Robust time-of-arrival self calibration with missing data and outliers

Batstone, Kenneth; Oskarsson, Magnus; Åström, Kalle

doi:10.1109/eusipco.2016.7760673

Cited by 14 publications

(9 citation statements)

References 20 publications

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“…The most robust self-calibration solution with noise is nonlinear optimization. 12 This solution suffers if the initial estimates are not close to the global minimum. [13][14][15] In Mekonnen and Wittneben 16 and Biswas et al, 17 it was proposed to use semi-definite relaxation (SDP) as an initialization for the maximum likelihood (ML) estimator.…”

Section: Introductionmentioning

confidence: 99%

“…Real measurement data are highly non-convex and nonlinear optimization still provides the most robust solutions. 12 We present a new approach which does not require an initial estimate at all. The idea is that an additional dimension in the l 2 norm transforms the local minimum of the ToA equation to a saddle point without adding more local minima.…”

Section: Introductionmentioning

confidence: 99%

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Improved Time of Arrival measurement model for non‐convex optimization

et al. 2019

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The quadratic system provided by the Time of Arrival technique can be solved analytically or by nonlinear 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 Systems (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

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Improved Time of Arrival measurement model for non‐convex optimization

et al. 2019

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“…The approach was based on non-linear regression analysis where the missing observations were treated as Missing Not at Random (MNAR). Similar ideas were proposed in [22,23]. However, the support for this technology depends on a used chipset.…”

Section: Related Workmentioning

confidence: 91%

Automatic Detection of Missing Access Points in Indoor Positioning System †

Górak

Luckner

2018

Sensors

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The paper presents a Wi-Fi-based indoor localisation system. It consists of two main parts, the localisation model and an Access Points (APs) detection module. The system uses a received signal strength (RSS) gathered by multiple mobile terminals to detect which AP should be included in the localisation model and whether the model needs to be updated (rebuilt). The rebuilding of the localisation model prevents the localisation system from a significant loss of accuracy. The proposed automatic detection of missing APs has a universal character and it can be applied to any Wi-Fi localisation model which was created using the fingerprinting method. The paper considers the localisation model based on the Random Forest algorithm. The system was tested on data collected inside a multi-floor academic building. The proposed implementation reduced the mean horizontal error by 5.5 m and the classification error for the floor’s prediction by 0.26 in case of a serious malfunction of a Wi-Fi infrastructure. Several simulations were performed, taking into account different occupancy scenarios as well as different numbers of missing APs. The simulations proved that the system correctly detects missing and present APs in the Wi-Fi infrastructure.

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“…The most common approach for self-calibration is to perform nonlinear optimization [3]. This solution has the disadvantage that if the initial estimates are unfavorable, the optimization becomes stuck in a local minimum [4].…”

Section: Related Workmentioning

confidence: 99%

Self-Calibration for the Time Difference of Arrival Positioning

Sidorenko

Schatz

Bulatov

et al. 2020

Sensors

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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.

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Robust time-of-arrival self calibration with missing data and outliers

Cited by 14 publications

References 20 publications

Improved Time of Arrival measurement model for non‐convex optimization

Improved Time of Arrival measurement model for non‐convex optimization

Automatic Detection of Missing Access Points in Indoor Positioning System †

Self-Calibration for the Time Difference of Arrival Positioning

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