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Outlier-Resistant Cooperative Positioning Method Using Robust factor graph optimization

IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2025年

作者： Wang, Jianrong Zhuang, Chen Zhao, Hongbo Liu, Rongke Beihang Univ Sch Elect & Informat Engn Beijing 100101 Peoples R China Beijing Inst Control Engn Beijing 100190 Peoples R China Beihang Univ Sch Elect & Informat Engn Beijing 100191 Peoples R China

Cooperative positioning (CP) is able to improve the vehicular positioning performance by introducing the data of multiple vehicles into the position estimation. However, CP methods are vulnerable to measurement outliers in dense urban areas. The existing outlier-resistant CP methods are easy to trap in local optimum and may wrongly reject the outliers when the ratio of outliers to inliers is relatively high. To deal with this problem, a factor graph optimization (FGO) based CP method using Graduated Non-Convexity (GNC) Welsch cost is proposed in this paper. The state-of-art FGO algorithm is used to integrate multi-node and multi-epoch measurements including the Global Navigation Satellite Systems (GNSS) pseudoranges, inter-epoch baselines estimated by GNSS time-differenced carrier phase (TDCP), and inter-vehicle ranging measurements in a centralized framework. The least-square cost in traditional FGO is replaced with the GNC-based Welsch cost so as to enhance the robustness of the proposed method to any kind of outliers in our CP system. The use of GNC can reduce the risk of local optimum by gradually increasing the non-convexity of the Welsch cost. The proposed method can de-weight the outliers correctly even if a large number of outliers exist. The experimental results show the superiority of the proposed method over the existing CP methods in resisting multiple outliers.

关键词： Cooperative positioning outlier-resistant factor graph optimization graduated non-convexity Welsch cost

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A factor graph optimization Method for High-Precision IMU-Based Navigation System

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2023年 72卷 1页

作者： Lyu, Pin Wang, Bingqing Lai, Jizhou Bai, Shiyu Liu, Ming Yu, Wenbin Nanjing Univ Aeronaut & Astronaut Coll Automat Engn Nanjing 210016 Peoples R China Hubei Aerosp Technol Acad Syst Design Inst Wuhan 430048 Peoples R China

Multisensor-integrated navigation systems based on factor graph are increasingly used on indoor robots, UAVs, and other vehicles. The output information of the equipped low-cost inertial measurement unit (IMU) is usually processed by IMU preintegration techniques. As the accuracy of IMU increases, the traditional factor graph using the IMU preintegration method needs to be improved. This article proposes a factor graph optimization algorithm for a high-precision IMU-based navigation system. An improved IMU preintegration method is used in the algorithm to deal with the data from inertial sensors. Different from traditional methods, the effect of the curvature of the Earth's surface on the IMU preintegration method is taken into account. Meanwhile, the parameters affecting the accuracy of the IMU preintegration method are corrected by the estimated navigation state of the carrier;thus, a more accurate relative constraint is constructed. After that, this constraint and other measurement information are fused by the factor graph optimization algorithm. Finally, different simulation tests and field vehicle tests are carried out to validate the performance of the proposed method. The test results show that the proposed method can improve the carrier positioning accuracy by 20%-90% when using high-precision inertial sensors under different conditions.

关键词： Navigation Inertial sensors Earth optimization optimization methods Accelerometers Velocity measurement factor graph optimization high-precision inertial measurement unit (IMU) preintegration navigation sensor fusion

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A Comparative Study of factor graph optimization-Based and Extended Kalman Filter-Based PPP-B2b/INS Integrated Navigation

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REMOTE SENSING 2023年第21期15卷 5144-5144页

作者： Xin, Shiji Wang, Xiaoming Zhang, Jinglei Zhou, Kai Chen, Yufei Chinese Acad Sci Aerosp Informat Res Inst Beijing 100094 Peoples R China Univ Chinese Acad Sci Sch Elect Elect & Communicating Engn Beijing 100049 Peoples R China Univ Chinese Acad Sci Coll Resources & Environm Beijing 100049 Peoples R China

