Optimal Linear Filter for Systems With Random Delay and Packet Dropout Compensations

In this article, the optimal linear filtering problem is investigated for networked control systems with random delays and packet dropouts. The filter may receive the current sensor measurement, the one-step delayed sensor measurement or nothing at each time. When nothing is received by the filter, the predictor of the current sensor measurement which may be delayed or lost is used for compensation. For this measurement compensation model, a new augmented system is established. Based on the established augmented dynamic system, an optimal linear filter dependent on probabilities in the linear minimum sense is developed by an innovation analysis approach. Compared with the filters based on the popular zero-input, hold-input, and modified hold-input compensation strategies, the presented filter has better estimation accuracy. The steady-state filter is also investigated. Simulation examples illustrate the efficiency of the developed filter.