The stability of the adaptive two-stage Extended Kalman filter

The well-known conventional Kalman filter requires an accurate system model and exact stochastic information. But in a number of situations, the system model has unknown bias, which may degrade the performance of the Kalman filter or may cause the filter to diverge. The effect of unknown bias may be more pronounced on the extended Kalman filter. The two-stage extended Kalman filter (TEKF) with respect to this problem has been receiving considerable attention for a long time. In the case of a random bias, the TEKF assumes that the information of a random bias is known. But the information of a random bias is unknown or partially known in general. To solve this problem, the adaptive two-stage extended Kalman filter (ATEKF) for nonlinear stochastic systems with unknown constant bias or unknown random bias was proposed by Kim and coauthors. This paper analyzes the stability of the ATEKF. To analyze the stability of the ATEKF, this paper shows that firstly the adaptive augmented state extended Kalman filter (ASEKF) is equivalent to the ATEKF and secondly the adaptive ASEKF is uniformly asymptotically stable. The analysis result shows that the upper bound of the error covariance must be appropriately bounded for the filter stability.