into Rinex observation files in GPS-only, GLONASS-only, and GPS+GLONASS hybrid modes. The converted Rinex observation data were uploaded to the Natural Resources of Canada (NRCan) online service to obtain the user fixed values of latitude, longitude and attitude, and the wet and dry tropospheric delay files via email. The converted Rinex observation files were post-processed using GNSS positioning analysis tool that estimate the GNSS positioning accuracy parameters namely Distance Root Mean Square (2DRMS), Circle of Error Probable (CEP), Spherical Error Probable (SEP), and Mean Radian Spherical Error (MRSE) from the users defined known fixed values of latitude, longitude and altitude. The total delay obtained from the two GNSS receivers were compared with their positioning accuracy parameters. The results showed better position solution on observation days with the least total zenith delay in all the constellations considered. The Leica GR 50 shows an average total zenith delay of 2.476 m in GPS mode, 2.486 m in GLONASS mode and 2.4680 m in GPS+GLONASS hybrid mode while the uBlox F9P shows 2.477 m in GPS mode, 2.494 m in GLONASS mode and 2.4684 m in GPS+GLONASS hybrid mode of operation. The GPS+GLONASS hybrid mode of operation reduces the total zenith delay and enhanced the position solution. Hence, there is no distinct difference between the two GNSS receivers, suggesting that compact, low-cost, GNSS receiver modules can be used for tropospheric study.

This paper explores the pervasive challenges of pedestrian positioning using smartphones in densely populated urban environments where Global Navigation Satellite System (GNSS) signals are inaccessible, for example, in indoor areas. Existing sensor-based positioning methods, such as inertial navigation systems (INS), GNSS, and visual-inertial odometry (VIO), suffer from inherent restrictions that compromise the accuracy and reliability of the positioning performance. An approach based on machine learning is proposed to address these limitations, employing the Support Vector Machine (SVM) algorithm to accurately distinguish indoor/outdoor (IO) based on the measurement of GNSS. The proposed approach in this study seamlessly incorporates 3D mapping aided (3DMA) GNSS measurements and localized estimations derived by VIO via factor graph optimization (FGO), complemented by an IO detection switch, to achieve accurate pose estimation and effectively eliminate global drift. The system's effectiveness and robustness are rigorously assessed through comprehensive extensive real-life experiments, with an average reduction of 4 meters, leading to noteworthy and statistically significant findings. Received: 1 April 2024 | Revised: 13 September 2024 | Accepted: 26 October 2024 Conflicts of Interest The authors declare that they have no conflicts of interest to this work. Data Availability Statement The source code that supports the findings of this study is openly available in 3DMAGNSSVINS-IOFGO at https://github.com/queenie-ho/3DMAGNSSVINS-IOFGO. Author Contribution Statement Hiu-Yi Ho and Hoi-Fung Ng: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing - original draft, Writing - review & editing, Visualization. Weisong Wen: Conceptualization, Resources, Writing - review & editing, Supervision, Project administration, Funding acquisition. Yanlei Gu: Resources, Writing - review & editing, Writing - review & editing. Li-Ta Hsu: Conceptualization, Resources, Writing - review & editing, Supervision, Project administration, Funding acquisition.

