Robust Extended Kalman Filter Research Articles

Ranging Offset Calibration and Moving Average Filter Enhanced Reliable UWB Positioning in Classic User Environments

With the rapid development of the Internet of Things (IoT), the positioning accuracy requirement of the IoT is increasing, especially for those applications without Global Navigation Satellite System (GNSS) signals. Ultra-Wideband (UWB) is treated as a high-accuracy positioning method that can be utilized in GNSS-blocked environments. However, UWB’s performance is still limited when it is applied in practical applications due to errors such as Non-Line-of-Sight (NLOS) errors, multipath errors, and systematic errors in UWB range values. To constrain the impacts of these mentioned errors on UWB positioning accuracy, this work proposes a novel UWB positioning model by introducing a UWB ranging offset calibration algorithm and a moving average filter into a robust extended Kalman filter. In such a UWB positioning model, the ranging offset calibration algorithm is employed to limit the infuence of UWB systematic errors, and the prior residual-based IGG-III weighting model is used to restrain the impacts of NLOS and multipath errors. The moving average filter is to further decrease the impact of the measuring noise on UWB positioning parameter estimation. To investigate the effectiveness of this proposed method, three sets of UWB experiments are arranged in three classic user environments. The experimental results show that (1) after applying the UWB ranging offset calibration algorithm, UWB positioning accuracies in classic environments, namely indoor condition, outdoor condition, and transition area are increased by 50.3%, 20.2%, and 46.9%, respectively; (2) the moving average filter can effectively improve the smoothness of UWB positioning results in terms of standard deviation; (3) the prior residual-based robust theory brings about 49.4% and 25.2% positioning improvements to horizontal and vertical components under poor measurement quality conditions, but such improvements are rather slight when there are good-quality measurements; and (4) after applying the ranging offset calibration algorithm and moving average filter to the robust EKF together, the elevation accuracy of UWB positioning is increased by 67.1%, 22.2%, and 50.5%, respectively, in the three classic user environments.

Ranging Offset Calibration and Moving Average Filter Enhanced Reliable UWB Positioning in Classic User Environments

With the rapid development of the Internet of Things (IoT), the positioning accuracy requirement of the IoT is increasing, especially for those applications without Global Navigation Satellite System (GNSS) signals. Ultra-Wideband (UWB) is treated as a high-accuracy positioning method that can be utilized in GNSS-blocked environments. However, UWB’s performance is still limited when it is applied in practical applications due to errors such as Non-Line-of-Sight (NLOS) errors, multipath errors, and systematic errors in UWB range values. To constrain the impacts of these mentioned errors on UWB positioning accuracy, this work proposes a novel UWB positioning model by introducing a UWB ranging offset calibration algorithm and a moving average filter into a robust extended Kalman filter. In such a UWB positioning model, the ranging offset calibration algorithm is employed to limit the infuence of UWB systematic errors, and the prior residual-based IGG-III weighting model is used to restrain the impacts of NLOS and multipath errors. The moving average filter is to further decrease the impact of the measuring noise on UWB positioning parameter estimation. To investigate the effectiveness of this proposed method, three sets of UWB experiments are arranged in three classic user environments. The experimental results show that (1) after applying the UWB ranging offset calibration algorithm, UWB positioning accuracies in classic environments, namely indoor condition, outdoor condition, and transition area are increased by 50.3%, 20.2%, and 46.9%, respectively; (2) the moving average filter can effectively improve the smoothness of UWB positioning results in terms of standard deviation; (3) the prior residual-based robust theory brings about 49.4% and 25.2% positioning improvements to horizontal and vertical components under poor measurement quality conditions, but such improvements are rather slight when there are good-quality measurements; and (4) after applying the ranging offset calibration algorithm and moving average filter to the robust EKF together, the elevation accuracy of UWB positioning is increased by 67.1%, 22.2%, and 50.5%, respectively, in the three classic user environments.