Recently, factor graph optimization (FGO)-based GNSS/INS integrated navigation has garnered widespread attention for its ability to provide more robust positioning performance in challenging environments like urban canyons, compared to traditional extended Kalman filter (EKF)-based methods. In existing GNSS/INS integrated navigation methods based on FGO, the primary approach involves combining single point positioning (SPP) or real-time kinematic (RTK) with INS by constructing factors between consecutive epochs to resist outliers and achieve robust positioning. However, the potential of a high-precision positioning system based on the FGO algorithm, combining INS and PPP-B2b and that does not rely on reference stations and network connections, has not been fully explored. In this study, we developed a loosely coupled PPP-B2b/INS model based on the EKF and FGO algorithms. Experiments in different urban road and overpass scenarios were conducted to investigate the positioning performance of the two different integration navigation algorithms using different degrades of inertial measurement units (IMUs). The results indicate that the FGO algorithm outperforms the EKF algorithm in terms of positioning with the combination of GNSS and different degrades of IMUs under various conditions. Compared to the EKF method, the application of the FGO algorithm leads to improvements in the positioning accuracy of approximately 15.8%similar to 45.9% and 19%similar to 41.3% in horizontal and vertical directions, respectively, for different experimental conditions. In scenarios with long and frequent signal obstructions, the advantages of the FGO algorithm become more evident, especially in the horizontal direction. An obvious improvement in positioning results is observed when the tactical-grade IMU is used instead of the microelectron-mechanical system (MEMS) IMU in the GNSS/INS combination, which is more evident for the FGO algorithm than for the EKF algorithm.

关键词： PPP-B2b inertial navigation systems factor graph optimization extended Kalman filter integrated navigation

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State Estimation Method for GNSS/INS/Visual Multi-sensor Fusion Based on factor graph optimization for Unmanned System

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Transactions of Nanjing University of Aeronautics and Astronautics 2024年第S01期41卷 43-51页

作者： ZHU Zekun YANG Zhong XUE Bayang ZHANG Chi YANG Xin College of Automation Engineering Nanjing University of Aeronautics and AstronauticsNanjing 211106P.R.China

With the development of unmanned driving technology,intelligent robots and drones,high-precision localization,navigation and state estimation technologies have also made great *** global navigation satellite system/inertial navigation system(GNSS/INS)integrated navigation systems can provide high-precision navigation information ***,when this system is applied to indoor or GNSS-denied environments,such as outdoor substations with strong electromagnetic interference and complex dense spaces,it is often unable to obtain high-precision GNSS positioning *** positioning and orientation errors will diverge and accumulate rapidly,which cannot meet the high-precision localization requirements in large-scale and long-distance navigation *** paper proposes a method of high-precision state estimation with fusion of GNSS/INS/Vision using a nonlinear optimizer factor graph optimization as the basis for multi-source *** the collected experimental data and simulation results,this system shows good performance in the indoor environment and the environment with partial GNSS signal loss.

关键词： state estimation multi-sensor fusion combined navigation factor graph optimization complex environments

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UAV Localization Algorithm Based on factor graph optimization in Complex Scenes

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SENSORS 2022年第15期22卷 5862-5862页

作者： Dai, Jun Liu, Songlin Hao, Xiangyang Ren, Zongbin Yang, Xiao Informat Engn Univ Inst Geospatial Informat Zhengzhou 450001 Peoples R China Zhengzhou Univ Aeronaut Sch Aerosp Engn Zhengzhou 450001 Peoples R China Dengzhou Water Conservancy Bur Dengzhou 474150 Peoples R China

With the increasingly widespread application of UAV intelligence, the need for autonomous navigation and positioning is becoming more and more important. To solve the problem that UAV cannot perform localization in complex scenes, a new multi-source fusion framework factor graph optimization algorithm is used for UAV localization state estimation in this paper, which is based on IMU/GNSS/VO multi-source sensors. Based on the factor graph model and the iSAM incremental inference algorithm, a multi-source fusion model of IMU/GNSS/VO is established, including the IMU pre-integration factor, IMU bias factor, GNSS factor, and VO factor. Mathematical simulations and validations on the EuRoC dataset show that, when the selected sliding window size is 30, the factor graph optimization (FGO) algorithm can not only meet the requirements of real time and accuracy at the same time, but it also achieves a plug-and-play function in the event of local sensor failures. Finally, compared with the traditional federated Kalman algorithm and the adaptive federated Kalman algorithm, the positioning accuracy of the FGO algorithm in this paper is improved by 1.5-2-fold, and can effectively improve autonomous navigation system robustness and flexibility in complex scenarios. Moreover, the multi-source fusion framework in this paper is a general algorithm framework that can satisfy other scenarios and other types of sensor combinations.

