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Error estimation for the linearized auto-localization algorithm.

Guevara J, Jiménez AR, Prieto JC, Seco F - Sensors (Basel) (2012)

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Centro de Automática y Robótica (CAR), Consejo Superior de Investigaciones Científicas (CSIC)-UPM, Madrid, Spain. jorge.guevara@csic.es

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.

No MeSH data available.


X-Y coordinates of beacon 5 obtained by simulation. The simulation does not presents the bias observed in the experimental test with the 3Dlocus LPS.
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f9-sensors-12-02561: X-Y coordinates of beacon 5 obtained by simulation. The simulation does not presents the bias observed in the experimental test with the 3Dlocus LPS.

Mentions: To evaluate these hypotheses, we simulated a LPS using the positions obtained with the inverse positioning as the real location of the beacons, but positioning them in the same plane (by setting the Z coordinate to be zero on all beacons) and using simulated measurements with the same standard deviation. The simulation showed no bias between the methods in any beacon, as can be seen for the fifth beacon in Figure 9, showing that the effect of the higher terms of the noise is negligible. When the beacons were not placed in the same plane, the simulation showed a bias between all the auto-localization methods. Using the beacon’s altitude obtained with the inverse positioning, the simulation showed a bias of 5 mm for the fifth beacon. Finally, systematic range errors originated from the actual LPS can also add to the bias observed [22] (e.g., the range measurement is affected by the orientation between the beacon and the mobile node). Any error originated by this bias and also the small height variation between beacons can be compensated using an optimization algorithm such as the ones used in [6–8]. The WLAL solution could be used as a first estimation of the beacons position, since with a 1.5 cm offset any optimization algorithm will easily converge to a more accurate solution.


Error estimation for the linearized auto-localization algorithm.

Guevara J, Jiménez AR, Prieto JC, Seco F - Sensors (Basel) (2012)

X-Y coordinates of beacon 5 obtained by simulation. The simulation does not presents the bias observed in the experimental test with the 3Dlocus LPS.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3376620&req=5

f9-sensors-12-02561: X-Y coordinates of beacon 5 obtained by simulation. The simulation does not presents the bias observed in the experimental test with the 3Dlocus LPS.
Mentions: To evaluate these hypotheses, we simulated a LPS using the positions obtained with the inverse positioning as the real location of the beacons, but positioning them in the same plane (by setting the Z coordinate to be zero on all beacons) and using simulated measurements with the same standard deviation. The simulation showed no bias between the methods in any beacon, as can be seen for the fifth beacon in Figure 9, showing that the effect of the higher terms of the noise is negligible. When the beacons were not placed in the same plane, the simulation showed a bias between all the auto-localization methods. Using the beacon’s altitude obtained with the inverse positioning, the simulation showed a bias of 5 mm for the fifth beacon. Finally, systematic range errors originated from the actual LPS can also add to the bias observed [22] (e.g., the range measurement is affected by the orientation between the beacon and the mobile node). Any error originated by this bias and also the small height variation between beacons can be compensated using an optimization algorithm such as the ones used in [6–8]. The WLAL solution could be used as a first estimation of the beacons position, since with a 1.5 cm offset any optimization algorithm will easily converge to a more accurate solution.

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Centro de Automática y Robótica (CAR), Consejo Superior de Investigaciones Científicas (CSIC)-UPM, Madrid, Spain. jorge.guevara@csic.es

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.

No MeSH data available.