Geometric Interpretation of Theoretical Bounds for RSS-based Source Localization with Uncertain Anchor Positions

TL;DR

This paper provides a geometric interpretation of theoretical bounds for RSS-based source localization with uncertain anchor positions, enhancing understanding of the problem's geometry and aiding in the design of better algorithms.

Contribution

It extends previous work by offering a geometric perspective on the bounds of joint source and anchor localization, utilizing properties of the Fisher Information Matrix and error ellipses.

Findings

Geometric interpretation clarifies the properties of the Fisher Information Matrix.

Insights into the design of efficient localization algorithms.

Numerical results demonstrate the practical usefulness of the geometric approach.

Abstract

The Received Signal Strength based source localization can encounter severe problems originating from uncertain information about the anchor positions in practice. The anchor positions, although commonly assumed to be precisely known prior to the source localization, are usually obtained using previous estimation algorithm such as GPS. This previous estimation procedure produces anchor positions with limited accuracy that result in degradations of the source localization algorithm and topology uncertainty. We have recently addressed the problem with a joint estimation framework that jointly estimates the unknown source and uncertain anchors positions and derived the theoretical limits of the framework. This paper extends the authors previous work on the theoretical performance bounds of the joint localization framework with appropriate geometric interpretation of the overall problem exploiting the properties of semi-definiteness and symmetry of the Fisher Information Matrix and the Cram{\`e}r-Rao Lower Bound and using Information and Error Ellipses, respectively. The numerical results aim to illustrate and discuss the usefulness of the geometric interpretation. They provide in-depth insight into the geometrical properties of the joint localization problem underlining the various possibilities for practical design of efficient localization algorithms.