关键词： UAV multi-source fusion factor graph optimization robustness

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An Integrated INS/Lidar Odometry/Polarized Camera Pose Estimation via factor graph optimization for Sparse Environment

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2022年 71卷 1页

作者： Du, Tao Shi, Shuyao Zeng, Yunhao Yang, Jian Guo, Lei North China Univ Technol Sch Informat Sci & Technol Beijing 100144 Peoples R China Beihang Univ Sch Automat Sci & Elect Engn Beijing 100191 Peoples R China

For the outdoor scenes with sparse features, the performance of inertial navigation system (INS)/Lidar odometry (LO)-based simultaneous localization and mapping (SLAM) pose estimation is drastically affected by the accumulated drift error and sparse features. A polarized camera (Polcam) that can obtain the absolute yaw angle from the polarized skylight is introduced to compensate for the accumulated drift error. A yaw measurement model based on the polarized camera is derived, and it will not suffer from the sparse and GNSS-denied environment. Moreover, it is integrated with INS/LO to construct a factor graph. The factor graph that consists of INS factor, polarized camera factor, lidar odometer factor, and motion model factor is optimized by nonlinear least squares. For the sparse environmental features, a robust and effective method named correntropy-based bidirectional generalized ICP (CoBigICP) has been adopted to register the sparse point cloud data. A loosely coupled INS/LO/Polcam integration based on factor graph optimization for sparse scenes is proposed, and it is tested and validated by an open dataset and experiment in the real-world environment, respectively. Different integration modes with different register methods are compared both in the simulation and experiment. The results show that the INS/LO integration with Polcam via factor graph optimization can realize better pose estimation accuracy than without in a sparse environment.

关键词： Cameras Simultaneous localization and mapping Laser radar optimization Global navigation satellite system Pose estimation Navigation factor graph optimization multisensor fusion polarized camera pose estimation simultaneous localization and mapping (SLAM) sparse scene

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Fault Detection and Interactive Multiple Models optimization Algorithm Based on factor graph Navigation System

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REMOTE SENSING 2024年第10期16卷 1651页

作者： Wang, Shouyi Zeng, Qinghua Shao, Chen Li, Fangdong Liu, Jianye Nanjing Univ Aeronaut & Astronaut Sch Coll Automat & Control Nanjing 211106 Peoples R China Jiangsu Univ Collaborat Innovat Ctr Satellite Commun & Nav Nanjing 211106 Peoples R China

Accurate and stable positioning is significant for vehicle navigation systems, especially in complex urban environments. However, urban canyons and dynamic interference make vehicle sensors prone to disturbance, leading to vehicle positioning errors and even failures. To address these issues, an adaptive loosely coupled IMU/GNSS/LiDAR integrated navigation system based on factor graph optimization with sensor weight optimization and fault detection is proposed. First, the factor nodes and system framework are constructed based on error models of sensors, and the optimization method principle is derived. Second, the interactive multiple-model algorithm based on factor graph optimization (IMMFGO) is utilized to calculate and adjust sensor weights for global optimization, which will reduce the impact of disturbed sensors. Finally, a multi-stage fault detection, isolation, and recovery (MSFDIR) strategy is implemented based on the IMMFGO results and IMU pre-integration measurements, which can detect significant sensor faults and optimize the system structure. Vehicle experiments show that our IMMFGO method generally obtains better performance in positioning accuracy by 23.7% compared to adaptive factor graph optimization (AFGO) methods, and the MSFDIR strategy possesses the capability of fault sensor detection, which provides an essential reference for multi-source vehicle navigation systems in urban canyons.

