An adaptive fading Kalman filter based on Mahalanobis distance

Abstract

An adaptive Kalman filter with fading factor is derived to address the modeling errors. In any recursion of the proposed filter, a judging index is defined as the square of the Mahalanobis distance of the innovation vector, which is found to be chi-square distributed. Modeling errors can be detected through doing hypothesis test of the index, and then the prior covariance matrix can be artificially inflated by introducing a fading factor which is calculated iteratively using Newton’s method. The proposed method has a stronger tracking ability to the true state than the standard Kalman filter in the presence of modeling errors. Furthermore, by selecting a relatively small significance level, the efficiency of the proposed filter almost does not decrease while the adaptivity is achieved. A simple and illustrative case of kinematic positioning, which is assumed with a constant velocity model is simulated, and an unknown constant acceleration or perturbing Gaussian distribution is artificially introduced to represent the functional and stochastic modeling errors respectively. Simulation results validate the better performance of the proposed method compared to the standard Kalman filter.