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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.


Evaluation of d12 when increasing the input standard deviation from 0 to 0.21 m. The used LPS configuration has a ddop12 of 1.52. In (a) the simulated, estimated offline and online output standard deviation. For the online estimates the mean and the 95% and 5% percentile are shown; In (b) the skewness of the distance d12 is shown.
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f4-sensors-12-02561: Evaluation of d12 when increasing the input standard deviation from 0 to 0.21 m. The used LPS configuration has a ddop12 of 1.52. In (a) the simulated, estimated offline and online output standard deviation. For the online estimates the mean and the 95% and 5% percentile are shown; In (b) the skewness of the distance d12 is shown.

Mentions: In Figure 4(a) the simulated and estimated output standard deviation of distance d12 is shown with respect to the input standard deviation. For the online estimates the mean and the 95% and 5% percentile are shown. The graph corresponds to a ddop12 of 1.52. For an input noise less than 0.1 m, the output standard deviation increments almost linearly with the input standard deviation, as predicted by Equation (18). For higher values the simulation shows that the simulated standard deviation is always higher than the obtained from Equation (18). This happens because for high input noises the assumption that the error distribution of the output distances is close to a zero mean Gaussian distribution is no longer valid. This can be verified in Figure 4(b), where it is shown how the skewness of the distance d12 increases with the input noise. Since the skewness calculated for d12 is positive, the estimated standard deviation will be always lower than the one obtained in the simulation. This shows that the estimated offline standard deviation should not be used for a high input noise. For example, a 0.1 m input noise limit can be chose for this particular LPS configuration. Figure 4(a) also shows, as expected, that the estimated online standard deviation presents a higher error with the increment of the input noise.


Error estimation for the linearized auto-localization algorithm.

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

Evaluation of d12 when increasing the input standard deviation from 0 to 0.21 m. The used LPS configuration has a ddop12 of 1.52. In (a) the simulated, estimated offline and online output standard deviation. For the online estimates the mean and the 95% and 5% percentile are shown; In (b) the skewness of the distance d12 is shown.
© Copyright Policy
Related In: Results  -  Collection

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

f4-sensors-12-02561: Evaluation of d12 when increasing the input standard deviation from 0 to 0.21 m. The used LPS configuration has a ddop12 of 1.52. In (a) the simulated, estimated offline and online output standard deviation. For the online estimates the mean and the 95% and 5% percentile are shown; In (b) the skewness of the distance d12 is shown.
Mentions: In Figure 4(a) the simulated and estimated output standard deviation of distance d12 is shown with respect to the input standard deviation. For the online estimates the mean and the 95% and 5% percentile are shown. The graph corresponds to a ddop12 of 1.52. For an input noise less than 0.1 m, the output standard deviation increments almost linearly with the input standard deviation, as predicted by Equation (18). For higher values the simulation shows that the simulated standard deviation is always higher than the obtained from Equation (18). This happens because for high input noises the assumption that the error distribution of the output distances is close to a zero mean Gaussian distribution is no longer valid. This can be verified in Figure 4(b), where it is shown how the skewness of the distance d12 increases with the input noise. Since the skewness calculated for d12 is positive, the estimated standard deviation will be always lower than the one obtained in the simulation. This shows that the estimated offline standard deviation should not be used for a high input noise. For example, a 0.1 m input noise limit can be chose for this particular LPS configuration. Figure 4(a) also shows, as expected, that the estimated online standard deviation presents a higher error with the increment of the input noise.

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.