An INS/UWB fusion localization scheme for wireless sensor network

Tightly coupled integrated navigation system via factor graph for UAV indoor localization

This paper considers the global localization of a pedestrian via an ultra-wideband (UWB) ranging aided inertial navigation system (INS) and aims to address the challenges involved in proper processing of UWB range measurements. Even though UWB offers a decimeter level accuracy in line-of-sight (LoS) ranging, its accuracy degrades significantly in non-line-of-sight (NLoS). This drop in accuracy is due to a significant unknown positive bias in the NLOS range measurements. Therefore, the measurement models used in UWB LoS and NLoS ranging conditions are different, and proper processing of NLoS measurements requires a bias compensation measure. Previous work on bias compensation for UWB ranging that is used to aid an INS based localization assumes that the LoS and NLoS measurements are identified and distinguished from each other with absolute certainty. However, in practice, this assumption is hard to satisfy, and identifiers that determine the type of UWB range measurements deliver their results with only some level of certainty. To take into account the probabilistic nature of the NLoS identifiers, in this paper, we propose an adaptive localization based on the first-order generalized pseudo Bayesian (GPB) method to seamlessly handle the measurement model switching between LoS and NLoS UWB range measurements. The effectiveness of our proposed method is demonstrated via an experiment for pedestrian geolocation using a shoe-mounted INS system aided by UWB range measurements with respect to beacons with known locations.

High-accuracy localization systems for non-line-of-sight (NLOS) environments have been a popular focus of research on indoor positioning. In particular, the use of ultra-wideband (UWB) technology for ranging is emerging as an effective method of indoor localization due to its high accuracy. To improve the overall performance of UWB systems, combining UWB technology with an inertial navigation system (INS) is a commonly used indoor positioning approach. However, UWB measurements are affected by outliers under the NLOS propagation of radio signals. In addition, INS tend to suffer from error accumulation without constraints imposed by observations from other sensors. To address these problems, an adaptive robust extended Kalman filter algorithm based on tightly coupled UWB/INS/floor map integration is proposed, with which the noise in the UWB observations can be adaptively adjusted. The integrated system performs NLOS identification based on a map line segment matching algorithm; then, abnormal observations are abandoned, or their weights are reduced to prevent the error accumulation of the INS from being incorrectly constrained. Finally, an evaluation based on experimental data shows the significant enhancement achieved with the proposed algorithm based on the integration of UWB technology, an INS and a floor map, which can achieve a 2-D positioning accuracy that corresponds to a root mean square error of 0.27 m. Thus, substantial improvements can be achieved for long-term operation in NLOS environments using the proposed integration scheme.

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).

The escalating development of Maritime Autonomous Surface Ships (MASS) has imposed rigorous demands on the precision, continuity, and resilience of onboard integrated navigation systems. However, in complicated marine settings, data from the Global Navigation Satellite System (GNSS) and Doppler Velocity Log (DVL) are frequently corrupted by multipath effects and non-line-of-sight (NLOS) interference. These disturbances introduce anomalous observations that violate Gaussian noise assumptions, thereby severely deteriorating the robustness and estimation quality of traditional sliding-window factor graph optimization (SW-FGO). To mitigate this problem, this study introduces a novel integrated navigation strategy termed Gradient-Adaptive Factor Graph Optimization (GA-FGO). By designing a gradient-adaptive robust objective function within the factor graph structure, the proposed method dynamically re-weights constraints from the Inertial Navigation System (INS), GNSS, and DVL. This mechanism effectively attenuates the influence of measurement outliers at the optimization level. Furthermore, a unified solution framework utilizing Iterative Reweighted Least Squares (IRLS) and the Gauss–Newton method is established to simultaneously perform adaptive weight updates and state estimation. Validation based on offline field data—benchmarked against the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and standard SW-FGO. Simulation results demonstrated that the GA-FGO algorithm achieves superior positioning accuracy and estimation stability under realistic measurement conditions.

INS/UWB fusion localization algorithm in indoor environment based on variational Bayesian and error compensation

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.

