Quantised innovation Kalman filter: performance analysis and design of quantised level

This study provides a performance analysis for the quantised innovation Kalman filter (QIKF). The covariance matrix of the estimation error is analysed with the correlation between the measurement error and the quantising error. By taking the quantisation errors as a random perturbation in the observation system, an equivalent state-observation system is obtained. Accordingly, the QIKF for the original system is equivalent to a Kalman-like filtering for the equivalent state-observation system. The boundedness of the error covariance matrix of the QIKF is obtained under some weak conditions. A sufficient condition for the stability of the QIKF is also obtained in the general vector case. Then, the relationship between the standard Kalman filtering and the QIKF for the original system is discussed. Based on the analysis of the stability of the QIKF, the design of number of quantised levels is discussed. The relationship between the filtering performance and the number of quantisation levels is also given. Finally, the validity of these results is demonstrated by numerical simulations.