Distributed Estimation of a Parametric Field Using Sparse Noisy Data

TL;DR

This paper presents a distributed estimation method for a parametric physical field using quantized noisy sensor data, employing an EM algorithm to improve estimation accuracy in a wireless sensor network.

Contribution

It introduces an EM-based iterative estimation approach for distributed sensor networks with quantized data, analyzing its performance under various noise and quantization conditions.

Findings

Estimation accuracy improves with increased quantization levels and sensors.

The EM algorithm effectively estimates parameters despite noisy, quantized data.

Performance depends on SNR in observation and transmission channels.

Abstract

The problem of distributed estimation of a parametric physical field is stated as a maximum likelihood estimation problem. Sensor observations are distorted by additive white Gaussian noise. Prior to data transmission, each sensor quantizes its observation to $M$ levels. The quantized data are then communicated over parallel additive white Gaussian channels to a fusion center for a joint estimation. An iterative expectation-maximization (EM) algorithm to estimate the unknown parameter is formulated, and its linearized version is adopted for numerical analysis. The numerical examples are provided for the case of the field modeled as a Gaussian bell. The dependence of the integrated mean-square error on the number of quantization levels, the number of sensors in the network and the SNR in observation and transmission channels is analyzed.