Robustifying Kalman filter to rapidly adapt to significant changes in system model parameters of state-space models

Abstract

A Kalman filter (KF) is state-of-the-art for estimating states of linear-Gaussian state-space models. The KF selects an expectation of a posterior probability density function of state and the expectation is an analytic solution for minimizing the square estimation error. The estimate of KF is therefore optimal, however, simultaneously inherits the problem of the variance/covariance matrix of the estimation error becoming too small as the filtering proceeds to some extent. In this paper, we tackle this problem by deliberately making a KF suboptimal in case of detecting a significantly large prediction error, which implies that the state estimate at this moment is no longer an expectation of the posterior probability density function. By this suboptimization, the resulting square estimation error becomes larger than that of the KF and we make the KF more responsive to upcoming observations. We call the new filter a robustified Kalman filter and demonstrate the revived ability to adapt to significant changes in system model parameters in a series of numerical experiments.