Substations are critical infrastructures in modern power systems, requiring accurate and reliable personnel positioning to ensure operational safety and inspection efficiency. Pedestrian dead reckoning (PDR) technology has emerged as a preferred solution for real-time seamless positioning due to its autonomous, anti-jamming and passive characteristics. However, in practical applications, the PDR algorithm faces challenges such as the inability to provide absolute positioning due to unknown starting points and cumulative errors over time. To address these challenges, this paper proposes a head-mounted pedestrian positioning system (HPPS) integrating fisheye camera/real-time kinematic (RTK)/PDR based on factor graph optimization (FGO). First, a skyward-facing fisheye camera identifies non-line-of-sight (NLOS) signals caused by architectural obstructions, improving the absolute positioning accuracy of RTK. Next, an adaptive pedestrian gait detection and step length estimation algorithm based on head-mounted inertial measurement units (IMU) is developed to enhance PDR robustness. Finally, the FGO framework integrates the inputs of the fisheye camera, RTK, and PDR to achieve seamless indoor-outdoor positioning. Experimental results demonstrate that the proposed system achieves horizontal root mean square error (RMSE) values of less than 0.42 m and 0.35 m in two distinct outdoor substation environments and less than 1.36 m in indoor-outdoor scenarios. This work highlights the integration of precise positioning technologies within the Internet of Things (IoT) framework, advancing smart grid applications and enabling effective location tracking in complex environments.

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.

The error compensation and suppression effects of traditional ultrawideband (UWB) ranging in non Line of Sight (NLOS) environments are limited. The contribution of specific occlusions to UWB spatial perception in NLOS is ignored. To achieve comprehensive sensing of spatial information by UWB, we initially analyze the channel impulse response (CIR) and the underlying parameters of registers during UWB communication. By comparing the difference between NLOS and line-of-sight (LOS) environments for each parameter on a continuous time series, a fast discriminative method for UWB environment conversion is proposed. Further, combining the ensemble learning XGBoost classifier, an efficient NLOS occlusion recognition method is proposed. At the same time, an algorithm optimization based on a discrete degree threshold is designed. It is based on loss function probability matrix-weighted predictive labeling. The prediction matrix of the loss function of the XGBoost algorithm is used as label weights. The UWB prediction labels of continuous time series are weighted, which mitigates the effect of low-probability data on the overall prediction results. Finally, UWB spatial sensing experiments are carried out to verify the reliability of the proposed method. The experimental results show that the mutation in the parameter profile can effectively perceive the LOS/NLOS transition. The recognition accuracy of the proposed occlusion recognition method in conditions of human, metal, and wall occlusion is 94.44%, 92.00%, and 95.87%, respectively. In contrast to the origin method, the suggested algorithm’s average recognition accuracy has increased by 16.71%. Its precise recognition accuracy makes UWB spatial sensing more effective.

During the past few decades, the presence of global navigation satellite systems (GNSSs) such as GPS, GLONASS, Beidou and Galileo has facilitated positioning, navigation and timing (PNT) for various outdoor applications. With the rapid increase in the number of orbiting satellites per GNSS, enhancements in the satellite-based augmentation systems (SBASs) such as EGNOS and WAAS, as well as commissioning new GNSS constellations, the PNT capabilities are maximized to reach new frontiers. Additionally, the recent developments in precise point positioning (PPP) and real time kinematic (RTK) algorithms have provided more feasibility to carrier-phase precision positioning solutions up to the third-dimensional localization. With the rapid growth of internet of things (IoT) applications, seamless navigation becomes very crucial for numerous PNT dependent applications especially in sensitive fields such as safety and industrial applications. Throughout the years, GNSSs have maintained sufficiently acceptable performance in PNT, in RTK and PPP applications however GNSS experienced major challenges in some complicated signal environments. In many scenarios, GNSS signal suffers deterioration due to multipath fading and attenuation in densely obscured environments that comprise stout obstructions. Recently, there has been a growing demand e.g. in the autonomous-things domain in adopting reliable systems that accurately estimate position, velocity and time (PVT) observables. Such demand in many applications also facilitates the retrieval of information about the six degrees of freedom (6-DOF - x, y, z, roll, pitch, and heading) movements of the target anchors. Numerous modern applications are regarded as beneficiaries of precise PNT solutions such as the unmanned aerial vehicles (UAV), the automatic guided vehicles (AGV) and the intelligent transportation system (ITS). Hence, multi-sensor fusion technology has become very vital in seamless navigation systems owing to its complementary capabilities to GNSSs. Fusion-based positioning in multi-sensor technology comprises the use of multiple sensors measurements for further refinement in addition to the primary GNSS, which results in high precision and less erroneous localization. Inertial navigation systems (INSs) and their inertial measurement units (IMUs) are the most commonly used technologies for augmenting GNSS in multi-sensor integrated systems. In this article, we survey the most recent literature on multi-sensor GNSS technology for seamless navigation. We provide an overall perspective for the advantages, the challenges and the recent developments of the fusion-based GNSS navigation realm as well as analyze the gap between scientific advances and commercial offerings. INS/GNSS and IMU/GNSS systems have proven to be very reliable in GNSS-denied environments where satellite signal degradation is at its peak, that is why both integrated systems are very abundant in the relevant literature. In addition, the light detection and ranging (LiDAR) systems are widely adopted in the literature for its capability to provide 6-DOF to mobile vehicles and autonomous robots. LiDARs are very accurate systems however they are not suitable for low-cost positioning due to the expensive initial costs. Moreover, several other techniques from the radio frequency (RF) spectrum are utilized as multi-sensor systems such as cellular networks, WiFi, ultra-wideband (UWB) and Bluetooth. The cellular-based systems are very suitable for outdoor navigation applications while WiFi-based, UWB-based and Bluetooth-based systems are efficient in indoor positioning systems (IPS). However, to achieve reliable PVT estimations in multi-sensor GNSS navigation, optimal algorithms should be developed to mitigate the estimation errors resulting from non-line-of-sight (NLOS) GNSS situations. Examples of the most commonly used algorithms for trilateration-based positioning are Kalman filters, weighted least square (WLS), particle filters (PF) and many other hybrid algorithms by mixing one or more algorithms together. In this paper, the reviewed articles under study and comparison are presented by highlighting their motivation, the methodology of implementation, the modelling utilized and the performed experiments. Then they are assessed with respect to the published results focusing on achieved accuracy, robustness and overall implementation cost-benefits as performance metrics. Our summarizing survey assesses the most promising, highly ranked and recent articles that comprise insights into the future of GNSS technology with multi-sensor fusion technique.

