Stochastic stability of the discrete-time constrained extended Kalman filter

In this paper, stability of the projection-based constrained discrete-time extended Kalman filter (EKF) as applied to nonlinear systems in a stochastic framework has been studied. It has been shown that like the unconstrained EKF, 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. Stability results are verified and performance of the constrained EKF is demonstrated through simulations on a nonlinear engineering example