Intermittent quantized Kalman filtering and LQG control based on Lloyd-Max quantizer

The purpose of this paper is to discuss the batch intermittent quantized Kalman filter(BIQKF) and LQG control over lossy digital links using dynamic Lloyd-Max quantizer. A necessary and sufficient condition is presented for the Stability of the BIQKF. The condition, which is expressed in terms of the bit rate and the arrival probability initially. Under the assumption that the observation is approximately Gaussian, it is shown that the separation principle remains valid under the quantized output signal which is used to be transmitted over lossy networks. The optimal LQG controller is then given in terms of two Riccati difference equations associated respectively with the Kalman filter with intermittent quantized observations and the standard LQR control. The corresponding minimum cost is also derived.