Limits...
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 3DLocus beacons’ positions obtained with the LAL algorithm, the WLAL algorithm and the inverse positioning method. The solid lines represent the 90% confidence ellipses of the estimated positions. (a) Beacon 2; (b) Beacon 3; (c) Beacon 4; (d) Beacon 5; (e) Beacon 6; (f) Beacon 7.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3376620&req=5

f8-sensors-12-02561: X-Y coordinates of 3DLocus beacons’ positions obtained with the LAL algorithm, the WLAL algorithm and the inverse positioning method. The solid lines represent the 90% confidence ellipses of the estimated positions. (a) Beacon 2; (b) Beacon 3; (c) Beacon 4; (d) Beacon 5; (e) Beacon 6; (f) Beacon 7.

Mentions: In Figure 8 the beacons’ position estimation obtained over one hundred trials with the LAL method, WLAL algorithm and the inverse positioning method is shown on the X-Y plane. A coordinate system was defined using the beacon 1 as origin and the beacon 2 as the X axis. As expected the standard deviation of the beacons’ position is improved by using the weighted mean instead of a simple mean of the estimated inter-beacon distances. On average, an improvement of 22% was obtained on the standard deviation on axis X and Y using the WLAL algorithm.


Error estimation for the linearized auto-localization algorithm.

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

X-Y coordinates of 3DLocus beacons’ positions obtained with the LAL algorithm, the WLAL algorithm and the inverse positioning method. The solid lines represent the 90% confidence ellipses of the estimated positions. (a) Beacon 2; (b) Beacon 3; (c) Beacon 4; (d) Beacon 5; (e) Beacon 6; (f) Beacon 7.
© Copyright Policy
Related In: Results  -  Collection

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

f8-sensors-12-02561: X-Y coordinates of 3DLocus beacons’ positions obtained with the LAL algorithm, the WLAL algorithm and the inverse positioning method. The solid lines represent the 90% confidence ellipses of the estimated positions. (a) Beacon 2; (b) Beacon 3; (c) Beacon 4; (d) Beacon 5; (e) Beacon 6; (f) Beacon 7.
Mentions: In Figure 8 the beacons’ position estimation obtained over one hundred trials with the LAL method, WLAL algorithm and the inverse positioning method is shown on the X-Y plane. A coordinate system was defined using the beacon 1 as origin and the beacon 2 as the X axis. As expected the standard deviation of the beacons’ position is improved by using the weighted mean instead of a simple mean of the estimated inter-beacon distances. On average, an improvement of 22% was obtained on the standard deviation on axis X and Y using the WLAL algorithm.

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.