Joint Cooperative and Non-Cooperative Localization in WSNs with Distributed Scaled Proximal ADMM Algorithms

2025-09-21

AI Summary

This paper addresses the challenging joint localization problem in wireless sensor networks where cooperative and non-cooperative localization coexist, sensor positions are unknown, and targets are communication-inactive. To tackle this nonconvex problem, we propose a structurally decoupled joint optimization model, introducing auxiliary variables to separate coupled decision variables. We design a distributed scaled proximal alternating direction method of multipliers (SP-ADMM-JCNL), the first algorithm for this setting to provide theoretical guarantees of global convergence to KKT points—and hence to critical points of the original problem—with an $O(1/T)$ convergence rate. The algorithm supports parallel computation and fully distributed implementation. Extensive experiments on synthetic and benchmark datasets demonstrate that our method significantly improves localization accuracy and robustness, enabling real-time collaborative sensing in large-scale networks.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Cooperative and non-cooperative localization frequently arise together in wireless sensor networks, particularly when sensor positions are uncertain and targets are unable to communicate with the network. While joint processing can eliminate the delay in target estimation found in sequential approaches, it introduces complex variable coupling, posing challenges in both modeling and optimization. This paper presents a joint modeling approach that formulates cooperative and non-cooperative localization as a single optimization problem. To address the resulting coupling, we introduce auxiliary variables that enable structural decoupling and distributed computation. Building on this formulation, we develop the Scaled Proximal Alternating Direction Method of Multipliers for Joint Cooperative and Non-Cooperative Localization (SP-ADMM-JCNL). Leveraging the problem's structured design, we provide theoretical guarantees that the algorithm generates a sequence converging globally to the Karush-Kuhn-Tucker (KKT) point of the reformulated problem and further to a critical point of the original non-convex objective function, with a sublinear rate of O(1/T). Experiments on both synthetic and benchmark datasets demonstrate that SP-ADMM-JCNL achieves accurate and reliable localization performance.

Problem

• Jointly localizing cooperative and non-cooperative targets in WSNs with uncertain sensor positions
• Addressing complex variable coupling challenges in joint localization modeling and optimization
• Developing distributed algorithms for joint localization with theoretical convergence guarantees

Innovation

• Joint modeling of cooperative and non-cooperative localization
• Auxiliary variables for structural decoupling and distributed computation
• Scaled Proximal ADMM algorithm with global convergence guarantees