Robust Filtering for Random Sensor Delay Systems

In this paper, we consider the robust filtering problem for discrete time-varying systems with sensor delayed measurement subject to norm-bounded parameter uncertainties. The sensor delayed measurement is assumed to be a linear function of a stochastic variable that satisfies Bernoulli random binary distribution. An upper bound for the actual covariance of uncertain stochastic parameter system is derived, and is used for the estimation variance constraints. Such an upper bound is then minimized over the filter parameters for all stochastic sensor delays and admissible deterministic uncertainties. It is shown that the desired filter can be obtained in terms of solutions to two discrete Riccati difference equations, which are of a form suitable for recursive computation in online applications. An illustrative example is presented to show the applicability of the proposed method.