Fast filtering algorithm for state estimation of lossy networks

The authors study the state estimation issue of networked control systems in which observations, control commands and acknowledgement (ACK) signals are randomly dropped. They show that unlike the transmission control protocol-like or user datagram protocol-like case, the probability density function of system state turns out to be Gaussian mixture with exponentially increasing terms because of the random losses of ACK signals, which makes the optimal filtering time-consuming. They develop a sub-optimal but computationally efficient filtering algorithm, named as fast filtering (FF), and establish a packet-loss-rate-based sufficient condition for the boundedness of the expected estimation error covariance matrices. By a numerical example, the effectiveness of the proposed FF algorithm is illustrated, and the mutual influences of the packet losses of observations, control commands and ACK signals on the estimation performance are analysed.