Estimation of machinery’s remaining useful life in the presence of non-Gaussian noise by using a robust extended Kalman filter

Estimation of the remaining useful life (RUL) of industrial machinery is essential for condition-based maintenance (CBM). While numerous papers have explored this issues, challenges arise as machinery often works in non-stationary conditions, particularly in harsh environments (like mining machines, wind turbines, helicopters, etc.). The data collected from such environments are affected by non-Gaussian noise, posing difficulties for traditional approaches to non-linear state estimation or prediction. The widely used extended Kalman filter (EKF) suffers from the non-Gaussian noise effect due to its recursive minimum L2-norm filtering. To address these issues, we propose a robust EKF based on the maximum correntropy criterion. This method effectively estimates the RUL of the time-varying degradation process in the presence of non-Gaussian noise, also enabling confidence interval computation for uncertainty management. The efficiency of our approach was confirmed through application to simulated and benchmark data sets, outperforming Kalman filter-based methods for both simulated and real-world scenarios.

An Adaptive Robust EKF Based on Mahalanobis Distance and Non-Holonomic Constraints for Enhancing Vehicle Positioning Accuracy

An Adaptive Robust EKF Based on Mahalanobis Distance and Non-Holonomic Constraints for Enhancing Vehicle Positioning Accuracy

Hybrid state-estimation in combined heat and electric network using SCADA and AMI measurements

State-estimation plays a vital role to monitor, observe and understand the combined heat and electric network. In this paper, a hybrid framework is presented to accurately estimate the system states of electric distribution network and heat network, using the limited non-redundant measurements obtained from supervisory control and data acquisition and advanced metering infrastructure systems. The presented hybrid framework involves two steps, namely, the state-forecasting and the state-estimation. The state-forecasting uses a deep neural network to forecast the system states at every fifteen minutes interval, while these forecasted states are further used by the hybrid estimator, which uses a robust extended Kalman filter to estimate the system states with help of both datasets corresponding to supervisory control and data acquisition and advanced metering infrastructure systems, at hourly interval. The proposed framework does not completely rely on the system model at different instants. The effectiveness of the method is validated through thorough comparisons with simulation studies carried out using the Barry Island test system, United Kingdom. Satisfactory performance is observed even with the presence of bad data in the measurements.

Pose estimation of an aerial construction robot based on motion and dynamic constraints

High accuracy pose estimation with high data rate of an aerial construction robot is the prerequisite for aerial construction robot control. A dynamic and motion constrained robust extended Kalman filter is developed for robot localization in aerial construction environment which is characterized by radio signal occlusion and few visual features. The motion constraints of the gondola are derived to estimate constrained pose of the gondola while the dynamic constraints of the gondola are introduced to inhibit spike-like data mutation when the gondola shakes back to the measurement range of the self-developed laser spot vision system. Moreover, the robust factor technique is adopted to inhibit instantaneous large outliers. The experimental results show that the pose estimation based on the dynamic and motion constrained robust extended Kalman filter achieves pose measurement of the aerial construction robot with mean position accuracy less than 0.015 m and mean attitude accuracy less than 0.003 rad.

Resilient Simultaneous Localization and Mapping Fusing Ultra Wide Band Range Measurements and Visual Odometry

In this paper we consider a Simultaneous Localization and Mapping (SLAM) problem for a moving agent using Visual Odometry (VO) while measuring the range from a set of Ultra Wide Band (UWB) antennas, deployed in unknown position in the environment. The solution approach is based on a switching observer which, under standard working conditions, for each observed UWB, uses a two dimensional Extended Kalman Filter (EKF) providing an estimate of the range and bearing of the observed UWB with respect to the agent. This information is then used in a Robust EKF algorithm which solves the SLAM problem with performances that, even before closing the loop, are comparable to the ones that a VO algorithm (namely ORB-SLAM2) would obtain only after closing the loop. Moreover, a resilient module is added to the algorithm to evaluate the reliability of the position estimate of each observed UWB. When the Visual Odometry is not available, the switching observer uses an auxiliary EKF to provide an estimate of the agent position. This makes the proposed approach robust with respect to several kinds of unmodeled disturbances, like multipath effects, and automatically adapts to sensor failures with resilience (e.g. when Visual Odometry or UWB measurements are not available).

