Stochastic Stability of Kalman-Type Nonlinear Filters

We analyze the stochastic stability of a class of generic Kalman-type nonlinear filtering algorithms with the aim of providing practically verifiable conditions. We investigate conditions under which the Kalman gain matrix and the approximate error covariance matrix are bounded in nonlinear systems. By stochastic Lyapunov stability theory, we show that the estimation error for the nonlinear filter is bounded exponentially in mean square, with its norm bounded in probability. The analysis in this work applies to popular nonlinear Kalman filter extensions such as the extended Kalman filter (EKF) and the constant-gain Kalman filter (CGKF).