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Improved Time of Arrival measurement model for non-convex optimization

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

Postprint urn:nbn:de:0011-n-5251117 (684 KByte PDF)
MD5 Fingerprint: fde47bece18808c93af51571bacada6b
Erstellt am: 09.01.2020

Navigation 66 (2019), Nr.1, S.117-128
ISSN: 2161-4296
ISSN: 0028-1522
Zeitschriftenaufsatz, Elektronische Publikation
Fraunhofer IOSB ()
navigation; time of arrival; non-linear optimization

The quadratic system provided by the Time of Arrival technique can be solved analytically or by non-linear least squares minimization. An important problem in quadratic optimization is the possible convergence to a local minimum, instead of the global minimum. This problem does not occur for global navigation satellite system (GNSS), due to the known satellite positions. In applications with unknown positions of the reference stations, such as indoor localization with self-calibration, local minima are an important issue. This article presents an approach showing how this risk can be significantly reduced. 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.