Convergence analysis of nonlinear Kalman filters with novel innovation-based method

The convergence of nonlinear Kalman filters has conventionally been analyzed in terms of the estimation error. In this paper, we present a new method for investigating the convergence performance of a class of nonlinear Kalman filters based on deterministic sampling. The systems considered here are described by nonlinear state equations with linear measurements. For this type of systems, our proposed convergence analysis is performed using “innovation” which is defined as the error between the measurement and its prediction. Specifically, we obtain a linear relationship between the innovation and the estimation error, and derive a set of sufficient conditions that ensures the convergence of nonlinear Kalman filters. Compared with the conventional convergence analysis method based on the estimation error, the proposed innovation-based method can obtain sufficient conditions for convergence more directly and readily. Simulation results show that the convergence of innovation generates the convergence of nonlinear Kalman filters.