Error Estimation for Indoor 802.11 Location Fingerprinting

Outline Introduction Error Estimation Experimental Setup and

MethodologyEvaluation Discussion

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 systemDeterministic: Bahl (Radar)Probability : Haeberlen

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

If (similarity between this cluster and

adjacent cluster)> threshold

Merged as a cluster

ap1 ap2 ap3 …

Cell1

-80 -70 -90 …

Cell2

-96 -55 -11 …

Cell3

-45 -100

-70 …

…

…

Random chose a cluster (single cell at initial time)

Yes

no

Training set fingerprint

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 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 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)

Ap1 Ap2

Cell 1

-89 -100

Cell 2

-97 -62

Cell 3

-45 -55

Cell 5

-64 -70

…

ap1 ap2

1 -100

-60

2 -100

-50

3 -100

-45

4 -100

-53

5 -100

-55

…

m samples of cell 4

Training set without cell 4

KNN Localization

m observed errors :e1,e2…em

Error estimation=mean +2*std

Cell 1

Cell 2

Cell 3

Cell 4

Cell 5

5 2 3 4.5 …

Error map

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 (KNN) Higher values of k made the error

estimates more conservative while gradually decreasing performance due to the inclusion of more faraway positions

Signal Strength Variance For each ap , find the largest rssiSubtract 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 Aarhus : 23 APs, 225 cells

Mannheim: 25 APs ,130 cells

Experimental Setup and Methodology-methodology

Evaluation

Evaluation-over estimate vs under estimate

Evaluation- accuracy vs reliability Fingerprint clustering: adjusting

the similarity threshold Best candidates: the number of

candidates

Evaluation – space and time complexity

c=number of celln=number of fingerprintsp=time complexity of the position

systemb= number of candidates a=number of APsh=number of stored samples

Conclusion The fingerprint clustering

algorithm and the best candidates set algorithm perform well.