Cooperative positioning enhances positioning performance but suffers significantly from unstable communication and measurement biases. To address these challenges, this work proposes a communication and measurement robust message passing (CMR-MP) method. First, we establish a multicentralized framework that decouples communication from measurement processes. Accordingly, a communication-robust factor graph is designed with constraints adapting to varying communication statuses, enabling neighbor state propagation without control information. This allows full data exploitation even when communication status changes. Second, to mitigate biases, we incorporate a general robust kernel into the Gaussian message passing process. This adaptive robust factor dynamically fits bias distributions to properly weight measurements. Experimental results demonstrate that CMR-MP outperforms state-of-the-art methods; specifically, its circular error probability is at least two times better than conventional approaches under unstable communication and mixed bias conditions.

Accurate and robust localization is critical for autonomous unmanned systems, particularly in challenging environments where conventional Global Navigation Satellite System (GNSS) integrated navigation can be highly susceptible to degeneration. This paper presents a trajectory cross-verification method for loosely coupled Visual-Inertial Navigation System (VINS)-GNSS integration system in GNSS degeneration environments. Our method does not depend on GNSS covariance or single-point measurements. Instead, it performs VINS and GNSS trajectory alignment and further cross-verification through a dual sliding window filtering algorithm. Our method decouples horizontal and vertical data, minimizing the adverse effects of invalid vertical data on the alignment and verification results. Furthermore, we propose a gravity-aware vertical verification strategy to ensure robust vertical trajectory alignment and outlier filtering. We evaluated our method both public and our real-world datasets, and compared it against both classic and state-of-the-art (SOTA) approaches. The experimental results demonstrate that our trajectory cross-verification algorithm exhibits accurate and robust localization performance in GNSS degeneration scenarios, outperforming SOTA algorithms in most datasets.

In Internet of Things (IoT)-driven vehicular networks, accurate and reliable positioning services are critical for enabling vehicle collaboration and intelligence. The integration of global navigation satellite systems (GNSSs) and ultrawideband (UWB) technologies is widely employed for cooperative positioning (CP) of vehicles in IoT applications. However, in practical CP state estimation, GNSS and UWB measurements are often affected by environmental uncertainties, such as non-line-of-sight (NLOS) conditions and multipath effects. This article proposes a novel cooperative fault-tolerant positioning scheme based on model-mixed robust Gaussian belief propagation (MMRGBP), designed for cooperative network positioning in interference environments. First, we utilize belief propagation (BP) within a factor graph model for CP estimation, deriving the messages in the message passing (MP) process in Gaussian form. Subsequently, we introduce an improved Huber M estimation model under the Gaussian BP framework, which approximates the non-Gaussian noise in the MP process as a Gaussian noise by dynamically adjusting the Huber function threshold to achieve more robust CP estimation. To address complex faulty measurements, we design an information interaction mechanism within the MP process, employing interactive multiple models for information fusion and switching the model of fault observation to prevent the introduction of serious positioning errors. Experimental results demonstrate that, compared to other advanced fault-tolerant CP methods, such as RAIM-CPKF and Huber-CPKF filters, MMRGBP exhibits superior performance in both positioning accuracy and robustness. This makes MMRGBP particularly suitable for cooperative fault-tolerant positioning networks.

Accurate position estimation is crucial for legged robots, the inertial odometry based on inertial measurement units (IMUs) is low-cost and easy to deploy, and inertial simultaneous localization and mapping (SLAM) methods can maintain stable performance on different robot platforms and degraded environments. In this paper, a single IMU is mounted on the robot foot to construct the inertial odometry without relying on kinematic modeling. The stance phase and optimal zero-velocity point (OZP) are detected through IMU outputs, and the once zero-velocity update is performed at each OZP to correct the drift of inertial odometry. Furthermore, the enhanced occupancy grid inertial SLAM framework is introduced. In the grid map update section, the motion control vectors derived from the inertial odometry are used with the Bresenham algorithm to calculate accessibility probabilities of grid cells, which addresses detail loss from grid map discretization and the imbalance in the accessibility probability resulting from repeated erroneous map updates. Experimental tests on the Unitree B1 robot demonstrate that our system provides further improvement in position estimation.

cooperative localization (CL) is a promising approach to improve the localization performance. However, many existing CL methods inadequately utilize the correlations within multiagent systems and underperform in scenarios involving nonlinear system model. To address this issue, this work proposes an unified CL (UCL) estimator for both cooperative self-localization (CSL) and cooperative relative-localization (CRL) processes. By incorporating an additional pseudo-CRL process, a consensus strategy and relative motion constraints, a novel augmented factor graph (FG) framework is designed to fully exploit the potential constraints in a multiagent system. Additionally, a novel error state message passing (ES-MP) scheme in error state domain is employed to improve the validity of linearization process when dealing with nonlinear system models, thereby further improving the estimation accuracy. The simulation and experimental results demonstrate that UCL outperforms many existing CL methods in both CSL and CRL accuracy. Moreover, UCL achieves a better performance compared to particle sampling-based methods with significant lower computational load, making it a computationally efficient choice for CL systems.

