1. Error Estimation for Indoor 802.11 Location Fingerprinting

2. Outline Introduction Error Estimation Experimental Setup and Methodology Evaluation Discussion

3. 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

4. Select of the position system Deterministic: Bahl (Radar) Probability : Haeberlen

5. 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

6. Fingerprint Clustering If (similarity between this cluster and adjacent cluster)> threshold Merged as a cluster ap1ap2ap3… 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

7. 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

8. 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.

9. 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

10. Leave Out Fingerprint (for instance) Ap1Ap2 Cell 1-89-100 Cell 2-97-62 Cell 3-45-55 Cell 5-64-70 … ap1ap2 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 1Cell 2Cell 3Cell 4Cell 5 5234.5… Error map

11. 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

12. 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

13. 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

14. Experimental Setup and Methodology- test environment Aarhus : 23 APs, 225 cells Mannheim: 25 APs,130 cells

15. Experimental Setup and Methodology-methodology

16. Evaluation

17. Evaluation-over estimate vs under estimate

18. Evaluation- accuracy vs reliability Fingerprint clustering: adjusting the similarity threshold Best candidates: the number of candidates

19. 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

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