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.


Solvable node subset composed by three beacon nodes and six virtual nodes on a plane.
© Copyright Policy
Related In: Results  -  Collection

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

f1-sensors-12-02561: Solvable node subset composed by three beacon nodes and six virtual nodes on a plane.

Mentions: In [10] a new solution for the auto-localization problem of 3D LPSs was presented based on the distance measurements between beacons and the mobile node. While other techniques require an external positioning system (e.g., a second LPS or an odometric sensor) to estimate the positions of the mobile node, the proposed method uses only the measurements available to the LPS being used for mobile node location. The method is based on the linearization of the trilateration equations by grouping nonlinear terms in additional variables. The LAL algorithm is defined for the case where all the beacons are located in a plane parallel to the plane containing the mobile node trajectory. For this particular configuration, a solvable initial subset of three beacon nodes is obtained based on [11]. Figure 1 shows the auto-localization configuration for n = 3 beacon nodes Ni, i = {1, 2, 3} and m measurement points Nj, j = {4, . . ., m + 3} from the mobile node path. For n = 3 beacons nodes a minimum of m = 6 measurements points are required [11], though more measurement points can be added to improve the estimated solution. From now on, the measurement points of the mobile node will be referred to as virtual nodes.


Error estimation for the linearized auto-localization algorithm.

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

Solvable node subset composed by three beacon nodes and six virtual nodes on a plane.
© Copyright Policy
Related In: Results  -  Collection

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

f1-sensors-12-02561: Solvable node subset composed by three beacon nodes and six virtual nodes on a plane.
Mentions: In [10] a new solution for the auto-localization problem of 3D LPSs was presented based on the distance measurements between beacons and the mobile node. While other techniques require an external positioning system (e.g., a second LPS or an odometric sensor) to estimate the positions of the mobile node, the proposed method uses only the measurements available to the LPS being used for mobile node location. The method is based on the linearization of the trilateration equations by grouping nonlinear terms in additional variables. The LAL algorithm is defined for the case where all the beacons are located in a plane parallel to the plane containing the mobile node trajectory. For this particular configuration, a solvable initial subset of three beacon nodes is obtained based on [11]. Figure 1 shows the auto-localization configuration for n = 3 beacon nodes Ni, i = {1, 2, 3} and m measurement points Nj, j = {4, . . ., m + 3} from the mobile node path. For n = 3 beacons nodes a minimum of m = 6 measurements points are required [11], though more measurement points can be added to improve the estimated solution. From now on, the measurement points of the mobile node will be referred to as virtual nodes.

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.