Two-stage Kalman Filter for Linear System with Correlated Noises

Abstract

The two-stage method is greatly effective to deal with state estimation for systems with unknown bias because it can improve the computation performance. Unfortunately, the current two-stage Kalman filters have some obvious limitations on noise formulation, for example, uncorrelated noises and white Gaussian noises and so on. The study on the common Kalman filtering methods has indicated that the simple noise assumptions cannot satisfy characteristics of practical systems. This paper designs a kind of two-stage Kalman estimator under the case with correlated noises. The idea is to introduce the Kalman filtering method with correlated noises to the design process of the two-stage Kalman filter with bias estimation. The purpose is to obtain an improved two-stage Kalman filter, which can deals with a kind of correlated noises, and extends practical application range. Moreover, changes on filtering formulas are clearly discovered after the noise correlation is considered compared to the current linear two-stage Kalman filters. The proposed method will be beneficial to the engineers and researches of corresponding fields. The effectiveness of this method can be verified by simulation.