Error Estimation for Indoor 802.11 Location Fingerprinting

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 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

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) 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

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.