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Sensors 2009, 9(6), 4211-4229; doi:10.3390/s90604211

RoPEUS: A New Robust Algorithm for Static Positioning in Ultrasonic Systems

1
LOPSI group, Instituto de Automática Industrial, Consejo Superior de Investigaciones Cient´ıficas (CSIC), Ctra. Campo Real Km 0.200, 28500 La Poveda-Arganda del Rey, Madrid, Spain
2
Faculty of Business and Economics, K.U.Leuven, Naamsestraat 69, 3000 Leuven, Belgium
*
Author to whom correspondence should be addressed.
Received: 8 April 2009 / Revised: 6 May 2009 / Accepted: 14 May 2009 / Published: 3 June 2009
(This article belongs to the Special Issue Sensor Algorithms)
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Abstract

A well known problem for precise positioning in real environments is the presence of outliers in the measurement sample. Its importance is even bigger in ultrasound based systems since this technology needs a direct line of sight between emitters and receivers. Standard techniques for outlier detection in range based systems do not usually employ robust algorithms, failing when multiple outliers are present. The direct application of standard robust regression algorithms fails in static positioning (where only the current measurement sample is considered) in real ultrasound based systems mainly due to the limited number of measurements and the geometry effects. This paper presents a new robust algorithm, called RoPEUS, based on MM estimation, that follows a typical two-step strategy: 1) a high breakdown point algorithm to obtain a clean sample, and 2) a refinement algorithm to increase the accuracy of the solution. The main modifications proposed to the standard MM robust algorithm are a built in check of partial solutions in the first step (rejecting bad geometries) and the off-line calculation of the scale of the measurements. The algorithm is tested with real samples obtained with the 3D-LOCUS ultrasound localization system in an ideal environment without obstacles. These measurements are corrupted with typical outlying patterns to numerically evaluate the algorithm performance with respect to the standard parity space algorithm. The algorithm proves to be robust under single or multiple outliers, providing similar accuracy figures in all cases.
Keywords: local positioning systems; robust positioning; robust statistics; ubiquitous computing local positioning systems; robust positioning; robust statistics; ubiquitous computing
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This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Prieto, J.C.; Croux, C.; Jiménez, A.R. RoPEUS: A New Robust Algorithm for Static Positioning in Ultrasonic Systems. Sensors 2009, 9, 4211-4229.

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