Convergence of Kalman filter with quantized innovations

This work provides a convergence analysis for the estimate error covariance of Kalman filtering based on quantized measurement innovations (QIKF). By taking the quantization errors as random perturbations in observation system, an equivalent state-observation system is given. Accordingly, the quantitative Kalman filter for the original system is equivalent to a Kalman-like filtering for the equivalent state-observation system. In this performance analysis framework, the true covariance matrix of estimating error is strictly analyzed without Gaussian assumption on predicted distribution. A necessary and sufficient condition for the stability of the QIKF is obtained. Then, the relationship between the standard Kalman filtering and the QIKF for the original system is discussed. Finally, the validity of these results are demonstrated by numerical simulations.