Lower bounds in parameter estimation based on quantized measurements

In this paper, we investigate the lower bounds on estimation error covariance (EEC) for parameter estimation based on quantized measurements. As the quantized measurements can present only the regions in which the raw measurements fall, the quantization uncertainties need to be considered in deriving the lower bounds. By extending the uniform explanation for various kinds of lower bounds proposed by Weinstein and Weiss, the Cramér-Rao Lower Bound (CRLB) and Weiss-Weinstein Lower Bound (WWLB) for the quantized systems are derived, which are named as QCRLB and QWWLB, respectively. Then a class of linear systems with Gaussian noises is illustrated as an example, for which the explicit calculations of the QCRLB as well as the QWWLB are presented. Besides, simulation results are provided to show that the EEC obtained by adopting minimum mean squares estimation (MMSE) is close to the QCRLB and QWWLB.