Robust Distributed Maximum Likelihood Estimation with Dependent Quantized Data

TL;DR

This paper proposes a robust distributed maximum likelihood estimation method using multiple quantizers to handle dependent quantized data, demonstrating improved stability and efficiency in non-Gaussian scenarios.

Contribution

It introduces a robust MLE approach with multiple quantizers for dependent data, providing theoretical efficiency proofs and practical validation in non-Gaussian contexts.

Findings

The asymptotic variance is the inverse of a weighted sum of Fisher information matrices.

The proposed method is robust against poor quantizer choices.

Simulations confirm improved performance with fewer measurements.

Abstract

In this paper, we consider distributed maximum likelihood estimation (MLE) with dependent quantized data under the assumption that the structure of the joint probability density function (pdf) is known, but it contains unknown deterministic parameters. The parameters may include different vector parameters corresponding to marginal pdfs and parameters that describe dependence of observations across sensors. Since MLE with a single quantizer is sensitive to the choice of thresholds due to the uncertainty of pdf, we concentrate on MLE with multiple groups of quantizers (which can be determined by the use of prior information or some heuristic approaches) to fend off against the risk of a poor/outlier quantizer. The asymptotic efficiency of the MLE scheme with multiple quantizers is proved under some regularity conditions and the asymptotic variance is derived to be the inverse of a weighted linear combination of Fisher information matrices based on multiple different quantizers which can be used to show the robustness of our approach. As an illustrative example, we consider an estimation problem with a bivariate non-Gaussian pdf that has applications in distributed constant false alarm rate (CFAR) detection systems. Simulations show the robustness of the proposed MLE scheme especially when the number of quantized measurements is small.