On the steady-state performance of Kalman filtering with intermittent observations for stable systems

Many recent problems in distributed estimation and control reduce to estimating the state of a dynamical system using sensor measurments that are transmitted across a lossy network. A framework for analyzing such systems was proposed in [1] and called Kalman filtering with intermittent observations. The performance of such a system, i.e., the error covariance matrix, is governed by the solution of a matrix-valued random Riccati recursion. Unfortunately, to date, the tools for analyzing such recursions are woefully lacking, ostensibly because the recursions are both nonlinear and random, and hence intractable if one wants to analyze them exactly. In this paper, we extend some of the large random matrix techniques first introduced in [2], [3] to Kalman filtering with intermittent observations. For systems with a stable system matrix and i.i.d. time-varying measurement matrices, we obtain explicit equations that allow one to compute the asymptotic eigendistribution of the error covariance matrix. Simulations show excellent agreement between the theoretical and empirical results for systems with as low as n = 10, 20 states. Extending the results to unstable system matrices and time-invariant measurement matrices is currently under investigation.