Abstract
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 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.
Highlights
Localization requires knowledge about the reference system, such as worldwide navigation satellites
In [17], we demonstrated that if the base station positions are known and only the tag positions have to be estimated, an additional dimension in the l 2 norm of the TOA objective function transforms the local minimum to a saddle point
The self-calibration presented for the UWB and Local Position Measurement (LPM) system was based on measurements between the base stations, the reference station, and the tag
Summary
Localization requires knowledge about the reference system, such as worldwide navigation satellites. The position of the satellites is well known, and it is unlikely that one satellite will disappear and reappear in a completely different orbit This is different for most ground localization systems. Here, the problem of self-localization becomes problematic, where neither the positions of the transmitters nor the receivers are known. This is analogous to the microphone-speaker problem, where systems of (sometimes redundant or self-contradicting) quadratic equations must be solved, sometimes resulting in zero and sometimes resulting in dozens of solutions for the minimum cases (see Chapter 10 in [2]). The notations used in the text and in the equations are shown in Tables 1 and 2
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