At present, people spend most of their time indoors, so it is necessary to study high-precision positioning. Ultra wide band (UWB) can obtain the ranging accuracy with centimeter-level error. However, since the indoor environment is more complex than the outdoor environment, positioning errors tend to be generated during the UWB positioning due to the influence of non-line of sight (NLOS). Therefore, this paper investigates how to identify the NLOS environment and reduce the NLOS error. This paper proposes a method to determine the line of sight (LOS) environment credibility and uses it to determine the NLOS environment. The data with NLOS error is determined according to the standard deviation of the residual between the square of the predicted ranging value and the square of the measured ranging value. Then the data with NLOS error is compensated by complementary filtering. Finally, the compensated measurement data and the optimal estimation of the state at the previous moment are imported into the Kalman filter (KF) to determine the optimal estimation at the current moment.

Multisource information fusion is a major area of interest within the field of unmanned technology. In comparison with utilizing the Kalman filter (KF)-based method, the factor graph optimization (FGO)-based method has recently been proposed as an innovative approach. However, the traditional FGO-based inertial measurement unit (IMU) preintegration process is designed for low-accuracy inertial sensors, which leads to insufficient utilization of information and a decrease in positioning accuracy, in the case of tactical-grade or higher accuracy IMUs. Therefore, this article refines the process on the manifold model and utilizes the equivalent rotation vector to accumulate IMU measurements. The main contribution of our work is the refined on-manifold IMU preintegration theory and the application of the multisample algorithm based on the equivalent rotation vector for obtaining more precise preintegrated IMU measurements. The refined on-manifold IMU preintegration theory is applied based on the FGO algorithm in the global navigation satellite system (GNSS)/inertial navigation system (INS) loosely integrated navigation system. The experiments based on simulated and real-world data were conducted and demonstrate that, compared to a high-precision extended KF (EKF) algorithm and optimization methods, the proposed method achieves more accuracy in a dynamic environment.

As one of the core technologies of the Internet of Things, wireless sensor network technology is widely used in indoor localization systems. Considering that sensors can be deployed to non-line-of-sight (NLOS) environments to collect information, wireless sensor network technology is used to locate positions in complex NLOS environments to meet the growing positioning needs of people. In this paper, we propose a novel time of arrival (TOA)-based localization scheme. We regard the line-of-sight (LOS) environment and non-line-of-sight environment in wireless positioning as a Markov process with two interactive models. In the NLOS model, we propose a modified probabilistic data association (MPDA) algorithm to reduce the NLOS errors in position estimation. After the NLOS recognition, if the number of correct positions is zero continuously, it will lead to inaccurate localization. In this paper, the NLOS tracer method is proposed to solve this problem to improve the robustness of the probabilistic data association algorithm. The simulation and experimental results show that the proposed algorithm can mitigate the influence of NLOS errors and achieve a higher localization accuracy when compared with the existing methods.