Abstract-We address the sensor network localization problem given noisy range measurements between pairs of nodes. We approach the nonconvex maximum-likelihood formulation via a known simple convex relaxation. We exploit its favorable optimization properties to the full to obtain an approach that: is completely distributed, has a simple implementation at each node, and capitalizes on an optimal gradient method to attain fast convergence. We offer a parallel but also an asynchronous flavor, both with theoretical convergence guarantees and iteration complexity analysis. Experimental results establish leading performance. Our algorithms top the accuracy of a comparable state of the art method by one order of magnitude, using one order of magnitude fewer communications.

Abstract-We propose a simple, stable and distributed algorithm which directly optimizes the nonconvex maximum likelihood criterion for sensor network localization, with no need to tune any free parameter. We reformulate the problem to obtain a gradient Lipschitz cost; by shifting to this cost function we enable a Majorization-Minimization (MM) approach based on quadratic upper bounds that decouple across nodes; the resulting algorithm happens to be distributed, with all nodes working in parallel. Our method inherits the MM stability: each communication cuts down the cost function. Numerical simulations indicate that the proposed approach tops the performance of the state of the art algorithm, both in accuracy and communication cost.

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How to self-localize large teams of underwater nodes using only noisy range measurements? How to do it in a distributed way, and incorporating dynamics into the problem? How to reject outliers and produce trustworthy position estimates? The stringent acoustic communication channel and the accuracy needs of our geophysical survey application demand faster and more accurate localization methods. We approach dynamic localization as a MAP estimation problem where the prior encodes dynamics, and we devise a convex relaxation method that takes advantage of previous estimates at each measurement acquisition step; The algorithm converges at an optimal rate for first order methods. LocDyn is distributed: there is no fusion center responsible for processing acquired data and the same simple computations are performed for each node. LocDyn is accurate: experiments attest to a smaller positioning error than a comparable Kalman filter. LocDyn is robust: it rejects outlier noise, while the comparing methods succumb in terms of positioning error.

Real-world network applications must cope with failing nodes, malicious attacks, or nodes facing corrupted data -data classified as outliers. Our work addresses these concerns in the scope of the sensor network localization problem where, despite the abundance of technical literature, prior research seldom considered outlier data. We propose robust, fast, and distributed network localization algorithms, resilient to high-power noise, but also precise under regular Gaussian noise. We use a Huber M-estimator, thus obtaining a robust (but nonconvex) optimization problem. We convexify and change the problem representation, to allow for distributed robust localization algorithms: a synchronous distributed method that has optimal convergence rate and an asynchronous one with proven convergence guarantees. A major highlight of our contribution lies on the fact that we pay no price for provable distributed computation neither in accuracy, nor in communication cost or convergence speed. Simulations showcase the superior performance of our algorithms, both in the presence of outliers and under regular Gaussian noise: our method exceeds the accuracy of alternative approaches, distributed and centralized, even under heavy additive and multiplicative outlier noise.

We propose hybrid methods for localization in wireless sensor networks fusing noisy range measurements with angular information (extracted from video). Compared with conventional methods that rely on a single sensed variable, this may pave the way for improved localization accuracy and robustness. We address both the single-source and network (i.e., cooperative multiple-source) localization paradigms, solving them via optimization of a convex surrogate. The formulations for hybrid localization are unified in the sense that we propose a single nonlinear least-squares cost function, fusing both angular and range measurements. We then relax the problem to obtain an estimate of the optimal positions. This contrasts with other hybrid approaches that alternate the execution of localization algorithms for each type of measurement separately, to progressively refine the position estimates. Single-source localization uses a semidefinite relaxation to obtain a one-shot matrix solution from which the source position is derived through factorization. Network localization uses a different approach where sensor coordinates are retained as optimization variables, and the relaxed cost function is efficiently minimized using fast iterations based on Nesterov's optimal method. Further, an automated calibration procedure is developed to express range and angular information, obtained through different devices, possibly deployed at different locations, in a single consistent coordinate system. This drastically reduces the need for manual calibration that would otherwise negatively impact the practical usability of hybrid range/video localization systems. We develop and test, both in simulation and experimentally, the new hybrid localization algorithms, which not only overcome the limitations of previous fusing approaches, but also compare favourably to state-of-the-art methods, even outperforming them in some scenarios.