Cláudia Soares

Simple and Fast Convex Relaxation Method for Cooperative Localization in Sensor Networks Using Range Measurements

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.

Distributed, simple and stable network localization

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.

FLORIS and CLORIS: Hybrid source and network localization based on ranges and video

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 via 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 Nesterovs optimal method. Further, an automated calibration procedure is developed to express range and angular information, obtained by 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 favorably to state-of-the-art methods, outperforming them in some scenarios.

LocDyn: Robust Distributed Localization for Mobile Underwater Networks

How do we self-localize large teams of underwater nodes using only noisy range measurements? How do we do it in a distributed way, and incorporating dynamics into the problem? How do we reject outliers and produce trustworthy position estimates? And what if some of the vehicles can measure angular information? The stringent acoustic communication constraints and accuracy needs of our geophysical survey application demand fast and very accurate localization methods. We address dynamic localization as a MAP estimation problem where the prior encodes kinematic information, and we apply a convex relaxation method that takes advantage of previous estimates at each measurement acquisition step. The resulting LocDyn algorithm is fast: It 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 at each node. LocDyn is accurate: Numerical experiments attest to about 30% smaller positioning error than a comparable Kalman filter. LocDyn is robust: It rejects outlier noise, while benchmarking methods succumb in terms of positioning error.