Effect in range difference position estimation due to stations' position errors

Manolakis, D.E.; Cox, M. E.

doi:10.1109/7.640291

Cited by 12 publications

(6 citation statements)

References 13 publications

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“…4(b), a privileged direction of low error arises coinciding with the axis along which the sum in (20) is minimum. Although the error analysis given in [18] is not carried out for Gaussian error distributions, the provided results are consistent with the results obtained here for the first case. The results of the second case cannot be compared with previous results, because it corresponds to a singularity in which the robot is located on the base plane, which cannot be treated by previous formulations.…”

Section: A Station Location Errorssupporting

confidence: 81%

“…In turn, the covariance matrix of the position estimate error can be evaluated as The resulting covariance matrix is isotropic: the variance in the robot location is the same along any direction, say . Then (17) Finally, in terms of volume, areas, and lengths, we have (18) Assuming that the three stations are not aligned, for high distances to the base plane, (18) can be approximated by (19) and for low distances by (20) . The data-acquisition area of the system is a square area at a distance of 8000 units from the base plane, spanning in each direction from 4000 to 4000 units [see Fig.…”

Section: A Station Location Errorsmentioning

confidence: 99%

“…The station location error analysis given in [18] requires the inversion of the Jacobian matrix resulting from the linearization of system (1). Unfortunately, this inversion becomes ill-conditioned near a singularity.…”

Section: A Station Location Errorsmentioning

confidence: 99%

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Revisiting trilateration for robot localization

2005

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Abstract-Locating a robot from its distances, or range measurements, to three other known points or stations is a common operation, known as trilateration. This problem has been traditionally solved either by algebraic or numerical methods. An approach that avoids the direct algebrization of the problem is proposed here. Using constructive geometric arguments, a coordinate-free formula containing a small number of Cayley-Menger determinants is derived. This formulation accommodates a more thorough investigation of the effects caused by all possible sources of error, including round-off errors, for the first time in this context. New formulas for the variance and bias of the unknown robot location estimation, due to station location and range measurements errors, are derived and analyzed. They are proved to be more tractable compared with previous ones, because all their terms have geometric meaning, allowing a simple analysis of their asymptotic behavior near singularities.

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Section: A Station Location Errorssupporting

confidence: 81%

Section: A Station Location Errorsmentioning

confidence: 99%

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Revisiting trilateration for robot localization

2005

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“…At least, three distances are required to solve the aforementioned trilateration problem. The problem can be solved in several ways, as described in [14][15][16][17][18]. Up to this point, the location problem does not seem particularly complex; the difficulties appear when the problem involves erroneous starting data.…”

Section: Problem Formulationmentioning

confidence: 99%

Robust Estimator for Non-Line-of-Sight Error Mitigation in Indoor Localization

Casas

Marco

Guerrero

et al. 2006

EURASIP J. Adv. Signal Process.

128

107

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Indoor localization systems are undoubtedly of interest in many application fields. Like outdoor systems, they suffer from nonline-of-sight (NLOS) errors which hinder their robustness and accuracy. Though many ad hoc techniques have been developed to deal with this problem, unfortunately most of them are not applicable indoors due to the high variability of the environment (movement of furniture and of people, etc.). In this paper, we describe the use of robust regression techniques to detect and reject NLOS measures in a location estimation using multilateration. We show how the least-median-of-squares technique can be used to overcome the effects of NLOS errors, even in environments with little infrastructure, and validate its suitability by comparing it to other methods described in the bibliography. We obtained remarkable results when using it in a real indoor positioning system that works with Bluetooth and ultrasound (BLUPS), even when nearly half the measures suffered from NLOS or other coarse errors.

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“…Manolakis provided a closed-form solution to the trilateration problem [1]. He also presented a systematic error analysis method, taking into account the distance measurement error [2]. Coope derived two alternative closed-form solutions for trilateration, one based on Gaussian elimination and the other based on orthogonal decomposition and transformation [3].…”

Section: Introductionmentioning

confidence: 99%

Robot Self-Localization based on a Single Image of Identified Landmarks

Liu

2007

2007 International Symposium on Computational Intelligence in Robotics and Automation

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This paper introduces a novel self-localization algorithm for mobile robots, which recovers the robot position from a single image of identified landmarks taken by an onboard camera. The visual angle between two landmarks can be derived from their projections in the same image. The distances between the optical center and the landmarks can be calculated from the visual angles and the known landmark positions based on the law of cosine. The robot position can then be determined using the principle of trilateration. Extensive simulation has been carried out. A comprehensive error analysis provides the insight on how to improve the localization accuracy. Recently, Thomas and Ros proposed a general formulation for the closed-form solution using the Cayley-Menger determinant defined by constructive geometric arguments [4].

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Effect in range difference position estimation due to stations' position errors

Cited by 12 publications

References 13 publications

Revisiting trilateration for robot localization

Revisiting trilateration for robot localization

Robust Estimator for Non-Line-of-Sight Error Mitigation in Indoor Localization

Robot Self-Localization based on a Single Image of Identified Landmarks

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