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

Chenghao Shan,Zihao Jiang,Yefeng Yang,Weidong Zhou

doi:10.3390/s21010198

Abstract

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.

Highlights

In many practical engineering applications, the actual values of the required state variables are often not directly available
Assuming that the prior distribution of the joint probability density function of the state variable and the measurement noise covariance matrix (MNCM) is the product of the Gaussian distribution and the inverse Wishart distribution, the prediction process can be defined as: p(X, Rk|Z1:k−1) = p(Xk|Z1:k−1)p(Rk|Zk−1) = N Xk−1; Xk:k−1, Pk:k−1 IW Rk−1; tk−1:k−1, Tk−1:k−1 (15)
Updated Monitoring Strategy Based on Maximum a Posterior (MAP) for Estimating the process noise covariance matrix (PNCM) Qk

Summary

Introduction

In many practical engineering applications, the actual values of the required state variables are often not directly available. Literature [26] proposed a variational adaptive Kalman filter (R-VBKF) but only estimated the system state vector and the measurement noise covariance matrix (MNCM); the accuracy is not satisfactory enough. Aiming at the linear Gaussian state–space model with slow time-varying covariance of process and measurement noise, taking into account the estimation accuracy, convergence performance, robustness, and the realization of simultaneous estimation of noise covariance matrices, the multi-fading factor and updated monitoring strategy, AKF-based variational Bayesian (MFMS-VBAKF) is proposed. Assuming that the prior distribution of the joint probability density function of the state variable and the MNCM is the product of the Gaussian distribution and the inverse Wishart distribution, the prediction process can be defined as: p(X, Rk|Z1:k−1) = p(Xk|Z1:k−1)p(Rk|Zk−1) = N Xk−1; Xk:k−1, Pk:k−1 IW Rk−1; tk−1:k−1, Tk−1:k−1

Variational Update Process

Improved by Introducing Multiple Fading Factors

Simulations and Results

Conclusions

Future Work