Adaptive two-stage Kalman filter in the presence of unknown random bias

The well-known conventional Kalman filter gives the optimal solution but requires an accurate system model and exact stochastic information. In a number of practical situations, the system model has unknown bias and the Kalman filter with unknown bias may be degraded or even diverged. The two-stage Kalman filter (TKF) to consider this problem has been receiving considerable attention for a long time. Until now, the optimal TKF for system with a constant bias or a random bias has been proposed by several researchers. In case of a random bias, the optimal TKF assumes that the information of a random bias is known. But the information of a random bias is unknown or incorrect in general. To solve this problem, this paper proposes two adaptive filters, such as an adaptive fading Kalman filter (AFKF) and an adaptive two-stage Kalman filter (ATKF). Firstly, the AFKF is designed by using the forgetting factor obtained from the innovation information and the stability of the AFKF is analysed. Secondly, the ATKF to estimate unknown random bias is designed by using the AFKF and the performance of the ATKF is verified by simulation. Copyright (c) 2006 John Wiley & Sons, Ltd.