State estimation for dynamic systems with higher-order autoregressive moving average non-Gaussian noise

Abstract

The classical Kalman filter is a very important state estimation approach, which has been widely used in many engineering applications. The Kalman filter is optimal for linear dynamic systems with independent Gaussian noises. However, the independence and Gaussian assumptions may not be satisfied in practice. On the one hand, modeling physical systems usually results in discrete-time state-space models with correlated process and measurement noises. On the other hand, the noise is non-Gaussian when the system is disturbed by heavy-tailed noise. In this case, the performance of the Kalman filter will deteriorate, or even diverge. This paper is devoted to addressing the state estimation problem of linear dynamic systems with high-order autoregressive moving average (ARMA) non-Gaussian noise. First, a triplet Markov model is introduced to model the system with high-order ARMA noise, since this model relaxes the independence assumption of the hidden Markov model. Then, a new filter is derived based on correntropy, instead of the commonly used minimum mean square error (MMSE), to deal with non-Gaussian noise. Unlike the MMSE, which uses only second-order statistics of error, correntropy can capture second-order and higher-order statistics. Finally, simulation results verify the effectiveness of the proposed algorithm.