Global Navigation Satellite Systems (GNSS) rely on one-way signal travel time measurements from satellites to receivers. To ensure accurate ranging, GNSS must estimate and compensate for clock offsets on at least one end of the transmitter-receiver system. Consequently, clock offsets are highly correlated with GNSS-derived parameters such as station coordinates, tropospheric delay estimates, satellite radial orbit parameters, and apparent geocenter coordinates. Improper handling of clock offsets can lead to their absorption into these parameters, degrading geodetic product accuracy. Traditionally, clocks have been handled within individual techniques without being specially addressed. However, some research efforts and experimental trials have explored using VLBI to synchronize clocks for GNSS and refining clock models to reduce correlations with other estimated parameters in GNSS, thereby improving overall precision.With recent advancements, high-precision optical clocks and fiber-optic time transfer technologies provide new possibilities for enhancing clock synchronization in GNSS. Optical fiber offers a stable, interference-free medium for time and frequency transfer, eliminating atmospheric effects such as ionospheric and tropospheric delays that impact GNSS-based synchronization. Moreover, fiber-optic time transfer is inherently two-way, removing the need for external clock offset estimation. Thus, fiber-optic clock synchronization represents the most precise timing technique currently available. Establishing a common clock by connecting multiple GNSS receivers via optical fiber could significantly reduce the number of estimated clock parameters in GNSS solutions, leading to improved geodetic measurement precision and a more accurate geodetic reference frame.Despite its potential, the approach of implementing a common clock with optical fiber for GNSS receivers remains largely untested. Although optical fiber links have been successfully used in clock synchronization, their integration into GNSS receiver clocking is still in an experimental stage. Notable existing efforts include: (1) the Geodetic Observatory Wettzell, where multiple receivers are connected to a single clock via optical fiber, representing a local baseline setup, and (2) the GFZ experiment, where a receiver is linked to the ultra-stable clock of PTB, representing a regional baseline approach.This study characterizes existing fiber-optic connections among GNSS receivers to identify practical challenges and evaluate their impact on GNSS parameter estimation. We process data from receivers sharing a common clock using Bernese GNSS Software. Initially, PPP will be performed to compare GNSS-derived clock parameters across receivers sharing a common clock, verifying the effectiveness of fiber-optic clock synchronization. Following this validation, we will leverage GNSS-derived clock parameters to evaluate inter-receiver clock differences measured via optical fiber. Subsequently, we will implement a strategy in which only one receiver’s clock parameters are estimated, using fiber-measured clock differences as a priori constraints for other receivers in the PPP solution. This approach reduces the number of estimated clock parameters and serves as a preliminary test of the feasibility of a GNSS common clock framework.Future developments will focus on refining our analysis framework to enable simultaneous estimation of GNSS receivers operating under a common clock. This research contributes to the broader goal of integrating ultra-stable clocks into global GNSS networks, ultimately enhancing the stability of geodetic reference frames and improving GNSS-derived geodetic products.

Extended Kalman Filter (EKF) is extensively employed in Global Navigation Satellite System (GNSS)-based real-time orbit determination (RTOD) for microsatellites due to its low complexity. However, the performance of EKF-RTOD is markedly degraded when the microsatellite deviates from a stable Earth-pointing attitude and employs a low-cost receiver. Factor graph optimization (FGO), which addresses nonlinear problems through multiple iterations and re-linearization, has demonstrated superior accuracy and robustness compared to EKF in challenging environments such as urban canyons. In this study, we introduce a novel FGO-based RTOD (FGO-RTOD) approach, which integrates state transfer factors to establish temporal connections between state nodes across multiple epochs. Real-time processing is achieved through a sliding window mechanism combined with marginalization. This paper evaluates the performance of the proposed algorithm in a regular scenario using data from GRACE-FO-A, which maintains the Earth-pointing attitude and employs a high-performance receiver. The positioning results of GRACE-FO-A indicate that FGO-RTOD marginally outperforms EKF-RTOD in accuracy. Furthermore, the performance of FGO-RTOD is assessed in challenging scenarios using simulation data and on-orbit data from Tianping-2B microsatellite, which is not in an Earth-pointing attitude and employs a low-cost receiver. The simulation results reveal that FGO-RTOD reduces the Root Mean Square (RMS) of positioning error by 79.0% relative to EKF-RTOD and exhibits significantly enhanced smoothing. In the Tianping-2B experiments, FGO-RTOD reduces the RMS of carrier-phase ionosphere-free combination residuals from 2 cm to 1 cm relative to EKF-RTOD, alongside a substantial improvement in the ratio of valid observations. These findings underscore the effectiveness of FGO-RTOD in managing outlier measurements in challenging scenarios.

Globally referenced and accurate positioning is of great significance for the application of intelligent vehicular systems. The visual and inertial measurement unit (IMU) integrated navigation system (VINS) is widely used in many intelligent positioning-based services. However, VINS are prone to drift over time and their performance is significantly compromised in urban canyons since the numerous outlier visual features caused by moving objects and unstable illuminations. Similarly, the global navigation satellite system (GNSS) is reliable in open areas but struggles with signal obstructions and reflections in urban canyons. To exploit the complementariness of the VINS and GNSS, this paper proposed a sliding window factor graph optimization (FGO)-based GNSS/Visual/IMU/Map (GVIM) integration, which exploits the full suit raw measurements from GNSS, IMU, and visual, together with the prior lightweight map. Unlike the existing tightly-coupled GNSS/Visual/IMU integration schemes, the potential of the carrier-phase measurement is fully explored using the recently developed window carrier phase (WCP) model. To further mitigate the impacts of the GNSS outliers, a novel sliding window (SW)-based map matching model is proposed to correct the states using the lightweight OpenStreetMap (OSM). Different from conventional filtering-based map matching, the states within the sliding window are associated with the lane information from the OSM which effectively exploits the measurement redundancy provided by the factor graph model. The experiments are conducted in the urban canyons of Hong Kong, utilizing a challenging dataset characterized by poor satellite visibility and numerous visual feature outliers, to verify the performance of the proposed method.

