Adaptive Quantizers for Estimation

TL;DR

This paper introduces an adaptive quantization algorithm for estimation from noisy, quantized data, analyzing its asymptotic bias and mean squared error across different models and validating results with simulations.

Contribution

It presents a low complexity adaptive quantizer with adjustable gain and offset, analyzing its performance for various stochastic models and noise types.

Findings

Algorithm is asymptotically unbiased for constant parameters.

Asymptotic MSE depends on Fisher information of quantized measurements.

Quantization loss relates to the ratio of Fisher information for quantized and continuous data.

Abstract

In this paper, adaptive estimation based on noisy quantized observations is studied. A low complexity adaptive algorithm using a quantizer with adjustable input gain and offset is presented. Three possible scalar models for the parameter to be estimated are considered: constant, Wiener process and Wiener process with deterministic drift. After showing that the algorithm is asymptotically unbiased for estimating a constant, it is shown, in the three cases, that the asymptotic mean squared error depends on the Fisher information for the quantized measurements. It is also shown that the loss of performance due to quantization depends approximately on the ratio of the Fisher information for quantized and continuous measurements. At the end of the paper the theoretical results are validated through simulation under two different classes of noise, generalized Gaussian noise and Student's-t noise.