Dynamical approach of Riccati difference equations to non linear filters stability in constrained state estimation systems

In this paper the stability of discrete time Extended Kalman Filter (EKF) when applied to non linear system with state estimation constraints are discussed. The stochastic stability of the constrained extended Kalman filter is considered then the analysis is extended to the estimation error-based constrained extended Kalman filter. The estimation error of the EKF with known constraints on the states remains bounded when the initial error and noise terms are small, and the solution of the Riccati difference equation remains positive definite and bounded. This leads to convergence of the filter and its stability. It is very sensitive to initialization and filter divergence is inevitable if the arbitrary noise matrices have not chosen appropriately.