Recursive quantized state estimation of discrete-time linear stochastic systems

This paper studies the state estimation problem for linear discrete-time systems based on the minimum mean square error (MMSE) criterion. Under the Gaussian assumption on the predicted density, the quantized MMSE filter is derived which has a similar form as the Kalman filter with the raw measurement simply replaced by its quantized version. The quantization effects are explicitly quantified by adding a nonnegative term to the filtering error covariance derived from the Kalman filter at the measurement update step. Finally, experimental results demonstrate the efficiency of the proposed filtering algorithms.