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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.


Experimental evaluation of the estimated distance d12 obtained with different beacons’ subsets. In (a) the estimated online and measured ddop12; In (b) the histogram of the calculated distance d12 obtained using the beacons’ subset {1, 2, 3}.
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f7-sensors-12-02561: Experimental evaluation of the estimated distance d12 obtained with different beacons’ subsets. In (a) the estimated online and measured ddop12; In (b) the histogram of the calculated distance d12 obtained using the beacons’ subset {1, 2, 3}.

Mentions: Figure 7(a) shows the estimated online and measured distance dilution of precision ddop12 obtained with different subsets of beacons. The measured ddop12 was calculated by dividing the standard deviation of the calculated distance d12 by the standard deviation of the distance measurements DM. In most cases the estimated value is slightly lower than the actual ddop12 obtained in the 3DLocus, though the difference is always below 30%. One reason for this difference is that we are using a mean standard deviation of 0.23 mm for all the 3DLocus measurements while the actual value of the measurements’ errors depends on various factors such as the distance and angle between nodes. In Figure 7(b) the histogram of the calculated distance d12 obtained using the beacons’ subset {1, 2, 3} is shown. As can be observed, the error distribution of the calculated distance resembles a Gaussian distribution. In order to verify the assumption of a Gaussian error distribution on all the calculated inter-beacon distances, we run a Lilliefors test for normality [20]. The test established with a p-value of 0.05 that the error distribution on the calculated inter-beacon distances approximates a normal distribution (i.e., there is a 5% probability that the normality is a false positive).


Error estimation for the linearized auto-localization algorithm.

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

Experimental evaluation of the estimated distance d12 obtained with different beacons’ subsets. In (a) the estimated online and measured ddop12; In (b) the histogram of the calculated distance d12 obtained using the beacons’ subset {1, 2, 3}.
© Copyright Policy
Related In: Results  -  Collection

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

f7-sensors-12-02561: Experimental evaluation of the estimated distance d12 obtained with different beacons’ subsets. In (a) the estimated online and measured ddop12; In (b) the histogram of the calculated distance d12 obtained using the beacons’ subset {1, 2, 3}.
Mentions: Figure 7(a) shows the estimated online and measured distance dilution of precision ddop12 obtained with different subsets of beacons. The measured ddop12 was calculated by dividing the standard deviation of the calculated distance d12 by the standard deviation of the distance measurements DM. In most cases the estimated value is slightly lower than the actual ddop12 obtained in the 3DLocus, though the difference is always below 30%. One reason for this difference is that we are using a mean standard deviation of 0.23 mm for all the 3DLocus measurements while the actual value of the measurements’ errors depends on various factors such as the distance and angle between nodes. In Figure 7(b) the histogram of the calculated distance d12 obtained using the beacons’ subset {1, 2, 3} is shown. As can be observed, the error distribution of the calculated distance resembles a Gaussian distribution. In order to verify the assumption of a Gaussian error distribution on all the calculated inter-beacon distances, we run a Lilliefors test for normality [20]. The test established with a p-value of 0.05 that the error distribution on the calculated inter-beacon distances approximates a normal distribution (i.e., there is a 5% probability that the normality is a false positive).

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.