Dual-antenna GNSS-aided robust MEMS IMU initial alignment under the earth-centered-earth-fixed frame

The micro-electro-mechanical system (MEMS), with its small size, low cost and low power, has attracted widespread attentions in recent year, and the initial alignment of the inertial measurement unit (IMU) is an indispensable step before the navigation computation. In the traditional alignment methods with only the velocity measurements, the yaw angle is subject to divergence under low dynamic scenarios, and the measurements are also susceptible to the external environments. Furthermore, the navigation frame (n frame) is usually chosen as the reference frame. Although intuitive, it is more computationally complex compared with the earth-centered-earth-fixed frame (e frame). Therefore, to improve the alignment performance and computational efficiency, a robust MEMS IMU initial alignment method with yaw assistance under the e frame is proposed. In this method, to address the issues of the yaw divergency and computational inefficiency in the traditional methods, the relationship between the yaw angle, derived from dual-antenna global navigation satellite system baseline solution, and IMU error is derived and incorporated into the state space model with e frame as the reference frame. Besides, a robust extended Kalman filtering is adopted to further improve the system’s performance of outlier resistance, whose robust factors are determined by the Institute of Geodesy and Geophysics Ⅲ model. To validate the performance of the proposed method, two field experiments with the velocity of about 0.7 m s−1 and 1.5 m s−1 was conducted, and the collected data were processed for contrastive analysis. The results show that the effectiveness of the proposed method at suppressing yaw angle divergence and improving the alignment accuracy by resisting outliers under low dynamic scenarios compared with the traditional method. Moreover, the elapsed time is reduced by about 11% when the reference frame in data processing is switched from the n frame to the e frame.

Split-KalmanNet: A Robust Model-Based Deep Learning Approach for State Estimation

Estimation of the state of a discrete-time state-space model from noisy measurements is a crucial aspect of signal processing. The extended Kalman filter (EKF) is widely used as a low-complexity solution based on a state evolution and measurement model of the state-space model. However, obtaining precise information about these models can be difficult in practice, and model mismatch greatly reduces state estimation accuracy. In this paper, we introduce Split-KalmanNet, a robust EKF algorithm that utilizes the power of deep learning for state estimation. Split-KalmanNet is inspired by the recent KalmanNet and calculates the Kalman gain using the Jacobian matrix of a measurement function and two recurrent neural networks (RNNs) with a split structure. The RNNs independently learn the covariance matrices of the prior state estimate and the innovation from data. The proposed split structure in calculating the Kalman gain allows for compensation of both state and measurement model mismatch effects. Numerical simulations show that Split-KalmanNet outperforms traditional EKF and the state-of-the-art KalmanNet algorithm in various scenarios of model mismatch.

A positioning algorithm based on improved robust extended Kalman filter with NLOS identification and mitigation

With the development of the information age and the maturity of Internet of Things technology, wireless sensor network has been widely applied in indoor localization. However, the non-line-of-sight (NLOS) propagation in complicated environment and the inherent noise of the sensor will introduce errors in the measurements, which will seriously lead to inaccurate positioning. In this paper, a novel localization scheme based on the mean reconstruction method is proposed, which reconstructs the distance measurements from all beacon nodes by taking the average twice to weaken the adverse effects of NLOS. At the same time, the noise average is re-estimated when the distance difference is not too large. Next, the robust extended Kalman filter (REKF) is used to process the reconstructed distance measurements to obtain positioning results. To make the positioning results more accurate, hypothesis test is used as NLOS identification to classify the position estimates generated from all distance combinations by least-squares. Then, the residual weighting (RWGH) method is utilized to combine the position estimates that fall into the validation region. At last, we merge the results from RWGH and REKF. The simulation and experimental results show that the proposed algorithm has high positioning accuracy and strong positioning robustness.

