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

arXiv: https://arxiv.org/abs/2509.18213 · HTML: https://mlsanity.com/paper/2509.18213/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 36 references that are in the map.
- First posted on arXiv 21 Sep 2025.

## Builds on (most cited first, 7 of 7)

- [NEXT: In-Network Nonconvex Optimization](https://mlsanity.com/paper/1602.00591/) (2016)
- [First Order Methods beyond Convexity and Lipschitz Gradient Continuity with Applications to Quadratic Inverse Problems](https://mlsanity.com/paper/1706.06461/) (2017)
- [Cooperative Localization and Multitarget Tracking in Agent Networks with the Sum-Product Algorithm](https://mlsanity.com/paper/2108.02573/) (2021)
- [Local Strong Convexity of Source Localization and Error Bound for Target Tracking under Time-of-Arrival Measurements](https://mlsanity.com/paper/2112.11045/) (2021)
- [A Distributed Approach for the Optimal Power Flow Problem Based on ADMM and Sequential Convex Approximations](https://mlsanity.com/paper/1401.4621/) (2014)
- [Alternating Minimization Based First-Order Method for the Wireless Sensor Network Localization Problem](https://mlsanity.com/paper/2010.06959/) (2020)
- [Distributed Scaled Proximal ADMM Algorithms for Cooperative Localization in WSNs](https://mlsanity.com/paper/2208.12005/) (2022)

## Abstract (arXiv)

The integration of cooperative and non-cooperative localization is fundamentally important, as these two modes frequently coexist in wireless sensor networks, especially when sensor positions are uncertain and targets are unable to communicate with the network. This paper presents a joint modeling approach that formulates cooperative and non-cooperative localization as a single optimization problem. By processing both tasks jointly, the proposed method eliminates the latency inherent in sequential approaches that perform cooperative localization first, followed by non-cooperative localization. However, this joint formulation introduces complex variable coupling, posing challenges in both modeling and optimization. To address this coupling, we introduce auxiliary variables that enable structural decoupling and facilitate 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 structured design of the problem, we provide theoretical guarantees that the algorithm generates a sequence converging globally to a KKT point of the reformulated problem, and further to a critical point of the original non-convex objective function, with the convergence rate of O(1/T). Experiments demonstrate that SP-ADMM-JCNL achieves accurate and reliable localization performance.