GNSS/Visual/Inertial Odometry (GVIO) has been widely applied in positioning systems for Internet of Things (IoT) applications. However, achieving robust and precise multi-sensor fusion in complex, dynamic environments remains a significant challenge, often hampered by unreliable zero-velocity detection and the inability of static robust filters to handle time-varying noise. To address these limitations, this paper proposes a Hierarchically Adaptive Robust GVIO (HAR-GVIO) framework. Our approach introduces two synergistically co-designed components. First, we propose a novel adaptive Zero Velocity Update (ZUPT) mechanism that moves beyond simple thresholding. It features a high-level adaptive fusion mechanism that dynamically arbitrates between three heterogeneous detectors based on their real-time inter-consistency, ensuring reliable ZUPT decisions even when individual sensor cues are ambiguous. Second, we propose an adaptive generalized robust filtering architecture that autonomously tunes the robust kernel’s shape according to residual distribution characteristics, enabling real-time suppression of sensor outliers. Experimental results demonstrate that this synergistic framework significantly outperforms traditional methods, offering superior estimation accuracy and robustness in environments with degraded sensor performance.

Accurate vehicle localization is crucial for urban vehicles. We propose a hybrid Gaussian variational message passing (HGVMP) scheme for cooperative relative localization. First, we propose a Gaussian variational message passing (GVMP) framework for state estimation of global navigation satellite system (GNSS) and vehicle-to-vehicle (V2V) observations from multiple vehicles, which puts the messages in GVMP in closed Gaussian form to ensure the stability and efficiency of estimation. In addition, we integrate GVMP with inertial navigation system (INS) via the extended kalman filter (EKF), which makes full use of the inertial information of INS to improve the system's localization accuracy and stability in dynamic and complex environments. Our experimental results show that in simulated GNSS signal blocked urban environment, the proposed HGVMP achieves a 32.19% improvement in localization accuracy compared to the cooperative localization extended kalman filter (CL-EKF), and the computational efficiency improves by 93.78% over the nonparametric belief propagation (NBP) method.

A belief propagation (BP) based cooperative integrity monitoring (BP-CIM) algorithm is proposed in this work. BP is widely adopted as the cooperative positioning (CP) estimator, however, the corresponding integrity problem is not solved which restricts its practical application. To guarantee the reliability of a BP-based CP system, our proposed BP-CIM can detect the faulty observations in a distributed approach. Meanwhile, error analysis for BP is performed to derive the CP estimation error bound, which is subsequently used to determine the protection level (PL) of BP-CIM. The simulation and experimental results show that BP-CIM outperforms many existing fault-tolerant CP algorithms in the sides of accuracy and robustness, and the calculated PL can provide a conservative error bound for the estimated CP states. BP-CIM framework can be further extended to many other multi-sensor CP systems to improve the system reliability.

The positioning accuracy of inertial pedestrian navigation system (IPNS) in indoor multi-story building scenarios is still unsatisfactory. In this paper, we propose an Escalator Landmark-based Occupancy Grid Inertial SLAM (EL-OGISLAM) framework, which mainly uses the pedestrian motion vectors and the associated escalator landmarks to constrain the positioning error of system. We obtain the pedestrian motion vectors from the traditional foot-mounted IMU-based PNS (Foot-PNS) and the system localization accuracy is maintained to a certain extent under the OGI-SLAM framework. Subsequently, the escalator landmarks are extracted, and the position, type, and heading angle of the escalator are considered as landmark descriptors to determine the landmark association relationship. After we use the associated landmarks to optimize the positions of all landmarks through full bundle adjustment, the trajectories between adjacent landmarks are affine transformed to achieve accurate simultaneous localization and mapping, and overall reduce the localization error. The experimental results show that the proposed system can achieve an average horizontal error of 0.74 m and an average height error of 0.11 m in the case of pedestrians walking and taking escalators.

This paper proposes a hybrid robust Gaussian belief propagation (HRGBP) as a fault-tolerant cooperative positioning (CP) system that can be used to support cooperative intelligent transportation applications. For fault-tolerant state estimation, it is well known that fault detection and exclusion (FDE) based methods and Huber’s M-estimation based methods have their own drawbacks when facing different forms of observation outliers, or faults. To solve this problem, our proposed HRGBP uses an interactive multiple model (IMM) framework to fuse these two strategies, which combines the advantages of both methods without their drawbacks. HRGBP can fully exploit the message passing process to mitigate the biased estimates, which further improves the system’s fault-tolerant robustness. HRGBP can be further adapted to fuse more fault-tolerant strategies to improve the robustness of the CP system, and be extended to other factor graph-based methods. Here, we evaluate HRGBP for observations from visual landmark range and bearing, neighboring vehicle range and bearing, and odometer. Our evaluations show that HRGBP outperforms other state-of-the-art CP methods.

