Adaptive Robust Kalman Filter Research Articles

A modified adaptive Kalman filtering method for maneuvering target tracking of unmanned surface vehicles

The filtering methods are crucial for an unmanned surface vehicle (USV) to realize target tracking. Due to the poor observation caused by the strong vibration during the navigation of the USV, the target tracking accuracy of the traditional filtering method has been significantly degraded. A modified strong tracking-based expended Sage-Husa adaptive robust Kalman filter (MST-ESHARKF) algorithm is proposed to overcome this problem in this paper. In the proposed algorithm, a modified fading factor for the strong tracking Kalman filter is introduced to eliminate disturbance-induced filter divergence. In addition, the adaptive factor of robust Kalman filtering is designed to balance the predicted and observed states dedicated to improving the robustness of the algorithm. Finally, the biased and unbiased estimators for measurement and process noise covariances are merged, and the measurement noise covariance matrix’s interval is constrained, resulting in a simultaneous evaluation of measurement and process noise covariance matrices with improved dependability of the proposed algorithm. The simulation and experiment results show that the proposed MST-ESHARKF outperforms the existing filters in target tracking.

Improving the performance of GNSS precise point positioning by developed robust adaptive Kalman filter

Global Navigation Satellite Systems (GNSS) Precise Point Positioning (PPP) is a great precision positioning method based on GNSS. PPP based on multi-constellation GNSS uses the extended Kalman filter (EKF). Inappropriately, the measurement outliers and the system's dynamic model might produce mistakes in the positioning accuracy acquired using this method. An adaptive robust Kalman filter (RKF) was recently developed in order to alleviate these errors. In addition, the preceding variance is sometimes used to determine the weights of different categories of observations, which has an effect on PPP performance. A novel developed robust adaptive filtering (DRKF) has been developed to provide better placement results. For the equivalent weight matrix to be generated, an equivalent weight model that is statistically robust by the chi-square test for classification is constructed in this technique. According to prior Kalman filter models employing International GNSS Service (IGS) final clock and orbit products, the performance of GNSS PPP using the DRKF is confirmed in contrast to those produced using the current model. DRKF surpasses traditional robust adaptive filters in terms of positioning accuracy, convergence time, and PPP sturdiness according to the results of this study. In comparison to RKF, DRKF improves the positioning solution by 201 mm with 119.10 %, 77 mm with 164.86 %, and 160 mm with 211.74 % in the east, north, and up (ENZ) directions, respectively. It is recommended to use the newly developed robust adaptive Kalman filter in kinematic mode, especially in urban areas, due to the noticeable improvement in position accuracy.

Robust adaptive cubature Kalman filter for tracking manoeuvring target by wireless sensor network under noisy environment

Robust adaptive cubature Kalman filter for tracking manoeuvring target by wireless sensor network under noisy environment

Integrated navigation system (INS/auxiliary sensor) based on adaptive robust Kalman filter with partial measurements

Inertial navigation system (INS) is the most common positioning system in the underwater vehicle due to the limitations of penetration of the global navigation system. Amendment of INS cumulative error is made possible using data of auxiliary sensors such as Doppler velocity log (DVL). Due to the environmental conditions of the seabed, access to full DVL beams is impractical. Moreover, the statistical characteristics of measuring noise are unknown. These dramatically reduce the performance of the navigation system. Therefore, a loosely coupled (LC) approach is used to fuse partial DVL measurements in this study. This approach benefits from a virtual beam containing the velocity obtained in the last INS step instead of inaccessible DVL beams. To deal with the unknown statistical characteristics of the measurement and the limitations of access to DVL beams, an adaptive robust Kalman filter (ARKF) based on the Huber cost function is proposed. The performance of the proposed integrated navigation system for a remotely operated vehicle is investigated in the presence of observation noise and outliers. Results show that the proposed ARKF is robust against vigorous maneuvers, improves the estimation accuracy effectively, and can effectively reject measurement outliers.

