Constrained Kalman Filtering with observation losses

In this paper, we consider networked constrained Kalman filtering with observation losses. The observation losses of communication network is modeled as an i.i.d. Bernoulli process. 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. Simulations are provided to demonstrate the effectiveness of the theoretical results.