Collaborative indoor positioning techniques for pedestrians have been extensively researched in the past years, particularly concerning the range-based collaborative indoor positioning system. However, range-based indoor collaboration methods suffer from nonline-of-sight (NLOS) and electromagnetic signal loss in indoor environments. Meanwhile, these methods require prior knowledge of the initial relative pose of the pedestrian, which is difficult to obtain in such an environment. To overcome the unreliable mutual observation and the lack of initial relative poses information in collaborative position systems, this article proposes a distributed collaborative inertial simultaneous localization and mapping (DCOGI-SLAM) framework for collaborative pedestrian positioning systems in unknown indoor environments without prior information. A coarse alignment method of relative poses based on encounter events is proposed to obtain the initial relative poses of pedestrians. A mutual position observation is constructed based on the map constructed through the occupancy grid-based inertial SLAM (OGI-SLAM) method to provide a stable innovation for collaborative correction of positioning errors, insulating the system from the NLOS and the loss of ranging signals. Moreover, a distributed collaborative occupancy grid-based inertial simultaneous localization and mapping (DCOGI-SLAM) framework is proposed to enable each pedestrian positioning system in a formation to operate independently. In a two-person collaborative experiment over a space of approximately 2500 m2, the proposed system can obtain comparable accuracy to single OGI-SLAM with known initial relative position information, when the initial relative position information is unknown. The average positioning error of the proposed method is 1.48 m.

Compared with simultaneous localization and mapping (SLAM) problems based on Lidar or visual sensors, range-only SLAM (RO-SLAM) is lacking bearing information. It brings challenges to particle sampling and SLAM estimation. This article proposes an efficient distributed particle filter (EDPF) for RO-SLAM problems. To overcome the difficulties of sampling in a high-dimensional state space, EDPF is decomposed into a set of subparticle filters (sub-PFs) with low dimensionality. Each sub-PF corresponds with an observed beacon, which directly reduces the sampling complexity. A joint weight update method is proposed to exploit the correlation among sub-PFs. It reweighs the particles via an auxiliary distribution after each sub-PF’s local filtering and embodies a better proposal distribution for distributed filtering. In addition, a beacon diagnosis method is proposed, it can detect and reinitialize the wrong converged beacon position estimates, which further reduces the SLAM error accumulation problem. We consider a RO-SLAM system with an odometer and ultrawideband (UWB) to verify the proposed EDPF. Results show that EDPF outperforms many existing RO-SLAM methods, which obtains the best performance with the acceptable computational load.

This letter proposes a message passing enhanced distributed Kalman filter (MP-KF) for cooperative localization (CL). By simplifying the factor graph (FG) model of the traditional belief propagation (BP) algorithm, MP-KF replaces part of the message passing (MP) process in BP with the distributed Kalman filtering. According to the analysis, the computational complexity of MP-KF is lower than that of the traditional BP estimator. The results based on the experimental data set verify the effectiveness and advantages of MP-KF, it outperforms KF-based methods by fully exploiting the correlation inside a CL system, and is better than the BP-based methods by avoiding the performance loss caused by data smoothing. Results also show that MP-KF is a cost-effective approach for CL systems with an acceptable real-time performance, which is suitable for practical CL systems.

This paper provides an adaptive hybrid robust filter (AHRF) for multi-sensor relative navigation systems that can be used to support cooperative intelligent transport systems. It is known that Huber’s M-estimation based robust filter and the fault detection and exclusion (FDE) based RAIM filter each has its own drawbacks, depending on the nature of the observation error biases. Based on the interactive multiple model (IMM) framework, our proposed AHRF in this paper can take advantage of both filters in a complementary sense. A new adaptive IMM (AIMM) algorithm with Markov transition probability prediction is proposed to allow AHRF to switch efficiently between the two filters. We consider the relative navigation system with Global Navigation Satellite System (GNSS) and ultra-wideband (UWB) as observations to verify AHRF in three cases of possible failure modes and multipath-induced errors. Our results show that AHRF outperforms both the FDE and robust filter in all cases. AHRF framework can be further adapted to include many other fault-tolerant filters to improve the robustness of multi-sensor relative navigation system even further.

A cooperative integrity monitoring (CIM) algorithm is proposed in this work. Under the CIM architecture, the algorithm can fully exploit the global navigation satellite system (GNSS) data and inter-vehicle measurements data to improve the detection and isolation of faulty measurements due to multipath or non line of sight (NLOS). Taking the advantages of cooperative scheme, a residual decomposition method is used to model the measurement errors into common and specific parts, a greedy search strategy is used to exclude the faulty measurements based on its sub-statistics. Simulation results show that CIM has better detection of GNSS fault than traditional receiver autonomous integrity monitoring (RAIM). Also, CIM is capable of detecting the faulty outliers in inter-vehicle measurements. The results indicate that CIM can be applied to many existing multi-sensor cooperative positioning algorithms.