Optimal Sensor Placement for Source Localization: A Unified ADMM Approach

TL;DR

This paper introduces a unified optimization framework called UTMOST that uses ADMM and MM techniques to determine optimal sensor placements for various source localization methods, improving accuracy and flexibility.

Contribution

The paper presents a novel unified approach for sensor placement optimization applicable to multiple localization models, without approximations or noise assumptions, adaptable to different design criteria.

Findings

UTMOST effectively finds optimal sensor placements for TOA, TDOA, and RSS models.

The framework adapts easily to different optimality criteria like A, D, and E.

Numerical experiments demonstrate the method's efficacy and flexibility.

Abstract

Source localization plays a key role in many applications including radar, wireless and underwater communications. Among various localization methods, the most popular ones are Time-Of-Arrival (TOA), Time-Difference-Of-Arrival (TDOA), and Received Signal Strength (RSS) based. Since the Cram\'{e}r-Rao lower bounds (CRLB) of these methods depend on the sensor geometry explicitly, sensor placement becomes a crucial issue in source localization applications. In this paper, we consider finding the optimal sensor placements for the TOA, TDOA and RSS based localization scenarios. We first unify the three localization models by a generalized problem formulation based on the CRLB-related metric. Then a unified optimization framework for optimal sensor placement (UTMOST) is developed through the combination of the alternating direction method of multipliers (ADMM) and majorization-minimization (MM) techniques. Unlike the majority of the state-of-the-art works, the proposed UTMOST neither approximates the design criterion nor considers only uncorrelated noise in the measurements. It can readily adapt to to different design criteria (i.e. A, D and E-optimality) with slight modifications within the framework and yield the optimal sensor placements correspondingly. Extensive numerical experiments are performed to exhibit the efficacy and flexibility of the proposed framework.