# Robust Simultaneous Localization of Nodes and Targets in Sensor Networks Using Range-Only Measurements - Mathematics > Optimization and Control

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Abstract: Simultaneous localization and tracking SLAT in sensor networks aims todetermine the positions of sensor nodes and a moving target in a network, givenincomplete and inaccurate range measurements between the target and each of thesensors. One of the established methods for achieving this is to iterativelymaximize a likelihood function ML, which requires initialization with anapproximate solution to avoid convergence towards local extrema. This paperdevelops methods for handling both Gaussian and Laplacian noise, the lattermodeling the presence of outliers in some practical ranging systems thatadversely affect the performance of localization algorithms designed forGaussian noise. A modified Euclidean Distance Matrix EDM completion problemis solved for a block of target range measurements to approximately set upinitial sensor-target positions, and the likelihood function is theniteratively refined through Majorization-Minimization MM. To avoid thecomputational burden of repeatedly solving increasingly large EDM problems intime-recursive operation an incremental scheme is exploited whereby a newtarget-node position is estimated from previously available node-targetlocations to set up the iterative ML initial point for the full spatialconfiguration. The above methods are first derived under Gaussian noiseassumptions, and modifications for Laplacian noise are then considered.Analytically, the main challenges to be overcome in the Laplacian case stemfrom the non-differentiability of $\ell 1$ norms that arise in the various costfunctions. Simulation results confirm that the proposed algorithmssignificantly outperform existing methods for SLAT in the presence of outliers,while offering comparable performance for Gaussian noise.

Autor: Pınar Oğuz-Ekim, João Gomes, João Xavier, Paulo Oliveira

Fuente: https://arxiv.org/