RSS-Based Localization: Ensuring Consistency and Asymptotic Efficiency

TL;DR

This paper introduces a computationally efficient two-step localization method using RSS measurements that achieves the same asymptotic accuracy as the maximum likelihood estimator, validated through theoretical analysis and simulations.

Contribution

It proposes a novel two-step estimator for RSS-based localization that is both computationally efficient and asymptotically optimal, overcoming challenges of non-convex optimization.

Findings

The two-step estimator is consistent and asymptotically efficient.

Simulation results confirm the theoretical properties and practical effectiveness.

Geometric conditions for sensor deployment ensure model localizability.

Abstract

We study the problem of signal source localization using received signal strength measurements. We begin by presenting verifiable geometric conditions for sensor deployment that ensure the model's asymptotic localizability. Then we establish the consistency and asymptotic efficiency of the maximum likelihood (ML) estimator. However, computing the ML estimator is challenging due to its reliance on solving a non-convex optimization problem. To overcome this, we propose a two-step estimator that retains the same asymptotic properties as the ML estimator while offering low computational complexity, linear in the number of measurements. The main challenge lies in obtaining a consistent estimator in the first step. To address this, we construct two linear least-squares estimation problems by applying algebraic transformations to the nonlinear measurement model, leading to closed-form solutions. In the second step, we perform a single Gauss-Newton iteration using the consistent estimator from the first step as the initialization, achieving the same asymptotic efficiency as the ML estimator. Finally, simulation results validate the theoretical property and practical effectiveness of the proposed two-step estimator.