In various practical applications, such as autonomous vehicle and unmanned aerial vehicle navigation, Global Navigation Satellite Systems (GNSSs) are commonly used for positioning. However, traditional GNSS positioning methods are often affected by disturbances due to external observational conditions. For instance, in areas with dense buildings, tree cover, or tunnels, GNSS signals may be obstructed, resulting in positioning failures or decreased accuracy. Therefore, improving the accuracy and stability of GNSS positioning in these complex environments is a critical concern. In this paper, we propose a novel multi-sensor fusion framework based on multi-frame residual optimization for GNSS/INS/LiDAR to address the challenges posed by complex satellite environments. Our system employs a novel residual detection and optimization method for continuous-time GNSS within keyframes. Specifically, we use rough pose measurements from LiDAR to extract keyframes for the global system. Within these keyframes, the multi-frame residuals of GNSS and IMU are estimated using the Median Absolute Deviation (MAD) and subsequently employed for the degradation detection and sliding window optimization of the GNSS. Building on this, we employ a two-stage factor graph optimization strategy, significantly improving positioning accuracy, especially in environments with limited GNSS signals. To validate the effectiveness of our approach, we assess the system’s performance on the publicly available UrbanLoco dataset and conduct experiments in real-world environments. The results demonstrate that our system can achieve continuous decimeter-level positioning accuracy in these complex environments, outperforming other related frameworks.

Multi-sensor fusion and precise point positioning real-time kinematic (PPP-RTK) techniques are gaining popularity in vehicle navigation studies. The integration of the Global Navigation Satellite System (GNSS), inertial navigation system (INS), and vision can significantly improve the accuracy and continuity of positioning. The methods used to integrate different measurements are usually divided into an extended Kalman filter and factor graph optimization (FGO). We propose an integration method of PPP-RTK/INS/Vision that utilizes both the square-root information filter (SRIF) and FGO, combining the merits of the two algorithms. The proposed PPP-RTK/INS/Vision integration consists of two parts: the first is reweighted PPP-RTK/INS tightly coupled integration based on SRIF, and the second is GNSS/INS/Vision integration based on a two-step FGO method with feature selection in the vision component. The first positioning result is integrated with the FGO-based visual INS with uniform depth distribution to generate the final navigation information. The real-world experiment, carried out in an urban area, includes many GNSS-challenged environments, such as high buildings, tunnels, and viaducts. The results demonstrate that the proposed method achieves a root mean square of 0.57, 0.65, and 0.86 m in the north, east, and down components of the entire trajectory, respectively. Compared to the PPP-RTK/INS/Vision tightly coupled integration with a multi-state constrained Kalman filter, it shows an 11.0% improvement in vertical accuracy and comparable horizontal accuracy. Moreover, in the GNSS-challenged environment, the performance of the proposed method is more outstanding in the vertical component, with an improvement of 83.0% in the vertical direction and similar horizontal accuracy. Our study provides a novel approach to integrating both measurements and optimal estimation methods.

In urban environments, cooperative positioning (CP) based on Global Navigation Satellite Systems (GNSS), inter-vehicle communication and integrated sensing and communication (ISAC) experiences non-line-of-sight (NLOS) receptions and multipath delays, limiting positioning reliability for safety-related applications. This paper proposes a factor graph optimization (FGO) method that integrates GNSS pseudorange, Doppler, and ultra-wideband (UWB) ranging in a distributed framework. The truncated least squares (TLS) cost is adopted to mitigate outliers, and a graduated non-convexity (GNC) strategy is further employed to address the local optimum issue arising from the non-convexity of the TLS cost. The experimental results demonstrate that, compared with traditional fault detection and exclusion (FDE) based CP method, the proposed approach reduces the mean horizontal positioning error from 1.76 m to 0.89 m.

