Estimation based on Quantized Observations

Abstract

System identification based on quantized observations requires either approximations of the quantization noise, leading to suboptimal algorithms, or dedicated algorithms taylored to the quantization noise properties. This contribution studies fundamental issues in estimation that relate directly to the core methods in system identification. As a first contribution, results from statistical quantization theory are surveyed and applied to both moment calculations (mean, variance etc) and the likelihood function of the measured signal. In particular, the role of adding dithering noise at the sensor is studied. The overall message is that taylored dithering noise can considerably simplify the derivation of optimal estimators. The price for this is a decreased signal to noise ratio, and a second contribution is a detailed study of these effects in terms of the Cramér-Rao lower bound. The common additive uniform noise approximation of quantization is discussed, compared, and interpreted in light of the suggested approaches.