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Improved time of arrival measurement model for non-convex optimization with noisy data

: Sidorenko, Juri; Schatz, Volker; Scherer-Negenborn, Norbert; Arens, Michael; Hugentobler, Urs


Institute of Electrical and Electronics Engineers -IEEE-:
IPIN 2018, Ninth International Conference on Indoor Positioning and Indoor Navigation : September 24-27, 2018, Nantes, France
Piscataway, NJ: IEEE, 2018
ISBN: 978-1-5386-5635-8
ISBN: 978-1-5386-5636-5
International Conference on Indoor Positioning and Indoor Navigation (IPIN) <9, 2018, Nantes>
Fraunhofer IOSB ()
localization; navigation; time of arrival

The quadratic system provided by the Time of Arrival technique can be solved analytical or by non-linear least squares minimization. In real environments the measurements are always corrupted by noise. This measurement noise effects the analytical solution more than non-linear optimization algorithms. On the other hand it is also true that local optimization tends to find the local minimum, instead of the global minimum. This article presents an approach how this risk can be significantly reduced in noisy environments. The main idea of our approach is to transform the local minimum to a saddle point, by increasing the number of dimensions. In addition to numerical tests we analytically prove the theorem and the criteria that no other local minima exists for non-trivial constellations.