Vehicle state estimation using a maximum likelihood based robust adaptive extended kalman filter considering unknown white Gaussian process and measurement noise signal

The stochastic nature of noise signals affects the vehicle’s internal states and the outputs, resulting in the difficulty in estimation. The unknown or time-varying nature of noise signals if not taken into account for estimation, the results will diverge and be highly deteriorated. In this paper, a maximum likelihood principle (MLP) based adaptive robust extended kalman filter for estimating the states of the adopted non-linear vehicle model is proposed. An observability test is done for the purpose of estimation. A covariance matching (CM) based robust adaptive high forgetting factor based fault tolerant technique is also employed on the robust adaptive extended and unscented kalman filters for comparison purpose. The Robustness of the filter is analyzed by varying the parameter of the vehicle through a local sensitivity analysis. The results show that the MLP based approach to the extended kalman filter performs well in three simulations for sinusoidal steering, Double Lance Change, J-Turn, Fishhook, Slalom maneuver in comparison to robust adaptive unscented kalman filter. Friction coefficient of 0.8 (dry road) and 0.4 (wet road) is chosen for the simulation. The sideslip angle RMSE value for MLP based estimation is obtained as 2.62e-05, 4.545e-06 for Sine and DLC maneuver.

Optimized adaptive filtering for fault estimation of the dynamics of high-speed train based on robust extended Kalman filter

In this paper, an optimized adaptive robust extended Kalman filter is proposed based on random weighting factors and an improved whale optimization algorithm for fault estimation of the dynamics of high-speed trains with constant time delays, drastically changing noise and stochastic uncertainties. Robust upper bounds are proposed to improve the performance of the extended Kalman filter by decreasing the influence of the linearization error on filtering for the dynamics of high-speed trains with constant time delays, and its robustness is proven to guarantee the feasibility of the proposed upper bounds. Furthermore, considering drastically changing noise with unknown statistics, a random weighting adaptive algorithm is proposed to implement unbiased noise estimation so that the robust extended Kalman filter can still be implemented well. In addition, a differential evolution algorithm and adaptive parameter are introduced to improve the performance of the whale optimization algorithm so that the stochastic uncertainties are optimized, and the influence of the stochastic uncertainties on filtering is further decreased. The simulation results in the three conditions show that, compared with the variational Bayes adaptive iterated extended Kalman filter, using the proposed method, the position, speed and fault estimation errors are decreased by 31.8%, 33.2% and 28.3%, respectively, on average, which depends on more accurate noise estimation.

Robust extended state estimation for nonlinear complex networks with colored noise

In this article, a robust extended state Kalman filter estimation algorithm for nonlinear complex networks is designed, fully considering the state coupling and colored noise among system nodes. The innovative measurement information subtraction method at adjacent moments deals with colored noise, making it more in line to meet engineering requirements. The states information of system nodes is redundant, and the collected data are processed by the quantizer, which greatly reduces the impact of network bandwidth constraints. Based on the bounds of the dynamic change rate of the nonlinear function rather than the bounds of the procedure itself, the upper bound of the error covariance is obtained, and real-time gain optimization is realized. Finally, the rationality and accuracy of the estimator are verified by simulation. According to the control variable method, the effects of the quantization density and quantization level of the quantizer on the stability of system are briefly demonstrated.

Robust Localization in Cellular Networks via Reinforced Iterative M-Estimation and Fuzzy Adaptation

We consider robust mobile location estimation using range measurements from multiple base stations under probabilistically mixed line-of-sight (LOS)/non-LOS (NLOS) conditions in a cellular network, where the NLOS statistics and occurrence probabilities (NOPs) are unknown. We develop new algorithms for achieving desirable performance under these challenging conditions. First, we propose a measurement preprocessing (MPP) scheme for dynamically bounding the NLOS influence on raw range measurements. The mobile positioning problem is cast as the state estimation of an MPP-based system model. Next, we introduce extended Kalman filter (EKF)-based reinforced robust regression and develop a gradient descent-type iterative M-estimation procedure with ensured stability, resulting in a reinforced M-estimation-based robust EKF (M-REKF). Subsequently, we present a fuzzy-tuning M-REKF (FTM-REKF) incorporating adequate fuzzy adaptation of measurement noise covariances in the M-REKF. A performance analysis provides insight into how adequate fuzzy rules can be established methodically for the FTM-REKF. Simulations demonstrate that despite varying NOPs and NLOS statistics, the FTM-REKF and M-REKF stably yield satisfactory location estimates of moving and stationary targets, with the former outperforming the latter, and they can meet the Enhanced 911 positioning requirements. Moreover, the proposed algorithms significantly outperform several salient iterative M-estimation-based EKFs, and their MPP-based counterparts.

