A Robust Kalman Filter Based on Kernel Density Estimation for System State Estimation Against Measurement Outliers

Abstract

This article investigates a novel robust Kalman filter (RKF) by incorporating kernel density estimation (KDE) in the Kalman filtering framework to address the disturbance of measurement outliers on system state estimation. It establishes a logarithmic Gaussian kernel function to approximate the unknown probability density function (pdf) of abrupt-change measurement noise covariance caused by measurement outliers. Based on the logarithmic Gaussian kernel function, a state estimation equation is derived according to the Bayesian estimation theory in the presence of measurement outliers. Upon the above, a novel RKF is established for system state estimation against measurement outliers. Simulation and experiment results demonstrate the superiority of the proposed RKF for integrated vehicle navigation in the presence of measurement outliers.