Fault-tolerant SINS/HSB/DVL underwater integrated navigation system based on variational Bayesian robust adaptive Kalman filter and adaptive information sharing factor

To solve the problem that position information obtained by SINS/DVL integrated navigation system is divergent in the underwater navigation applications, this paper introduces hydroacoustic single beacon (HSB) into the underwater integrated system and proposes a novel SINS/HSB/DVL fault-tolerant federated variational Bayesian robust adaptive Kalman filter (FVBRAKF). In the FVBRAKF, the traditional KF is replaced by VBRAKF, which not only suppress the adverse influence of outliers based on Mahalanobis distance (MD) effectively, but also estimate the unknown measurement noise covariance based on variational Bayesian (VB) approximation adaptively. Meanwhile, a novel adaptive information sharing factor (ISF) method is proposed during the information fusion process to form an improved FVBRAKF（IFVBRAKF）, which can adjust the fusion weights in real-time according to the accuracy of local filter. The semi-physical simulation experiments for SINS/HSB/DVL underwater integrated navigation system based on the test data are carried out to verify the adaptive ability of the ISF and the robust adaptive ability of the method, respectively. Experimental results demonstrate that the proposed algorithm can not only improve the estimation accuracy, but also enhance the fault-tolerant performance.

Radar Target Tracking for Unmanned Surface Vehicle Based on Square Root Sage-Husa Adaptive Robust Kalman Filter.

Dynamic information such as the position and velocity of the target detected by marine radar is frequently susceptible to external measurement white noise generated by the oscillations of an unmanned surface vehicle (USV) and target. Although the Sage–Husa adaptive Kalman filter (SHAKF) has been applied to the target tracking field, the precision and stability of SHAKF remain to be improved. In this paper, a square root Sage–Husa adaptive robust Kalman filter (SR-SHARKF) algorithm together with the constant jerk model is proposed, which can not only solve the problem of filtering divergence triggered by numerical rounding errors, inaccurate system mathematics, and noise statistical models, but also improve the filtering accuracy. First, a novel square root decomposition method is proposed in the SR-SHARKF algorithm for decomposing the covariance matrix of SHAKF to assure its non-negative definiteness. After that, a three-segment approach is adopted to balance the observed and predicted states by evaluating the adaptive scale factor. Finally, the unbiased and the biased noise estimators are integrated while the interval scope of the measurement noise is constrained to jointly evaluate the measurement and observation noise for better adaptability and reliability. Simulation and experimental results demonstrate the effectiveness of the proposed algorithm in eliminating white noise triggered by the USV and target oscillations.

A Compensation Algorithm with Motion Constraint in DVL/SINS Tightly Coupled Positioning

Integration of strapdown inertial navigation system (SINS) and doppler velocity log (DVL) is usually applied in underwater applications, wherein DVL provides the three-dimensional velocity, and hence the accumulated error of SINS can be compensated. However, the DVL/SINS loosely coupled approach fails in the complex environments on the condition of fewer than three available beams. And the tightly coupled approach divergences with only one direction velocity information from the beam measurement. To solve the problems, a novel tightly coupled method is proposed in this paper, in which the state of UUV motion is considered, and a robust adaptive Kalman filter is utilized to dynamically estimate the observation noise. Experiment results indicate that the proposed method is efficient in UUV missions for beam limited environment.

Posture adjustment and robust microinjection of zebrafish larval heart.

Unlike cells or embryos, zebrafish have a complex physiological structure, which poses challenges to posture recognition and adjustment during microinjection. Furthermore, zebrafish surface pigments exhibit strong interference with visual servo-based injection control, thus, affecting the success of microinjection and the subsequent survival rate. To address these challenges, we developed an automated microinjection system for the zebrafish heart that has advantages of high accuracy and success rate and avoids biological sample contamination. A convolutional neural networks (CNN) deep learning model is employed to determine the body axis posture. To solve the problems of blocked needle and abnormal tip positioning induced by zebrafish surface pigment during the injection process, an adaptive robust Kalman filter is proposed to suppress the abnormal values of visual feedback. Experimental results show that the success rate of body axis recognition based on the employed deep learning model exceeds 95%, and the proposed adaptive Kalman filter effectively suppresses the visual outliers, satisfying the requirements of high-precision injection for the zebrafish heart.