BDS/GPS/UWB Adaptively Robust EKF Tightly Coupled Navigation Model Considering Pedestrian Motion Characteristics

In the indoor and outdoor transition area, due to its poor availability in a complex positioning environment, the BDS/GPS SPP (single-point positioning by combining BeiDou Navigation Satellite System (BDS) and Global Positioning System (GPS)) is unable to provide an effective positioning service. In view of the poor positioning accuracy and low sampling rate of the BDS/GPS SPP and the gross error, such as the non-line-of-sight error of UWB (Ultra-Wide-Band), making the accuracy of positioning results poor, a BDS/GPS/UWB tightly coupled navigation model considering pedestrian motion characteristics is proposed to make positioning results more reliable and accurate in the transition area. The core content of this paper is divided into the following three parts: (1) Firstly, the dynamic model and positioning theories of BDS/GPS SPP and UWB are introduced, respectively. (2) Secondly, the BDS/GPS/UWB tightly coupled navigation model is proposed. An environment discrimination factor is introduced to adaptively adjust the variance factor of the system state. At the same time, the gross error detection factor is constructed by using the a posteriori residuals to make the variance factor of the measurement information of the combined positioning system able to be adjusted intelligently for the purpose of eliminating the interference of gross error observations on positioning results. On the other hand, pedestrian motion characteristics are introduced to establish the constraint equation to improve the consistency of positioning accuracy. (3) Thirdly, the actual measured data are used to demonstrate and analyze the reliability of the positioning model proposed by this paper. The experimental results show that the BDS/GPS/UWB tightly coupled navigation model can effectively improve the accuracy and availability of positioning. Compared with BDS/GPS SPP, the accuracy of this model is improved by 57.8%, 76.0% and 56.5% in the E, N and U directions, respectively.

Improved-UWB/LiDAR-SLAM Tightly Coupled Positioning System with NLOS Identification Using a LiDAR Point Cloud in GNSS-Denied Environments

Reliable absolute positioning is indispensable in long-term positioning systems. Although simultaneous localization and mapping based on light detection and ranging (LiDAR-SLAM) is effective in global navigation satellite system (GNSS)-denied environments, it can provide only local positioning results, with error divergence over distance. Ultrawideband (UWB) technology is an effective alternative; however, non-line-of-sight (NLOS) propagation in complex indoor environments severely affects the precision of UWB positioning, and LiDAR-SLAM typically provides more robust results under such conditions. For robust and high-precision positioning, we propose an improved-UWB/LiDAR-SLAM tightly coupled (TC) integrated algorithm. This method is the first to combine a LiDAR point cloud map generated via LiDAR-SLAM with position information from UWB anchors to distinguish between line-of-sight (LOS) and NLOS measurements through obstacle detection and NLOS identification (NI) in real time. Additionally, to alleviate positioning error accumulation in long-term SLAM, an improved-UWB/LiDAR-SLAM TC positioning model is constructed using UWB LOS measurements and LiDAR-SLAM positioning information. Parameter solving using a robust extended Kalman filter (REKF) to suppress the effect of UWB gross errors improves the robustness and positioning performance of the integrated system. Experimental results show that the proposed NI method using the LiDAR point cloud can efficiently and accurately identify UWB NLOS errors to improve the performance of UWB ranging and positioning in real scenarios. The TC integrated method combining NI and REKF achieves better positioning effectiveness and robustness than other comparative methods and satisfactory control of sensor errors with a root-mean-square error of 0.094 m, realizing subdecimeter indoor positioning.

