Optimal Linear Exponential Quadratic Gaussian Estimation With Intermittent Observations

Abstract

This letter is concerned with the problem of optimal linear exponential quadratic state estimation for discrete-time Gauss–Markov systems with intermittent observations. The optimal estimator and optimal cost are derived via an information state approach. The necessary and sufficient condition for the existence of the estimator is provided. For a special case when a scalar parameter in the exponential cost goes to zero, the derived estimator reduces to the corresponding Kalman filter. It is also interesting to note that the resulting estimator has the same form as that obtained from the $H_{\infty }$ setting.