Self-Calibration for the Time-of-Arrival Positioning

Juri Sidorenko, Volker Schatz, Dimitri Bulatov, Norbert Scherer-Negenborn, Michael Arens, Urs Hugentobler

Research output: Contribution to journalArticlepeer-review


Self-calibration of time-of-arrival positioning systems is made difficult by the non-linearity of the relevant set of equations. This work applies dimension lifting to this problem. The objective function is extended by an additional dimension to allow the dynamics of the optimization to avoid local minima. Next to the usual numerical optimization, a partially analytical method is suggested, which makes the system of equations overdetermined proportionally to the number of measurements. Results with the lifted objective function are compared to those with the unmodified objective function. For evaluation purposes, the fractions of convergence to local minima are determined, for both synthetic data with random geometrical constellations and real measurements with a reasonable constellation of base stations. It is shown that the lifted objective function provides improved convergence in all cases, often significantly so.

Original languageEnglish
Article number9056481
Pages (from-to)65726-65733
Number of pages8
JournalIEEE Access
StatePublished - 2020


  • Dimension lifting
  • self-calibration
  • time-of-arrival (TOA)


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