INS’s Error Compensation via Measurement Differencing Kalman Filter

The Inertial Navigation System (INS) error compensation for the case of time-correlated measurement errors is proposed in this study. Measurement differences are derived in the filter for the solution of the state estimation problem. In this case, the measurement noise for the derived measurements is no longer correlated in time, but it is correlated with the process noise. Therefore, in this study, the measurement differencing approach based Kalman filter (KF) is designed for the case of correlated system and measurement noise. The innovation properties of the proposed Measurement Differencing Kalman filter (MDKF) are investigated. Conventional KF, robust adaptive KF, and proposed MDKF were applied to estimate the states of a multi-input /output aircraft model in the presence of time-correlated INS measurements, and the obtained results were compared. It is shown that MDKF is also robust to the noise increment type INS errors.

Smartphone-Based Pedestrian Dead Reckoning for 3D Indoor Positioning.

Indoor localization based on pedestrian dead reckoning (PDR) is drawing more and more attention of researchers in location-based services (LBS). The demand for indoor localization has grown rapidly using a smartphone. This paper proposes a 3D indoor positioning method based on the micro-electro-mechanical systems (MEMS) sensors of the smartphone. A quaternion-based robust adaptive cubature Kalman filter (RACKF) algorithm is proposed to estimate the heading of pedestrians based on magnetic, angular rate, and gravity (MARG) sensors. Then, the pedestrian behavior patterns are distinguished by detecting the changes of pitch angle, total accelerometer and barometer values of the smartphone in the duration of effective step frequency. According to the geometric information of the building stairs, the step length of pedestrians and the height difference of each step can be obtained when pedestrians go up and downstairs. Combined with the differential barometric altimetry method, the optimal height can be computed by the robust adaptive Kalman filter (RAKF) algorithm. Moreover, the heading and step length of each step are optimized by the Kalman filter to reduce positioning error. In addition, based on the indoor map vector information, this paper proposes a heading calculation strategy of the 16-wind rose map to improve the pedestrian positioning accuracy and reduce the accumulation error. Pedestrian plane coordinates can be solved based on the Pedestrian Dead-Reckoning (PDR). Finally, combining pedestrian plane coordinates and height, the three-dimensional positioning coordinates of indoor pedestrians are obtained. The proposed algorithm is verified by actual measurement examples. The experimental verification was carried out in a multi-story indoor environment. The results show that the Root Mean Squared Error (RMSE) of location errors is 1.04–1.65 m by using the proposed algorithm for three participants. Furthermore, the RMSE of height estimation errors is 0.17–0.27 m for three participants, which meets the demand of personal intelligent user terminal for location service. Moreover, the height parameter enables users to perceive the floor information.

An Improved Adaptive Kalman Filter for a Single Frequency GNSS/MEMS-IMU/Odometer Integrated Navigation Module

Aiming at the GNSS receiver vulnerability in challenging urban environments and low power consumption of integrated navigation systems, an improved robust adaptive Kalman filter (IRAKF) algorithm with real-time performance and low computation complexity for single-frequency GNSS/MEMS-IMU/odometer integrated navigation module is proposed. The algorithm obtains the scale factor by the prediction residual, and uses it to adjust the artificially set covariance matrix of the observation vector under different GNSS solution states, so that the covariance matrix of the observation vector changes continuously with the complex scene. Then, the adaptive factor is calculated by the Mahalanobis distance to inflate the state prediction covariance matrix. In addition, the one-step prediction Kalman filter is introduced to reduce the computational complexity of the algorithm. The performance of the algorithm is verified by vehicle experiments in the challenging urban environments. Experiments show that the algorithm can effectively weaken the effects of abnormal model deviations and outliers in the measurements and improve the positioning accuracy of real-time integrated navigation. It can meet the requirements of low power consumption real-time vehicle navigation applications in the complex urban environment.

