Stability analysis of the discrete-time difference SDRE state estimator in a noisy environment

The state-dependent Riccati equation filter (SDREF) is a recent nonlinear estimation technique which has yielded a number of impressive results. However, the theoretical investigations of the filter have been carried out only in a deterministic environment. In this paper a discrete time difference SDRE-based observer for general nonlinear systems in a stochastic framework is considered, and its error behavior has been also analyzed. It is proved that, the estimation error remains bounded in mean square if the system to be observed satisfies certain conditions, and both the initial estimation error and the disturbing noise terms are small enough. Moreover, the results are verified thorough a simulation study of an example system.