Distributed Scaled Proximal ADMM Algorithms for Cooperative Localization in WSNs

TL;DR

This paper introduces distributed scaled proximal ADMM algorithms for cooperative localization in wireless sensor networks, reformulating the problem for improved accuracy and efficiency, with proven convergence and superior experimental performance.

Contribution

The paper proposes two novel distributed SP-ADMM algorithms for cooperative localization, offering better accuracy and lower complexity than existing semi-definite programming methods.

Findings

Algorithms converge globally to a KKT point

Achieve sublinear convergence rate of O(1/T)

Outperform state-of-the-art methods in accuracy and efficiency

Abstract

Distributed cooperative localization in wireless networks is a challenging problem since it typically requires solving a large-scale nonconvex and nonsmooth optimization problem. In this paper, we reformulate the classic cooperative localization problem as a smooth and constrained nonconvex minimization problem while its loss function is separable over nodes. By utilizing the structure of the reformulation, we propose two novel scaled proximal alternating direction method of multipliers (SP-ADMM) algorithms, which can be implemented in a distributed manner. Compared with the classic semi-definite programming relaxation techniques, the proposed algorithms can provide more accurate position estimates with significantly lower computation complexity. The associated theoretical analysis shows that our algorithms {\blue globally converge to a KKT point} of the reformulated problem and a critical point of the original problem, with a favorable sublinear $\mathcal{O}\left(1/T\right)$ convergence rate, where $T$ is the iteration counter. Numerical experiments have consistently shown that the proposed SP-ADMM algorithms are superior to state-of-the-art methods in terms of localization accuracy and computational complexity across all tested scenarios, varying network size, number of anchors, average number of neighbors, and noise variance levels.