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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.


Output quadratic mean standard deviation σmean obtained when changing the center of the virtual nodes path: (a) obtained by simulation (1,000 times); (b) estimated offline. In (c) estimated σmean obtained with the offline and online methods compared to simulation.
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f3-sensors-12-02561: Output quadratic mean standard deviation σmean obtained when changing the center of the virtual nodes path: (a) obtained by simulation (1,000 times); (b) estimated offline. In (c) estimated σmean obtained with the offline and online methods compared to simulation.

Mentions: To evaluate the DSA method we calculated the quadratic mean output standard deviation , of the inter-beacon distances DU, obtained when shifting the center of the virtual nodes path of the LPS configuration (Figure 2). The resultant standard deviation maps obtained by simulation (Figure 3(a)) and by offline estimation (Figure 3(b)) match almost exactly. The advantage of the offline estimation over the simulation is that the calculation processes of the maps are computationally more efficient. The evaluation of the standard deviation maps can be very useful to analyse the ideal route path of the virtual nodes. For example, in Figure 3(b) it is shown that the ideal position of the center of the path is near the central point of the beacons (1.5 m,1.3 m). If the center of the path is far from the central point, σmean can increase up to 8 cm, that is, eight times the input standard deviation.


Error estimation for the linearized auto-localization algorithm.

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

Output quadratic mean standard deviation σmean obtained when changing the center of the virtual nodes path: (a) obtained by simulation (1,000 times); (b) estimated offline. In (c) estimated σmean obtained with the offline and online methods compared to simulation.
© Copyright Policy
Related In: Results  -  Collection

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

f3-sensors-12-02561: Output quadratic mean standard deviation σmean obtained when changing the center of the virtual nodes path: (a) obtained by simulation (1,000 times); (b) estimated offline. In (c) estimated σmean obtained with the offline and online methods compared to simulation.
Mentions: To evaluate the DSA method we calculated the quadratic mean output standard deviation , of the inter-beacon distances DU, obtained when shifting the center of the virtual nodes path of the LPS configuration (Figure 2). The resultant standard deviation maps obtained by simulation (Figure 3(a)) and by offline estimation (Figure 3(b)) match almost exactly. The advantage of the offline estimation over the simulation is that the calculation processes of the maps are computationally more efficient. The evaluation of the standard deviation maps can be very useful to analyse the ideal route path of the virtual nodes. For example, in Figure 3(b) it is shown that the ideal position of the center of the path is near the central point of the beacons (1.5 m,1.3 m). If the center of the path is far from the central point, σmean can increase up to 8 cm, that is, eight times the input standard deviation.

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.