Constrained two-stage Kalman filter for real-time state estimation of systems with time-varying measurement noise covariance

Aiming at the problem that the performance of Adaptive Kalman filter estimation will be affected when the statistical characteristics of the process and measurement noise matrix are inaccurate and time-varying in the linear Gaussian state-space model, an algorithm of Multi-fading factor and update monitoring strategy adaptive Kalman filter based variational Bayesian is proposed. Inverse Wishart distribution is selected as the measurement noise model, the system state vector and measurement noise covariance matrix are estimated with the variational Bayesian method. The process noise covariance matrix is estimated by the maximum a posteriori principle, and the update monitoring strategy with adjustment factors is used to maintain the positive semi-definite of the updated matrix. The above optimal estimation results are introduced as time-varying parameters into the multiple fading factors to improve the estimation accuracy of the one-step state predicted covariance matrix. The application of the proposed algorithm in target tracking is simulated. The results show that compared with the current filters, the proposed filtering algorithm has better accuracy and convergence performance, and realizes the simultaneous estimation of inaccurate time-varying process and measurement noise covariance matrices.

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Adaptive Unscented Kalman Filter for Target Tacking with Time-Varying Noise Covariance Based on Multi-Sensor Information Fusion

Sensors ◽

10.3390/s21175808 ◽

2021 ◽

Vol 21 (17) ◽

pp. 5808

Author(s):

Dapeng Wang ◽

Hai Zhang ◽

Baoshuang Ge

Keyword(s):

Kalman Filter ◽

Information Fusion ◽

Stochastic Systems ◽

Unscented Kalman Filter ◽

Minimum Variance ◽

Measurement Noise ◽

Time Varying ◽

Measurement Noise Covariance ◽

Noise Covariance ◽

Sensor Information

In this paper, an innovative optimal information fusion methodology based on adaptive and robust unscented Kalman filter (UKF) for multi-sensor nonlinear stochastic systems is proposed. Based on the linear minimum variance criterion, this multi-sensor information fusion method has a two-layer architecture: at the first layer, a new adaptive UKF scheme for the time-varying noise covariance is developed and serves as a local filter to improve the adaptability together with the estimated measurement noise covariance by applying the redundant measurement noise covariance estimation, which is isolated from the state estimation; the second layer is the fusion structure to calculate the optimal matrix weights and gives the final optimal state estimations. Based on the hypothesis testing theory with the Mahalanobis distance, the new adaptive UKF scheme utilizes both the innovation and the residual sequences to adapt the process noise covariance timely. The results of the target tracking simulations indicate that the proposed method is effective under the condition of time-varying process-error and measurement noise covariance.

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A Novel Adaptive Two-Stage Information Filter Approach for Deep-Sea USBL/DVL Integrated Navigation

Sensors ◽

10.3390/s20216029 ◽

2020 ◽

Vol 20 (21) ◽

pp. 6029

Author(s):

Kaifei He ◽

Huimin Liu ◽

Zhenjie Wang

Keyword(s):

Deep Sea ◽

Underwater Vehicle ◽

Measurement Noise ◽

Doppler Velocity ◽

Time Varying ◽

Integrated Navigation ◽

Two Stage ◽

Information Filter ◽

Measurement Noise Covariance ◽

Noise Covariance

An accurate observation model and statistical model are critical in underwater integrated navigation. However, it is often the case that the statistical characteristics of noise are unknown through the ultra-short baseline (USBL) system/Doppler velocity log (DVL) integrated navigation in the deep-sea. Additionally, the velocity of underwater vehicles relative to the bottom of the sea or the currents is commonly provided by the DVL, and an adaptive filtering solution is needed to correctly estimate the velocity with unknown currents. This paper focuses on the estimation of unknown currents and measurement noise covariance for an underwater vehicle based on the USBL, DVL, and a pressure gauge (PG), and proposes a novel unbiased adaptive two-stage information filter (ATSIF) for the underwater vehicle (UV) with an unknown time-varying currents velocity. In the proposed algorithm, the adaptive filter is decomposed into a standard information filter and an unknown currents velocity information filter with interconnections, and the time-varying unknown ocean currents and measurement noise covariance are estimated. The simulation and experimental results illustrate that the proposed algorithm can make full use of high-precision observation information and has better robustness and navigation accuracy to deal with time-varying currents and measurement outliers than existing state-of-the-art algorithms.

