Observation Noise Covariance Matrix Initialization-Based Objective State Estimation for Kalman Filter Using SVR

Abstract

Kalman filtering is a filtering algorithm for optimal estimation of the system state. The optimal estimate of the system state is obtained through iteratively updating the mean and variance of the system by establishing the equations of motion and observation equations for the system. In this paper, the Kalman filtering algorithm is used to estimate the state of multiple targets which is collected by vehicle radar. Since the true values are not accurate enough, support vector regression (SVR) is applied to fit the multi-target data collected by the radar to obtain the approximate true values. Then, the observation error and the sample variance of the observation error are calculated. Finally, the mean of the variances of the different physical quantities is formed into a diagonal matrix as the initialized value of the observation noise covariance matrix $R_{k}$. The Kalman filtering of mean initialized $R_{k}^{{{\text{mean}}}}$ is then compared with the empirically initialized $R_{k}^{{{\text{emp}}1}}$ for state estimation, it is found that our method can improve the accuracy of the Kalman filtering for state estimation of the target.