# A Two-Step SD/SOCP-GTRS Method for Improved RSS-Based Localization in Wireless Sensor Networks

## TL;DR

This paper introduces a two-step method for improving the accuracy of location tracking in wireless sensor networks using signal strength measurements.

## Contribution

The novel SD/SOCP-GTRS framework combines convex relaxation and trust region optimization for improved RSS-based localization.

## Key findings

- The SD/SOCP-GTRS method reduces root mean square error compared to existing approaches.
- Simulations show the method approaches theoretical performance limits in high-precision localization.
- The framework is robust against signal noise and attenuation in wireless environments.

## Abstract

Wireless localization is a fundamental component of modern sensor networks, with applications spanning environmental monitoring and smart cities. Ensuring accurate and efficient localization is critical for enhancing network performance and reliability, particularly in the presence of signal attenuation and noise. This study proposes a novel two-step localization framework, SD/SOCP-GTRS, to improve the precision of target localization using received signal strength (RSS) measurements. In the first step (SD/SOCP), semidefinite programming (SDP) and second-order cone programming (SOCP)-based convex relaxation are applied to the maximum likelihood (ML) estimator, generating an initial coarse estimate. The second step (GTRS) refines this estimate using weighted least squares (WLS) and the generalized trust region subproblem (GTRS), mitigating performance degradation caused by relaxation. Monte Carlo simulations validate that the proposed SD/SOCP-GTRS approach effectively reduces root mean square error (RMSE) compared to other methods. These findings demonstrate that the SD/SOCP-GTRS framework consistently outperforms existing techniques, approaching the theoretical performance limit and offering a robust solution for high-precision localization in wireless sensor networks.