Error estimation for indoor 802 11 location fingerprinting
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Error Estimation for Indoor 802.11 Location Fingerprinting. Outline. Introduction Error Estimation Experimental Setup and Methodology Evaluation Discussion. Introduction.

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Outline
Outline

  • Introduction

  • Error Estimation

  • Experimental Setup and Methodology

  • Evaluation

  • Discussion


Introduction
Introduction

  • Most of the research focused on the calculation of position estimates, while few attention is pay on the error estimation

  • End user could be informed about the estimated position error to avoid frustration in case the system gives faulty position information


Select of the position system
Select of the position system

  • Deterministic: Bahl (Radar)

  • Probability : Haeberlen


Error estimation
Error Estimation

  • 4 novel algorithms for error estimation

    • Off line phase

      • Fingerprint Clustering

      • Leave out Fingerprint

    • On line phase

      • Best Candidate set

      • Signal Strength Variance


Fingerprint clustering
Fingerprint Clustering

Random chose a cluster (single cell at initial time)

If (similarity between this cluster and adjacent cluster)> threshold

no

Training set fingerprint

Yes

Merged as a cluster


Fingerprint clustering1
Fingerprint Clustering

  • If the cluster which only comprise one single cell, it is merged with its most similar adjacent cluster without considering the threshold.

  • In the end, the estimated error for an estimated position is deduced from the size of the region(cluster) the estimated position is located within


Fingerprint clustering2
Fingerprint Clustering

  • Similarity measurement:

    • For each AP of a pair of clusters ,computing their mean and variance

    • Generating two Gaussian distributions:

      • Xk~G(Mxk,Uxk), Yk~G(Myk,Uyk),

      • k is the id of each ap, k=1….n

    • For each AP, computing the overlay area of their PDF : A1,A2…,An

    • If ( A1+A2+…An)/n > threshold (o.5)

      • Merge as a bigger cluster! Zk=Xk+Yk~G(Mzk,Uzk)

      • Mzk=Mxk+Myk , Uzk=Uxk+Uyk.


Leave out fingerprint
Leave Out Fingerprint

  • Create a error map

    • Create a radio map using all fingerprint except the one for position p

    • Run emulation using m samples as test data taken randomly from the fingerprint for position p

    • Calculate the observed error

    • Calculate the error estimate for position p as the average of observed errors + 2*std


Leave out fingerprint for instance
Leave Out Fingerprint (for instance)

m samples of cell 4

m observed errors :e1,e2…em

Error estimation=mean +2*std

KNN Localization

Training set without cell 4

Error map


Best candidate set knn
Best candidate set (KNN)

  • The rationale for using the n best estimates is based on the observation that positioning algorithms will often estimate a user to be at any of the nearby positions to his actual position

    • Form the set of the k best estimates as outputted from positioning system

    • Computes the distance between the position of the best estimate and all the other (k-1) best estimates.

    • Return the average distance as the estimated error


Best candidate set knn1
Best candidate set (KNN)

  • Higher values of k made the error estimates more conservative while gradually decreasing performance due to the inclusion of more faraway positions


Signal s trength v ariance
Signal Strength Variance

  • For each ap , find the largest rssi

  • Subtract the largest rssi from all the rssi samples

  • For each ap , compute the variance of samples

  • Average the variances from all the ap

  • This overall variance value can be perceived as an indicator of the expected position error


Experimental setup and methodology test environment
Experimental Setup and Methodology- test environment

  • Aarhus : 23 APs, 225 cells

  • Mannheim: 25 APs ,130 cells


Experimental setup and methodology methodology
Experimental Setup and Methodology-methodology



Evaluation over estimate vs under estimate
Evaluation-over estimate vs under estimate


Evaluation accuracy vs reliability
Evaluation- accuracy vs reliability

  • Fingerprint clustering: adjusting the similarity threshold

  • Best candidates: the number of candidates


Evaluation space and time complexity
Evaluation – space and time complexity

  • c=number of cell

  • n=number of fingerprints

  • p=time complexity of the position system

  • b= number of candidates

  • a=number of APs

  • h=number of stored samples


Conclusion
Conclusion

  • The fingerprint clustering algorithm and the best candidates set algorithm perform well.


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