Robust state estimation for uncertain linear discrete systems with state delay and random measurement losses

This paper investigates state estimation problems of linear discrete systems with uncertain parameters, deterministic external inputs, d-step state delay, and random measurement losses. Firstly, based on the state augmentation method, the original time-delay system is modified to a non-time-delay system. On this basis, the expectation minimization based robust state estimation is put forward, and the detailed derivation process of the estimator is described. At the same time, a new recursive form of estimation error pseudo-covariance matrix is derived. It can be seen that the robust estimator derived is similar to the intermittent observation of the Kalman filter in form, but the estimator parameters need to be adjusted when the plant output measurement arrives. Besides, it is proved that the pseudo-covariance matrix of estimation errors converges to the corresponding stationary distribution with probability one under the condition that some matrices are controllable and observable. Finally, the effectiveness of this robust state estimation algorithm is demonstrated through numerical simulations.