An upper bound of mean-square error in state estimation with quantized measurements:

In this paper, we study the state estimation for a linear time-invariant (LTI) discrete-time system with quantized measurements. The quantization law under consideration has a time-varying data rate. To cope with nonlinearities in quantization laws and to analyse stability in the state estimation problem, a Kalman-filter-based sub-optimal state estimator is developed and an upper bound of its estimation error covariance is minimized. It turns out that, to guarantee the convergence of the upper bound, the averaged data rate of the quantization law must be greater than a minimum rate. This minimum data rate for the quantization law is presented in terms of the poles of the system and design parameters in the state estimator. Numerical examples are presented to illustrate the results in this work.