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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.


Calculated standard deviation errors of distance d12 using a LPS configuration with ddop12 = {7.79, 3.57, 1.52} and a standard deviation input error ranging from 0 to 0.21 m. The correlation between the value τ and the estimated standard deviation error is shown for offline estimation in (a) and for online estimates (the 95% percentile) in (b).
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f5-sensors-12-02561: Calculated standard deviation errors of distance d12 using a LPS configuration with ddop12 = {7.79, 3.57, 1.52} and a standard deviation input error ranging from 0 to 0.21 m. The correlation between the value τ and the estimated standard deviation error is shown for offline estimation in (a) and for online estimates (the 95% percentile) in (b).

Mentions: Figure 5 shows the offline and 95% percentile online standard deviation error in percentage (compared to the one obtained by simulation) as a function of the τ value. These results are obtained for a ddop12 = {7.79, 3.57, 1.52} and a standard deviation input error ranging from 0 to 0.21 m. The graphics are limited to values of 0 ≤ τ ≤ 1.5 to focus within a reasonable range, since for values of τ > 1.5 the errors are much higher than the ones shown in the graphics.


Error estimation for the linearized auto-localization algorithm.

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

Calculated standard deviation errors of distance d12 using a LPS configuration with ddop12 = {7.79, 3.57, 1.52} and a standard deviation input error ranging from 0 to 0.21 m. The correlation between the value τ and the estimated standard deviation error is shown for offline estimation in (a) and for online estimates (the 95% percentile) in (b).
© Copyright Policy
Related In: Results  -  Collection

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

f5-sensors-12-02561: Calculated standard deviation errors of distance d12 using a LPS configuration with ddop12 = {7.79, 3.57, 1.52} and a standard deviation input error ranging from 0 to 0.21 m. The correlation between the value τ and the estimated standard deviation error is shown for offline estimation in (a) and for online estimates (the 95% percentile) in (b).
Mentions: Figure 5 shows the offline and 95% percentile online standard deviation error in percentage (compared to the one obtained by simulation) as a function of the τ value. These results are obtained for a ddop12 = {7.79, 3.57, 1.52} and a standard deviation input error ranging from 0 to 0.21 m. The graphics are limited to values of 0 ≤ τ ≤ 1.5 to focus within a reasonable range, since for values of τ > 1.5 the errors are much higher than the ones shown in the graphics.

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.