A Robust Adaptive Unscented Kalman Filter for Floating Doppler Wind-LiDAR Motion Correction

This study presents a new method for correcting the six degrees of freedom motion-induced error in ZephIR 300 floating Doppler Wind-LiDAR-derived data, based on a Robust Adaptive Unscented Kalman Filter. The filter takes advantage of the known floating Doppler Wind-LiDAR (FDWL) dynamics, a velocity–azimuth display algorithm, and a wind model describing the LiDAR-retrieved wind vector without motion influence. The filter estimates the corrected wind vector by adapting itself to different atmospheric and motion scenarios, and by estimating the covariance matrices of related noise processes. The measured turbulence intensity by the FDWL (with and without correction) was compared against a reference fixed LiDAR over a 25-day period at “El Pont del Petroli”, Barcelona. After correction, the apparent motion-induced turbulence was greatly reduced, and the statistical indicators showed overall improvement. Thus, the Mean Difference improved from −1.70% (uncorrected) to 0.36% (corrected), the Root Mean Square Error (RMSE) improved from 2.01% to 0.86%, and coefficient of determination improved from 0.85 to 0.93.

UWB/PDR integrated indoor positioning method based on robust adaptive square root cubature Kalman filter

Aiming at the problem that the ultra wide band (UWB) wireless signal is easy to be interfered, a robust adaptive square root cubature Kalman filter (RA-SRCKF) is proposed to be used in UWB/PDR integrated indoor positioning. RA-SRCKF is based on square root cubature Kalman filter (SRCKF) and its statistical characteristic of measurement noise is updated with the method of first estimating and then modifying. The experimental results show that the proposed RA-SRCKF can effectively improve the accuracy and stability of UWB/PDR integrated positioning.

Robust adaptive Kalman filter for strapdown inertial navigation system dynamic alignment

The measurement noise covariance R plays a vital role in the Kalman filter (KF) algorithm. Traditionally, a constant R is obtained by experience or experiments. However, the KF cannot achieve optimal estimation using constant R under non-Gaussian conditions. A robust strategy for adaptive estimation of R is proposed to suppress the influence of non-Gaussian noise on the in-motion alignment performance of the Doppler velocity log (DVL) velocity-aided strapdown inertial navigation system (SINS). Furthermore, an improved Sage–Husa robust adaptive KF algorithm (SHRAKF) based on the Mahalanobis distance (MD) algorithm is proposed to handle the outliers that frequently occur within the complicated underwater environment. The contributions of this work are twofold—the SHRAKF (1) designs a robust strategy to adaptively estimate R in real time and (2) further improves filtering robustness and adaptability with the MD algorithm, conditional on the DVL outputs being contaminated by non-Gaussian noise. A semi-physical simulation experiment for SINS/DVL in-motion alignment based on the test data is carried out, and the experimental results show that the SHRAKF adaptively estimates R in real time and effectively suppresses observational outliers. For non-Gaussian noise pollution, including outliers and heavy-tailed noise, the SHRAKF performs better than traditional methods.

Ultra-Low-Cost Tightly Coupled Triple-Constellation GNSS PPP/MEMS-Based INS Integration for Land Vehicular Applications

The rapid rise of ultra-low-cost dual-frequency GNSS chipsets and micro-electronic-mechanical-system (MEMS) inertial sensors makes it possible to develop low-cost navigation systems, which meet the requirements for many applications, including self-driving cars. This study proposes the use of a dual-frequency u-blox F9P GNSS receiver with xsens MTi670 industrial-grade MEMS IMU to develop an ultra-low-cost tightly coupled (TC) triple-constellation GNSS PPP/INS integrated system for precise land vehicular applications. The performance of the proposed system is assessed through comparison with three different TC GNSS PPP/INS integrated systems. The first system uses the Trimble R9s geodetic-grade receiver with the tactical-grade Stim300 IMU, the second system uses the u-blox F9P receiver with the Stim300 IMU, while the third system uses the Trimble R9s receiver with the xsens MTi670 IMU. An improved robust adaptive Kalman filter is adopted and used in this study due to its ability to reduce the effect of measurement outliers and dynamic model errors on the obtained positioning and attitude accuracy. Real-time precise ephemeris and clock products from the Centre National d’Etudes Spatials (CNES) are used to mitigate the effects of orbital and satellite clock errors. Three land vehicular field trials were carried out to assess the performance of the proposed system under both open-sky and challenging environments. It is shown that the tracking capability of the GNSS receiver is the dominant factor that limits the positioning accuracy, while the IMU grade represents the dominant factor for the attitude accuracy. The proposed TC triple-constellation GNSS PPP/INS integrated system achieves sub-meter-level positioning accuracy in both of the north and up directions, while it achieves meter-level positioning accuracy in the east direction. Sub-meter-level positioning accuracy is achieved when the Stim300 IMU is used with the u-blox F9P GNSS receiver. In contrast, decimeter-level positioning accuracy is consistently achieved through TC GNSS PPP/INS integration when a geodetic-grade GNSS receiver is used, regardless of whether a tactical- or an industrial-grade IMU is used. The root mean square (RMS) errors of the proposed system’s attitude are about 0.878°, 0.804°, and 2.905° for the pitch, roll, and azimuth angles, respectively. The RMS errors of the attitude are significantly improved to reach about 0.034°, 0.038°, and 0.280° for the pitch, roll, and azimuth angles, respectively, when a tactical-grade IMU is used, regardless of whether a geodetic- or low-cost GNSS receiver is used.