The availability of global navigation satellite systems (GNSS) on consumer devices has caused a dramatic change in every-day life and human behaviour globally. Although GNSS generally performs well outdoors, unavailability, intentional and unintentional threats, and reliability issues still remain. This has motivated the deployment of other complementary sensors in such a way that enables reliable positioning, even in GNSS-challenged environments. Besides sensor integration on a single platform to remedy the lack of GNSS, data sharing between platforms, such as in collaborative positioning, offers further performance improvements for positioning. An essential element of this approach is the availability of internode measurements, which brings in the strength of a geometric network. There are many sensors that can support ranging between platforms, such as LiDAR, camera, radar, and many RF technologies, including UWB, LoRA, 5G, etc. In this paper, to demonstrate the potential of the collaborative positioning technique, we use ultra-wide band (UWB) transceivers and vision data to compensate for the unavailability of GNSS in a terrestrial vehicle urban scenario. In particular, a cooperative positioning approach exploiting both vehicle-to-infrastructure (V2I) and vehicle-to-vehicle (V2V) UWB measurements have been developed and tested in an experiment involving four cars. The results show that UWB ranging can be effectively used to determine distances between vehicles (at sub-meter level), and their relative positions, especially when vision data or a sufficient number of V2V ranges are available. The presence of NLOS observations is one of the principal factors causing a decrease in the UWB ranging performance, but modern machine learning tools have shown to be effective in partially eliminating NLOS observations. According to the obtained results, UWB V2I can achieve sub-meter level of accuracy in 2D positioning when GNSS is not available. Combining UWB V2I and GNSS as well V2V ranging may lead to similar results in cooperative positioning. Absolute cooperative positioning of a group of vehicles requires stable V2V ranging and that a certain number of vehicles in the group are provided with V2I ranging data. Results show that meter-level accuracy is achieved when at least two vehicles in the network have V2I data or reliable GNSS measurements, and usually when vehicles lack V2I data but receive V2V ranging to 2–3 vehicles. These working conditions typically ensure the robustness of the solution against undefined rotations. The integration of UWB with vision led to relative positioning results at sub-meter level of accuracy, an improvement of the absolute positioning cooperative results, and a reduction in the number of vehicles required to be provided with V2I or GNSS data to one.

Global Navigation Satellite System (GNSS)-based cooperative positioning is highly degraded in dense urban areas due to non-line-of-sight (NLOS) and multipath effects. Multiple simultaneous faulty GNSS measurements can result in traditional fault detection and exclusion (FDE) methods finding a consistent but erroneous group of satellites. This paper describes a novel distributed FDE method based on cooperative reliability message (CRM), which is suitable for cooperative positioning system in connected vehicles. The idea is to take into account not only the consistency check on raw GNSS measurements, but also the prior knowledge about the quality of GNSS measurements offered by nearby cooperators so as to improve the ability to exclude multiple GNSS faults. The line-of-sight (LOS) satellites identified by cooperators are stored in CRMs, which will be shared to the host vehicle to generate the candidates for the set of LOS satellites observed locally. Based on the candidates, a bottom-up searching strategy is designed to find the healthy satellites and isolate the faulty ones precisely. Several experiments involving four moving vehicles were conducted in dense urban areas. Results indicate the superiority of CRM-based method in excluding multiple faults over existing methods.

Smartphones typically compute position using duty-cycled Global Navigation Satellite System (GNSS) L1 code measurements and Single Point Positioning (SPP) processing with the aid of cellular and other measurements. This internal positioning solution has an accuracy of several tens to hundreds of meters in realistic environments (handheld, vehicle dashboard, suburban, urban forested, etc.). With the advent of multi-constellation, dual-frequency GNSS chips in smartphones, along with the ability to extract raw code and carrier-phase measurements, it is possible to use Precise Point Positioning (PPP) to improve positioning without any additional equipment. This research analyses GNSS measurement quality parameters from a Xiaomi MI 8 dual-frequency smartphone in varied, realistic environments. In such environments, the system suffers from frequent phase loss-of-lock leading to data gaps. The smartphone measurements have low and irregular carrier-to-noise (C/N0) density ratio and high multipath, which leads to poor or no positioning solution. These problems are addressed by implementing a prediction technique for data gaps and a C/N0-based stochastic model for assigning realistic a priori weights to the observables in the PPP processing engine. Using these conditioning techniques, there is a 64% decrease in the horizontal positioning Root Mean Square (RMS) error and 100% positioning solution availability in sub-urban environments tested. The horizontal and 3D RMS were 20 cm and 30 cm respectively in a static open-sky environment and the horizontal RMS for the realistic kinematic scenario was 7 m with the phone on the dashboard of the car, using the SwiftNav Piksi Real-Time Kinematic (RTK) solution as reference. The PPP solution, computed using the YorkU PPP engine, also had a 5–10% percentage point more availability than the RTK solution, computed using RTKLIB software, since missing measurements in the logged file cause epoch rejection and a non-continuous solution, a problem which is solved by prediction for the PPP solution. The internal unaided positioning solution of the phone obtained from the logged NMEA (The National Marine Electronics Association) file was computed using point positioning with the aid of measurements from internal sensors. The PPP solution was 80% more accurate than the internal solution which had periodic drifts due to non-continuous computation of solution.

