Quantized filtering of linear stochastic systems

In this paper we investigate a general multi-level quantized filter of linear stochastic systems. For a given multi-level quantization and under the Gaussian assumption on the predicted density, a quantized innovations filter that achieves the minimum mean square error is derived. The filter is given in terms of quantization thresholds and a simple modified Riccati difference equation. By optimizing the filtering error covariance with respect to quantization thresholds, the associated optimal thresholds and the corresponding filter are obtained. Furthermore, the convergence of the filter to the standard Kalman filter is established. We also discuss the design of a robust minimax quantized filter when the innovation covariance is not exactly known. Simulation and experimental results illustrate the effectiveness and advantages of the proposed quantized filter.