Multi-kernel correntropy based extended Kalman filtering for state-of-charge estimation

As a powerful tool for real-time battery management, the extended Kalman filter (EKF) can achieve an online estimation for state of charge (SOC). The EKF, however, may yield biased estimates since the measured system suffers from the abnormal operation conditions, i.e., sensor faults, sensor bias and sensor noise. Thus, this paper proposes a robust extended Kalman filter based on maximum multi-kernel correntropy (MMKC-EKF) for SOC estimate when the system is subjected to complex non-Gaussian disturbances. To derive MMKC-EKF, a batch-mode regression is formulated by integrating the uncertainties of process and measurement, which is solved by using maximum multi-kernel correntropy (MMKC) criterion to suppress the influences of abnormal conditions. An effective optimization method is introduced to determine the free parameters of MMKC, and a fixed-point iteration method gives the state estimation. Then, the posterior error covariance matrix is updated with the help of total influence function, which contributes to the robustness improvement. In addition, a novel filtering scheme is presented for reducing computational complexity, which is beneficial for solving battery pack state estimation in practice. Extensive simulations are carried out for SOC estimate to validate the accuracy and robustness of the proposed MMKC-EKF in the Gaussian and non-Gaussian distributed process and measurement noises.

A Novel NLOS Suppression Algorithm for Indoor Location based on FCM and REKF

Abstarct. The indoor positioning based on wireless sensor networks (WSN) has become one of the research hotpots. However, the NLOS propagation of the distance signals greatly challenges the accuracy and robustness of the algorithm. In this paper, we take the suppression of NLOS as the core goal and proposed the FCM-REKF-based positioning method. We firstly identify the signal states through the fuzzy c-means clustering (FCM), for the measurement distance judged to be NLOS, a refactoring method based on FCM is used. Then the corrected distance is smoothed by Kalman filter, and the Robust Extended Kalman Filter is used to calculate the final position. The simulation results show that our method has higher accuracy than EKF, REKF and IMM-EKF under NLOS environment.

Robust Extended Kalman Filtering for Systems With Measurement Outliers

Outliers can be caused by sensor errors, model uncertainties, changes in the ambient environment, data loss, or malicious cyberattacks to contaminate the measurement process of many nonlinear dynamic systems. When the extended Kalman filter (EKF) is applied to such systems for state estimation, the outliers can seriously reduce the estimation accuracy. This brief proposes an innovation saturation mechanism to make the EKF robust against outliers. This mechanism applies a saturation function to the innovation process that the EKF leverages to correct the state estimation. As such, when outliers occur, the distorted innovation is saturated, so as not to undermine the state estimation. The mechanism features an adaptive adjustment of the saturation bounds. The design leads to the development of robust EKF approaches for both continuous- and discrete-time systems. The stability of the proposed approaches when applied to linear systems is characterized, showing that they are capable of performing bounded-error estimation in the presence of bounded outlier disturbances in this case. A simulation study about mobile robot localization is presented to illustrate the efficacy of the proposed design. Compared to existing methods, the proposed approaches can effectively reject outliers of various magnitudes, types, and durations, at significant computational efficiency and without requiring additional measurement redundancy.

State Estimation and Control with a Robust Extended Kalman Filter for a Fabric Soft Robot

Soft robots have shown great potential in safe human-robot interaction. However, their compliant nature makes posture measurement and trajectory tracking a challenging task. Accurate sensing systems such as motion capture devices aren't portable enough to use in any environment, while body-integrated soft sensors create problems like hysteresis. In this work, a robust extended Kalman filter (REKF) based sensor fusion method with an accelerometer, gyroscope, and draw wire sensor is introduced to estimate the bending angle of a fabric-based inflatable bending actuator. The REKF improves upon similar estimation techniques by ensuring a robust estimate regardless of non-linearity or uncertainty in the model. Linear Quadratic Gaussian (LQG) control is integrated with the proposed REKF to demonstrate the REKF based sensor fusion method is useful in control. The results show that the REKF based sensor fusion system presents a portable, robust, accurate estimation of the actuator's bending angle.