State estimation with quantized measurements: Approximate MMSE approach

This paper addresses the problem of state estimation with quantized measurements. In a system with quantized measurements, due to the nonlinearity of the quantizer, estimating the system state is a nonlinear and non-Gaussian estimation problem even if the system is linear and Gaussian. A numerical algorithm for approximate minimum mean square error (MMSE) state estimation with quantized measurement is proposed. Performance evaluation and comparison of the proposed algorithm with the theoretical solution, the posterior Cramer-Rao lower bound (PCRLB), and other existing methods by simulation of a typical aircraft altitude tracking scenario in air traffic control (ATC) systems are presented.