关键词： factor graph optimization interactive multiple models vehicle navigation complex environment fault detection isolation and recovery

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Pedestrian Smartphone Navigation Based on Weighted graph factor optimization Utilizing GPS/BDS Multi-Constellation

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REMOTE SENSING 2023年第10期15卷 2506页

作者： Chen, Chen Zhu, Jianliang Bo, Yuming Chen, Yuwei Jiang, Changhui Jia, Jianxin Duan, Zhiyong Karjalainen, Mika Hyyppae, Juha Nanjing Univ Sci & Technol Sch Automat Nanjing 210094 Peoples R China Finnish Geospatial Res Inst Dept Remote Sensing & Photogrammetry FI-02150 Espoo Finland Gustave Eiffel Univ AME GEOLOC F-44340 Bouguenais France Zhengzhou Univ Sch Phys & Microelect Zhengzhou 450001 Peoples R China

Many studies have focused on the smartphone-based global navigation satellite system (GNSS) for its portability. However, complex urban environments, such as urban canyons and tunnels, can easily interfere with GNSS signal qualities. Current smartphone-based positioning technologies using the GNSS signal still pose great challenges. Since the last satellite of the BeiDou navigation system (BDS) was successfully launched on 23 June 2020, it is possible to use a low-cost Android device to realize the localization based on the BDS signals worldwide. This research focuses on smartphone-based outdoor pedestrian navigation utilizing the GPS/BDS multi-constellation system. To improve the localization accuracy, we proposed the Weighted factor graph optimization localization model (W-FGO). In this paper, firstly, we evaluate the signal qualities of the BDS via the data collected by the static experiment. Then, we structure the cost function based on the pseudo-range and the time series data for the traditional factor graph optimization (FGO). Finally, we design the weight model based on the signal quality of each satellite and the time fading factor to further improve the localization accuracy of the conventional FGO method. An Android smartphone is utilized to collect the GNSS data for the evaluation and the localization. The experiment results demonstrate the superior performance of the proposed method.

关键词： factor graph optimization weighting model GPS/BDS BDS pedestrian navigation

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A robust factor graph framework for navigation on PDR/magnetic field integration

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MEASUREMENT 2025年 245卷

作者： Li, Zehua Shang, Junna Liao, Wei Hangzhou Dianzi Univ Coll Telecommun Engn Hangzhou 310018 Peoples R China

An improved factor graph model based on Measurement Rationality is proposed in the paper, and combines PDR (Pedestrian Dead Reckoning) with magnetic vector fingerprints using this model to achieve stable indoor navigation. Initially, the existing factor graph, especially the factor graph model based on weight coefficients, is analyzed for its inherent model flaws. By introducing the definition of measurement rationality, an improved factor graph model is derived, which avoids the problems in the existing factor graph from a principled standpoint. Both in simulation experiments and field experiments, the improved factor graph model has demonstrated superior performance in terms of accuracy and anti-interference capability compared to other models.

关键词： factor graph optimization Integrated navigation PDR Magnetic fingerprints Anti-interference navigation

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Enhanced low drift LiDAR SLAM with dynamic noise using ground principal plane constraint

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MEASUREMENT 2025年 245卷

作者： Wei, Dunwen Ran, Hu Li, Ziliang Gao, Tao Univ Elect Sci & Technol China Sch Mech & Elect Engn Chengdu 611731 Peoples R China

Existing LiDAR-based simultaneous localization and mapping (SLAM) methods are susceptible to drift in the vertical direction, adversely affecting both localization accuracy and mapping quality, particularly for unmanned ground vehicles (UGVs) equipped with low vertical resolution LiDARs. We propose a LiDAR SLAM backend optimization method that leverages a factor graph with ground constraint to mitigate vertical drift. Ground landmarks are generated by evaluating the quality of ground principal plane (GPP) extracted from ground point cloud (GPC) in keyframes, and ground constraint is implemented through the matching of the GPP and ground landmarks. Additionally, we introduce a dynamic noise model to adjust the weight of ground constraint dynamically, enhancing the method's adaptability to terrain variations. Experimental results on a public dataset with a 32-line LiDAR reveal that the absolute trajectory error (ATE) of the proposed GCSLAM-B is reduced by 16.85% in translation and by 20.47% along Z-axis on average compared to LIO-SAM, thereby improving the mapping quality. Furthermore, campus experiments on our custom-built 16-line LiDAR platform demonstrate a significantly greater improvement, with a 79.65% reduction in translation of ATE and a 79.26% reduction along Z-axis. These results highlight the superior performance and robustness of our proposed method, particularly on platforms with low vertical resolution LiDARs.

关键词： LiDAR SLAM Ground constraint Vertical drift Ground principal plane factor graph optimization

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