Constrained kalman filtering for nonlinear dynamical systems with observation losses

In this paper, the constrained extended Kalman filter (EKF) is discussed for nonlinear dynamical systems when observations are available according to a Bernoulli process. First, by using EKF approach, we provide a sufficient condition such that computing of the error covariance of nonlinear system is converted into the corresponding computing of linear system. Then based on physical consideration, at each time step through projecting the unconstrained Kalman filter solution onto the state constraint surface, the constrained estimation can be derived, which significantly improves the prediction accuracy of the filter. We study the statistical convergence properties of the error covariance matrix, showing the existence of a critical value for the arrival rate of the observation, beyond which a transition to an unbounded state error covariance occurs. We show that, when the system observation matrix restricted to the observable subspace is invertible, the critical probability is an exact value. Simulations are provided to demonstrate the effectiveness of the theoretical results.