Kalman Filtering for networked control systems with random delay and packet loss

In this paper we study optimal estimation design for sampled linear systems where the sensors measurements are transmitted to the estimator site via a generic digital communication network. Sensor measurements are subject to random delay or might even be completely lost. We show that the minimum error covariance estimator is timevarying, stochastic, and it does not converge to a steady state. Moreover, this estimator is independent of the communication protocol and can be implemented using a finite memory buffer if and only if the delivered packets have a finite maximum delay. We also present an alternative estimator with constant gains and finite buffer menory for which, surprisingly, the stability does not depend on packet delay but only on the packet loss probability. Finally, algorithms to compute critical packet loss probability and estimators performance in terms of their error covariance are given and applied to some numerical examples. Keywords— Networked control systems, packet loss, random delay, optimal estimation, stability