Self-Calibration for the Time Difference of Arrival Positioning

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 l 2 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.2 of 15 common and often combined systems are the DecaWave Ultra-Wideband (UWB) and the Abatec Local Position Measurement (LPM) system. The DecaWave UWB system is less affected by reflections, but is, due to regulations, limited in its transmitting power. The LPM system faces the opposite problem. However, 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]). In the few related works outlined below, it is therefore commonplace to find overdetermined systems of equations. From a reliable solution and a suitable optimizer, these systems are developed to converge to the global minimum and thus successfully self-localize the sensors.The notations used in the text and in the equations are shown in Tables 1 and 2.

Future Research and Trends in Ultra-Wideband Indoor Tag Localization

“…Hammer uses another method using TWR and Gauss-Newton algorithms for localization estimation [102], and Batstone proposes self-calibration in the 3D environment for LOS conditions [166]. Self-calibration using TDoA is proposed by Sidorenko et al for dimension lifting [167].…”

Low-Cost UWB Based Real-Time Locating System: Development, Lab Test, Industrial Implementation and Economic Assessment

“…[ 26 ] designed and manufactured a mechanically flexible textile antenna-backed sensor node by applying Qorvo MDEK1001, again without any real application; Ref. [ 27 ] deepened the topic of self-calibration for the time difference of arrival positioning when dealing with the system in question; Ref. [ 28 ] dealt with its clock drift and signal power, from a technical perspective, while ref.…”

Distance Measurements in UWB-Radio Localization Systems Corrected with a Feedforward Neural Network Model

“…In real-time localization systems (RTLSs), the tags (agents, mobile units) are localized by measuring the distances from the tag to the anchors (ground station, static units) with known positions. The distances between the anchors and the tags can be measured with the time-of-arrival (TOA) [ 8 ] or the time-difference-of-arrival (TDOA) [ 9 ] methods. The accuracy of the measured distances depends on the accuracy of the tag’s position [ 10 ].…”