A Robust Adaptive Cubature Kalman Filter Based on SVD for Dual-Antenna GNSS/MIMU Tightly Coupled Integration

In complex urban environments, a single Global Navigation Satellite System (GNSS) is often not ideal for navigation due to a lack of sufficient visible satellites. Additionally, the heading angle error of a GNSS/micro-electro-mechanical system–grade inertial measurement unit (MIMU) tightly coupled integration based on the single antenna is large, and the attitude angle, velocity, and position calculated therein all have large errors. Considering the above problems, this paper designs a tightly coupled integration of GNSS/MIMU based on two GNSS antennas and proposes a singular value decomposition (SVD)-based robust adaptive cubature Kalman filter (SVD-RACKF) according to the model characteristics of the integration. In this integration, the high-accuracy heading angle of the carrier is obtained through two antennas, and the existing attitude angle information is used as the observation to constrain the filtering estimation. The proposed SVD-RACKF uses SVD to stabilize the numerical accuracy of the recursive filtering. Furthermore, the three-stage equivalent weight function and the adaptive adjustment factor are constructed to suppress the influence of the gross error and the abnormal state on the parameter estimation, respectively. A set of real measured data was employed for testing and analysis. The results show that dual antennas and dual systems can improve the positioning performance of the integrated system to a certain extent, and the proposed SVD-RACKF can accurately detect the gross errors of the observations and effectively suppress them. Compared with the cubature Kalman filter, the proposed filtering algorithm is more robust, with higher accuracy and reliability of parameter estimation.

Combined adaptive robust Kalman filter algorithm

The precise positioning of dynamic and static objects such as vehicles and pedestrians is a key technology. A global navigation satellite system signal is the primary signal source required to achieve precise positioning, and the optimal estimation method used in precise positioning is Kalman filtering (KF). Standard KF can only achieve optimal estimation results under the conditions that the mathematical model has been determined and the noise characteristics are known. However, when there are measurement outliers and prior noise information deviations, the accuracy of KF cannot be guaranteed. To effectively solve the above problems, a combined adaptive robust Kalman filter (CARKF) algorithm is proposed. First, the influence of measurement outliers on KF accuracy is resisted using the robust Kalman filter method. Then, the influence of an anomalous innovation on its autocorrelation sequence and cross-correlation sequence is resisted by the robust estimator for correlated observations based on the IGGIII method, to ensure the correct estimation of the correlation function sequence of the filtered innovation statistics. Finally, the autocovariance least-squares method is used to eliminate the coupling effect between noise covariances and accurately estimate the unknown noise covariance information. Moreover, an iterative strategy is adopted to eliminate the effect of errors caused by prior noise covariance deviations. The results of the three experiments show that the CARKF method can not only effectively resist the influence of measurement outliers on filtering accuracy and noise covariance valuation but also overcome the influence of errors caused by prior noise deviations and accurately simultaneously estimate two kinds of unknown noise covariance information.

