A Distributed and Maximum-Likelihood Sensor Network Localization Algorithm Based Upon a Nonconvex Problem Formulation

Abstract

We propose a distributed algorithm for sensor network localization, which is based upon a decomposition of the nonlinear nonconvex maximum likelihood (ML) localization problem. Decomposition and coordination are obtained by applying the alternating direction method of multipliers (ADMM), to provide a distributed, synchronous, and nonsequential algorithm. When penalty coefficients are locally increased under specific conditions, the algorithm is proved to converge irrespective of the chosen starting point. It is also shown to be fast and accurate, providing a performance, which is equivalent to that of a centralized solver. In the comparison with existing literature on distributed sensor network localization, the proposed method involves a much lighter local processing effort, an improved robustness in non-Gaussian scenarios, and a better adherence to the original problem

Cooperative Localization in WSNs: A Hybrid Convex/Nonconvex Solution

“…This gives a gain in localization accuracy over [11], which will be shown to be rather significant. The localization accuracy of the proposed solution is equivalent to the one that can be obtained by [12], but with two relevant enhancements: a faster convergence speed and, even more importantly, a strong resilience with respect to the parameters choice which improves the algorithm robustness.…”

“…The above problem has been previously considered, e.g., in [3]- [12]. We concentrate on the more relevant solutions.…”

“…In this interpretation, working directly on the non-convex problem (1) might be a viable option. This option was investigated by Erseghe in [12], which proposes a solution based upon the alternating direction method of multipliers (ADMM) method, suitably modified in order to guarantee convergence to a local minimum also in the presence of harsh non-convexities. The plain ADMM solution is in fact known to converge only under convex problem formulations.…”

“…In this paper, we aim at bringing together the positive aspects of [11] and [12], by proposing an hybrid solution to the WSN cooperative localization problem (1). The leading idea is to exploit the convex relaxation method introduced in [11] in order to identify a starting solution which is then refinedand guaranteed to be at least a local optimum -by using the ideas developed in [12].…”

“…The leading idea is to exploit the convex relaxation method introduced in [11] in order to identify a starting solution which is then refinedand guaranteed to be at least a local optimum -by using the ideas developed in [12]. By using a relaxation we also expect to obtain a faster convergence rate than with the standard nonconvex approach, the reason simply being the higher level of coordination ensured by removing non-convexities.…”