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Multi-Fading Factor and Updated Monitoring Strategy Adaptive Kalman Filter-Based Variational Bayesian

Sensors ◽

10.3390/s21010198 ◽

2020 ◽

Vol 21 (1) ◽

pp. 198

Author(s):

Chenghao Shan ◽

Weidong Zhou ◽

Yefeng Yang ◽

Zihao Jiang

Keyword(s):

Kalman Filter ◽

Covariance Matrix ◽

Measurement Noise ◽

Time Varying ◽

Monitoring Strategy ◽

Adaptive Kalman Filter ◽

Variational Bayesian ◽

Measurement Noise Covariance ◽

Noise Covariance ◽

Fading Factor

Aiming at the problem that the performance of adaptive Kalman filter estimation will be affected when the statistical characteristics of the process and measurement of the noise matrices are inaccurate and time-varying in the linear Gaussian state-space model, an algorithm of multi-fading factor and an updated monitoring strategy adaptive Kalman filter-based variational Bayesian is proposed. Inverse Wishart distribution is selected as the measurement noise model and the system state vector and measurement noise covariance matrix are estimated with the variational Bayesian method. The process noise covariance matrix is estimated by the maximum a posteriori principle, and the updated monitoring strategy with adjustment factors is used to maintain the positive semi-definite of the updated matrix. The above optimal estimation results are introduced as time-varying parameters into the multiple fading factors to improve the estimation accuracy of the one-step state predicted covariance matrix. The application of the proposed algorithm in target tracking is simulated. The results show that compared with the current filters, the proposed filtering algorithm has better accuracy and convergence performance, and realizes the simultaneous estimation of inaccurate time-varying process and measurement noise covariance matrices.

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Strong Tracking PHD Filter Based on Variational Bayesian with Inaccurate Process and Measurement Noise Covariance

Sensors ◽

10.3390/s21041126 ◽

2021 ◽

Vol 21 (4) ◽

pp. 1126

Author(s):

Zhentao Hu ◽

Linlin Yang ◽

Yong Jin ◽

Han Wang ◽

Shibo Yang

Keyword(s):

Real Time ◽

Gaussian Mixture ◽

Measurement Noise ◽

Tracking Accuracy ◽

Process Noise ◽

Probability Hypothesis Density ◽

Measurement Noise Covariance ◽

Multi Target Tracking ◽

Noise Covariance ◽

Fading Factor

Assuming that the measurement and process noise covariances are known, the probability hypothesis density (PHD) filter is effective in real-time multi-target tracking; however, noise covariance is often unknown and time-varying for an actual scene. To solve this problem, a strong tracking PHD filter based on Variational Bayes (VB) approximation is proposed in this paper. The measurement noise covariance is described in the linear system by the inverse Wishart (IW) distribution. Then, the fading factor in the strong tracking principle uses the optimal measurement noise covariance at the previous moment to control the state prediction covariance in real-time. The Gaussian IW (GIW) joint distribution adopts the VB approximation to jointly return the measurement noise covariance and the target state covariance. The simulation results show that, compared with the traditional Gaussian mixture PHD (GM-PHD) and the VB-adaptive PHD, the proposed algorithm has higher tracking accuracy and stronger robustness in a more reasonable calculation time.

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Passive Location of Angle Sensors Using Extend Square-Root Cubature Kalman Filter

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.143-144.577 ◽

2011 ◽

Vol 143-144 ◽

pp. 577-581 ◽

Cited By ~ 1

Author(s):

Yang Zhang ◽

Guo Sheng Rui ◽

Jun Miao

Keyword(s):

Kalman Filter ◽

Unscented Kalman Filter ◽

Measurement Noise ◽

Filter Method ◽

Square Root ◽

Passive Location ◽

Mode Decomposition ◽

Measurement Noise Covariance ◽

Cubature Kalman Filter ◽

Noise Covariance

A new nonlinear filter method Cubature Kalman Filter (CKF) is improved for passive location with moving angle-measured sensors’ measurements.Firstly,it used Empirical Mode Decomposition (EMD) algorithm to estimate measurement noise covariance; And then the covariance of the procession noise and measurement noise is brought into the circle; Meanwhile,CKF is improved by the way of square root to keep its stability and positivity,and the results of track by Extend SCKF are compared with the results by Unscented Kalman Filter (UKF) in the text;By the tracking results to the velocity of the target, Extend SCKF algorithm can not only track the target with unknown measurement noise but also improve the passive position precision remarkably as the same difficulty as UKF.