Robust Cascade Vision/Force Control of Industrial Robots Utilizing Continuous Integral Sliding-Mode Control Method

This article presents a robust cascade vision/force approach to control industrial robots interacting with unknown workpieces considering model uncertainties. This cascade structure, consisting of an inner vision loop and an outer force loop, avoids the conflict between the force and vision control in the traditional hybrid methods without decoupling force and vision systems. To apply an advanced image-based visual servoing (IBVS) compensator, some newly modified image features are used that render an invertible image interaction matrix. A practical task-based method is proposed to extract the features corresponding to the desired path in a three-dimensional space. An adaptive robust Kalman filter is adopted for filtering the noise in the force feedback signal. A robust continuous integral sliding-mode control (CISMC) method is developed for both IBVS and force compensators. CISMC exploits the advantages of the modified supertwisting algorithm to reduce the chattering. The stability of the proposed cascade controller is proved. Additionally, a contact detector algorithm is developed to manage the robot's free motion and its interaction with the workpiece. To evaluate the performance of the proposed method, several experimental tests are performed and compared with other well-known methods. The results show the superiority of the proposed approach.

Global Sensitivity Analysis on Temperature-Dependent Parameters of A Reduced-Order Electrochemical Model And Robust State-of-Charge Estimation at Different Temperatures

In this paper, a robust estimator is designed based on a reduced-order electrochemical model to achieve accurate state-of-charge estimation of lithium ion batteries at different ambient temperatures. The reduced-order electrochemical model, containing only two estimation states, describes the first principles within the battery and incorporates temperature-dependent properties, making it an ideal candidate for accurate estimation applications. A global sensitivity analysis based on Sobol indices is then conducted, investigating the impact of different temperatures on the model performance by changing the electrochemical properties of lithium ion batteries. The first-order and total Sobol indices obtained by Monte Carlo method show that variations of temperature-dependent parameters make different influence on the overall model uncertainties at different temperatures. Then, a robust adaptive extended Kalman filter based on the electrochemical model is designed for state-of-charge estimation to actively compensate such potential model uncertainties. Results against multiple experimental datasets at 45, 25 and 0°C indicate that the proposed state-of-charge estimation algorithm is robust to imposed initial estimation errors, different driving cycle inputs and ambient temperatures. An extensive comparative analysis between the adaptive extended Kalman filter and a conventional extended Kalman filter is also presented.

Real-time GNSS precise point positioning using improved robust adaptive Kalman filter

Multi-constellation GNSS precise point positioning (PPP) typically uses the extended Kalman filter (EKF) for kinematic applications. Unfortunately, the obtained positioning accuracy in this approach is prone to errors caused by measurement outliers and the system’s dynamic model. An adaptive robust Kalman filter (RKF) was recently developed to mitigate these errors. However, RKF uses empirical values as detection thresholds for the outliers, which requires the measurements to be from the same constellation and of equal precision to obtain an optimal PPP solution. The classification robust adaptive Kalman filter (CAKF) has subsequently been developed to deal with measurements of different precisions, namely pseudorange and carrier-phase measurements. This paper proposes a real-time GPS/Galileo PPP system, which employs a modified version of CAKF called the Improved Robust adaptive Kalman Filter (IRKF). The positioning performance of GPS/Galileo PPP through the IRKF is initially verified in comparison with those obtained through the EKF, RKF, and CAKF using the Centre for Orbit Determination in Europe (CODE) final orbit and clock products in both of static and kinematic modes. The real-time GPS/Galileo PPP solution through the IRKF is then assessed in comparison with its near-real-time counterpart. The results indicate that when the IRKF approach is utilised, the positioning accuracy is significantly improved and the convergence behaviour is enhanced compared with results from EKF, conventional RKF, and CAKF. In the real-time mode, centimeter-level horizontal positioning accuracy is achieved under an open sky environment, while decimeter-level horizontal positioning accuracy is achieved under a challenging environment. On the other hand, decimeter-level accuracy is achieved for the vertical positioning component under all environmental scenarios. Moreover, the positioning accuracy of the real-time solution is comparable to the near-real-time counterpart.