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.

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Bibtex:

@article{Soares_2015,
    author = "Soares, Claudia and Xavier, Joao and Gomes, Joao",
    title = "Simple and Fast Convex Relaxation Method for Cooperative Localization in Sensor Networks Using Range Measurements",
    volume = "63",
    ISSN = "1941-0476",
    url = "http://dx.doi.org/10.1109/tsp.2015.2454853",
    DOI = "10.1109/tsp.2015.2454853",
    number = "17",
    journal = "IEEE Transactions on Signal Processing",
    publisher = "Institute of Electrical and Electronics Engineers (IEEE)",
    year = "2015",
    month = "Sept",
    pages = "4532-4543",
    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.",
    keywords = "Complexity theory;Convergence;Maximum likelihood estimation;Noise measurement;Optimization;Robot sensing systems;Signal processing algorithms;Convex relaxations;distributed algorithms;distributed iterative sensor localization;maximum likelihood estimation;nonconvex optimization;wireless sensor networks"
}