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A Novel Adaptive Kalman Filter With Inaccurate Process and Measurement Noise Covariance Matrices

IEEE Transactions on Automatic Control ◽

10.1109/tac.2017.2730480 ◽

2018 ◽

Vol 63 (2) ◽

pp. 594-601 ◽

Cited By ~ 93

Author(s):

Yulong Huang ◽

Yonggang Zhang ◽

Zhemin Wu ◽

Ning Li ◽

Jonathon Chambers

Keyword(s):

Kalman Filter ◽

Covariance Matrices ◽

Measurement Noise ◽

Adaptive Kalman Filter ◽

Measurement Noise Covariance ◽

Noise Covariance

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DTM-Aided Adaptive EPF Navigation Application in Railways

Sensors ◽

10.3390/s18113860 ◽

2018 ◽

Vol 18 (11) ◽

pp. 3860 ◽

Cited By ~ 1

Author(s):

Chengming Jin ◽

Baigen Cai ◽

Jian Wang ◽

Allison Kealy

Keyword(s):

Particle Filter ◽

Real Time ◽

Sampling Period ◽

Adaptive Method ◽

Measurement Noise ◽

Filter Method ◽

Operating Environments ◽

Measurement Noise Covariance ◽

Noise Covariance ◽

Point Positioning

The diverse operating environments change GNSS measurement noise covariance in real time, and different GNSS techniques hold different measurement noise covariance as well. Mismodelling the covariance causes undependable filtering results and even degenerates the GNSS/INS Particle Filter (PF) process, due to the fact that INS error-state noise covariance is much smaller than that of GNSS measurement noise. It also makes the majority of existing methods for adaptively adjusting filter parameters incapable of performing well. In this paper, a feasible Digital Track Map-aided (DTM-aided) adaptive extended Kalman particle filter method is introduced in GNSS/INS integration in order to adjust GNSS measurement noise covariance in real time, and the GNSS down-direction offset is also estimated along with every sampling period through making full use of DTM information. The proposed approach is successfully examined in a railway environment, and the on-site experimental results reveal that the adaptive approach holds better positioning performance in comparison to the methods without adaptive adjustment. Improvements of 62.4% and 14.9% in positioning accuracy are obtained in contrast to Standard Point Positioning (SPP) and Precise Point Positioning (PPP), respectively. The proposed adaptive method takes advantage of DTM information and is able to automatically adapt to complex railway environments and different GNSS techniques.

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Adaptive Unscented Kalman Filter for Target Tracking with Unknown Time-Varying Noise Covariance

Sensors ◽

10.3390/s19061371 ◽

2019 ◽

Vol 19 (6) ◽

pp. 1371 ◽

Cited By ~ 7

Author(s):

Baoshuang Ge ◽

Hai Zhang ◽

Liuyang Jiang ◽

Zheng Li ◽

Maaz Butt

Keyword(s):

Kalman Filter ◽

Target Tracking ◽

Unscented Kalman Filter ◽

Nonlinear Problems ◽

Linear Matrix ◽

Time Varying ◽

Tracking Accuracy ◽

Linear Matrix Equation ◽

Measurement Noise Covariance ◽

Noise Covariance

The unscented Kalman filter (UKF) is widely used to address the nonlinear problems in target tracking. However, this standard UKF shows unstable performance whenever the noise covariance mismatches. Furthermore, in consideration of the deficiencies of the current adaptive UKF algorithm, this paper proposes a new adaptive UKF scheme for the time-varying noise covariance problems. First of all, the cross-correlation between the innovation and residual sequences is given and proven. On this basis, a linear matrix equation deduced from the innovation and residual sequences is applied to resolve the process noise covariance in real time. Using the redundant measurements, an improved measurement-based adaptive Kalman filtering algorithm is applied to estimate the measurement noise covariance, which is entirely immune to the state estimation. The results of the simulation indicate that under the condition of time-varying noise covariances, the proposed adaptive UKF outperforms the standard UKF and the current adaptive UKF algorithm, hence improving tracking accuracy and stability.

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Kalman Filter and Complementary Filter in Attitude Estimation of APM

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.577.794 ◽

2014 ◽

Vol 577 ◽

pp. 794-797 ◽

Cited By ~ 1

Author(s):

Feng Lin ◽

Xi Lan Miao ◽

Xiao Guang Qu

Keyword(s):

Kalman Filter ◽

Covariance Matrix ◽

Attitude Estimation ◽

Measurement Noise ◽

Experimental Results ◽

Extend Kalman Filter ◽

Noise Covariance Matrix ◽

Complementary Filter ◽

Measurement Noise Covariance ◽

Noise Covariance

This paper presents the results of a quaternion based extend Kalman filter (EKF) and complementary filter for ArduPilotMega (APM) attitude estimation. In addition, a new method to get the measurement noise covariance matrix R is proposed. Experimental results show that the two algorithms can meet the requirements, but the complementary filter can yield better performance than EKF.

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