Linear Filter for Uncertain System with Transmission Delays and Losses

This paper is concerned with the optimal linear filtering problem for systems with incomplete measurements and white multiplicative noises. The measurement data suffers from one-step delay and packet dropouts in transmission from the sensor to the filter. At each moment, the filter may receive one or two data packets or nothing. First, the multiplicative noises are transferred to the additive noises. Then, a new augmented state vector with a lower order is proposed. Based on the new state vector, the optimal linear filter is obtained. Moreover, the steady-state behavior of the proposed filter is studied.