Kalman filtering with intermittent observations: Bounds on the error covariance distribution

When measurements are subject to random losses, the covariance of the estimation error of a state estimator becomes a random variable. In this paper we present bounds on the cumulative distribution function of the covariance of the estimation error for a discrete time linear system. We also show that the bounds can be arbitrarily tight if sufficient computational power is available. Numerical simulations show that the proposed method provides tighter bounds than the ones available in the literature.