| Summary: | The time-difference-of-arrival (TDOA) self-calibration is an important topic for many applications, such as indoor navigation. One of the most common methods is to perform nonlinear optimization. Unfortunately, optimization often gets stuck in a local minimum. Here, we propose a method of dimension lifting by adding an additional variable into the <inline-formula> <math display="inline"> <semantics> <msup> <mi>l</mi> <mn>2</mn> </msup> </semantics> </math> </inline-formula> norm of the objective function. Next to the usual numerical optimization, a partially-analytical method is suggested, which overdetermines the system of equations proportionally to the number of measurements. The effect of dimension lifting on the TDOA self-calibration is verified by experiments with synthetic and real measurements. In both cases, self-calibration is performed for two very common and often combined localization systems, the DecaWave Ultra-Wideband (UWB) and the Abatec Local Position Measurement (LPM) system. The results show that our approach significantly reduces the risk of becoming trapped in a local minimum.
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