Global navigation satellite system (GNSS) plays a crucial role in providing the globally referenced positioning for self-driving systems. Unfortunately, the numerous multipath or non-line-of-sight (NLOS) receptions (known as outlier observations) caused by the signal reflections from buildings reduce the positioning accuracy of GNSS in dense urban environments. The recently investigated factor graph- based GNSS positioning formulation simultaneously considers the historical information, which significantly increases the measurement redundancy of state estimation. Taking this advantage, this paper proposes an outlier mitigation method where the bias involved in the outliers is estimated simultaneously with the position of the receiver. Specifically, the outliers are firstly detected using a pre-trained deep learning network. Secondly, an unknown variable associated with the bias is assigned to each identified outlier measurement. Then the position of the GNSS receiver, together with the bias of outlier measurements, is estimated simultaneously via the factor graph optimization (FGO) based on the pseudorange measurements and Doppler frequency shift. Finally, the effectiveness of the proposed method is validated using a dataset collected in the urban canyon by a low-cost automobile- level GNSS receiver.

For location based services (LBS), especially when it comes to safety-critical applications, a both accurate and high-integrity position solution is essential. As part of the Ghosthunter project, in which wrong-way drivers are to be detected reliably on German highways, the accuracy of the positioning solution must be better than one lane width, i.e. less than 3 m, but the integrity of the position must also be guaranteed in order to avoid false alarms. So far, only Android smartphones have been examined in terms of the two performance parameters (accuracy and integrity) as part of this project. Since Android dominates the market for mobile devices with a share of just under 70% and iOS with a share of just under 30%, and since new application areas for precise and reliable positioning such as augmented reality (AR) or virtual reality (VR) and other safety critical applications are constantly growing, this work will examine the internal positioning solutions of both operating systems. Different iOS devices (iPhones, iPads) and some Android smartphones (including Xiaomi Mi 8) are available as test platforms. In direct comparison, the Android Location application programming interface (API) has also offered the option of directly acquiring the GNSS raw data and implementing one’s own positioning algorithms accordingly since 2016 (Banville and Diggelen, 2016), but the focus here will be on the various internal positioning modes to compare them with the internal positioning modes of iOS. Currently iOS does not offer the option of accessing the global navigation satellite system (GNSS) raw data. The Core Location API only provides positions and estimated accuracy. For iOS applications that require an exact knowledge of the position performance, this data must be used. To what extent the positions from the Core Location API fulfill integrity requirements for various applications has not been investigated yet in depth. For automotive applications, a measurement vehicle with geodetic GNSS equipment, namely Trimble NetR9 GNSS receiver with Trimble Zephyr geodetic GNSS antenna is available, which provides highly precise reference trajectories even in challenging environments. This will be used as ground-truth (GT) to analyze the positioning performance of the two operating systems under investigation. By comparing the trajectories in the kinematic case or the positions in the static case with the respective reference solution, the positioning performances (deviations, gaps, etc.) can be examined. By comparing the internally estimated accuracy and the true deviation from the reference solutions, statements can be made about the integrity of the positioning solution. On the one hand, a general statement shall be made, and on the other hand, different scenarios (shading by vegetation, urban environment, perfect open sky conditions) shall be considered separately.

In recent years, the significant growth of positioning applications has come with the development of low-cost dual frequency Global Navigation Satellite Systems (GNSS) receivers. Such receivers allow high precision positioning to be achieved. They are becoming increasingly popular for geosciences as they allow for large numbers of equipment at affordable prices. Founded in 2019, the Centipede network is a collaborative permanent GNSS network that aims to offer free real-time centimetric positioning to any user. The network is currently made up of more than 330 low-cost reference stations located mainly in France and has nearly 500 regular users. Since July 2022, the GNSS raw data acquired by the stations forming this network have been archived by the Réseau National GNSS (RENAG) scientific network data centre in order to evaluate their suitability for geosciences applications such as tectonic, sea-level monitoring, troposphere and ionosphere studies. In this study, we present a first evaluation of the use of this dataset for the retrieval of integrated water vapour content (IWV) over five months in 2022. Troposphere delays are estimated from a PPP analysis and are converted to IWV using a standard procedure. Then, the IWV are compared with those retrieved for GNSS stations from the “conventional” French permanent GNSS networks, the Réseau GNSS Permanent (RGP) and RENAG. The results of these comparisons are conclusive, with root mean square differences in the range of 0.5-2 kg/m2 and high correlations of the time series registered by nearby low-cost and geodetic-class receivers. These results confirm the high potential of low-cost GNSS networks. The development of such network is a real opportunity for geoscience applications, particularly in poorly instrumented areas.  In such areas, their contribution could be especially significant for meteorological or climatological applications for which the monitoring of water vapour by GNSS is widely used.