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Sensors 2012, 12(3), 2561-2581; doi:10.3390/s120302561
Article

Error Estimation for the Linearized Auto-Localization Algorithm

* ,
,
 and
Centro de Automática y Robótica (CAR), Consejo Superior de Investigaciones Científicas (CSIC)-UPM, Ctra. Campo Real km 0.2, La Poveda-Arganda del Rey, 28500, Madrid, Spain
* Author to whom correspondence should be addressed.
Received: 6 January 2012 / Revised: 17 February 2012 / Accepted: 20 February 2012 / Published: 24 February 2012
(This article belongs to the Special Issue Sensorial Systems Applied to Intelligent Spaces)
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Abstract

The Linearized Auto-Localization (LAL) algorithm estimates the position of beacon nodes in Local Positioning Systems (LPSs), using only the distance measurements to a mobile node whose position is also unknown. The LAL algorithm calculates the inter-beacon distances, used for the estimation of the beacons’ positions, from the linearized trilateration equations. In this paper we propose a method to estimate the propagation of the errors of the inter-beacon distances obtained with the LAL algorithm, based on a first order Taylor approximation of the equations. Since the method depends on such approximation, a confidence parameter τ is defined to measure the reliability of the estimated error. Field evaluations showed that by applying this information to an improved weighted-based auto-localization algorithm (WLAL), the standard deviation of the inter-beacon distances can be improved by more than 30% on average with respect to the original LAL method.
Keywords: auto-localization; auto-calibration; local positioning systems; differential sensitivity analysis; uncertainty propagation auto-localization; auto-calibration; local positioning systems; differential sensitivity analysis; uncertainty propagation
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Guevara, J.; Jiménez, A.R.; Prieto, J.C.; Seco, F. Error Estimation for the Linearized Auto-Localization Algorithm. Sensors 2012, 12, 2561-2581.

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