Exploring Positive Noise in Estimation Theory

TL;DR

This paper investigates estimation techniques for deterministic quantities in non-Gaussian positive noise environments, focusing on order statistics-based estimators and their performance compared to traditional methods.

Contribution

It introduces new order statistic-based estimators for positive and mixed noise distributions, deriving MVU estimators and unbiased estimators without hyperparameter knowledge.

Findings

Order statistic estimators outperform BLUE in certain noise conditions.

Unbiased estimators without hyperparameters are feasible for specific distributions.

Performance varies with sample size and noise distribution.

Abstract

Estimation of a deterministic quantity observed in non-Gaussian additive noise is explored via order statistics approach. More specifically, we study the estimation problem when measurement noises either have positive supports or follow a mixture of normal and uniform distribution. This is a problem of great interest specially in cellular positioning systems where the wireless signal is prone to multiple sources of noises which generally have a positive support. Multiple noise distributions are investigated and, if possible, minimum variance unbiased (MVU) estimators are derived. In case of uniform, exponential and Rayleigh noise distributions, unbiased estimators without any knowledge of the hyper parameters of the noise distributions are also given. For each noise distribution, the proposed order statistic-based estimator's performance, in terms of mean squared error, is compared to the best linear unbiased estimator (BLUE), as a function of sample size, in a simulation study.