Mismatched Estimation in the Distance Geometry Problem

TL;DR

This paper examines the limitations of least-squares methods in the distance geometry problem and shows that likelihood-based estimation can significantly improve accuracy in determining point locations from noisy distance measurements.

Contribution

It introduces a likelihood-based estimation approach for the DGP, demonstrating its superiority over traditional least-squares methods through numerical results.

Findings

Likelihood-based estimates outperform least-squares by several dB.

Least-squares estimates are often suboptimal in noisy DGP scenarios.

Likelihood approach improves accuracy in point localization.

Abstract

We investigate mismatched estimation in the context of the distance geometry problem (DGP). In the DGP, for a set of points, we are given noisy measurements of pairwise distances between the points, and our objective is to determine the geometric locations of the points. A common approach to deal with noisy measurements of pairwise distances is to compute least-squares estimates of the locations of the points. However, these least-squares estimates are likely to be suboptimal, because they do not necessarily maximize the correct likelihood function. In this paper, we argue that more accurate estimates can be obtained when an estimation procedure using the correct likelihood function of noisy measurements is performed. Our numerical results demonstrate that least-squares estimates can be suboptimal by several dB.