Continuous Estimation in WLAN Positioning

1. Continuous Estimation in WLAN Positioning By Tilen Ma Clarence Fung

2. Objective • Area-Based Probability (ABP) • Continuous Space Estimation(CSE) • Center of Mass • Time-Averaging • Point Mapping • Conclusion

3. Applying Area-based Approach

4. Area-Based Probability (ABP) Advantages: • Presents the user an understanding of the system in a more natural and intuitive manner • High accuracy • More mathematical approach

5. Steps in using ABP Decide the Areas Measure Signals at Different Areas Create a Training Set Create a Testing Set Measure Signals at Current Position Find out the Probability of Being at Different Areas Calculate Probability Density Return the Area with Highest Probability

6. Area Based Probability • We compute P(St |Ai) for every area Ai ,i=1…m, using the Gaussian assumption • Finding Probability Density • the object must be at one of the 12 areas • ΣP(Ai | St) =1 for all i • Max{P(Ai |St) } = Max{c*P(St |Ai) } = Max{P(St |Ai) } • Return the area Ai with top probability

7. Applying Area-based Approach • There are two approach to estimate position: • Discrete Space Estimation • Continuous Space Estimation

8. Discrete Space Estimation Limitation • Only one of the discrete locations in the training set is returned • Cannot return the intermediate locations • Low accuracy • Not desirable for location-based application. Eg. Tour guide

9. Introduction to CSE • Continuous Space Estimation • Advantage: • Return locations may or may not be in the training set • Higher accuracy • Suitable for mobile application • Two techniques: • Center of Mass • Time-Averaging

10. Center of Mass • Assume n locations • Treat each location in the training set as an object • Each object has a weight equals to its probability density • Obtain Center of Mass of n objects using their weighted positions

11. Center of Mass • Let p(i) be the probability of a location xi, i=1,2 …n • Let Y be the set of locations in 2D space and Y(i) is the corresponding position of xi • The Center of Mass is given by:

12. Center of Mass

13. Example

14. Time-Averaging • Use a time-average window to smooth the resulting location estimated • Obtain the result location by averaging the last W locations estimated by discrete-space estimator

15. Time-Averaging • Given a stream of location estimates x1,x2,…,xt • The current location xc is estimated by

16. Time-Averaging

17. Problem with CSE Locations in training set Estimated position

18. Point Mapping • Goal : Map the result to the closest point in the set of all possible locations • Step 1: Divide the corridor into several line segments L i

20. Step 2: We define each line segment L i by an equation: • P = Pi1 + ui (Pi2 – Pi1) • Pi1 (xi1,yi1) is the starting point of L i • Pi2 (xi2,yi2) is the end point of L i

21. Let the point E(xe,ye) be the estimated point • Let Ii be the point of intersection between Li(Pi1Pi2) and the line at the tangent to Li passing through E

22. Step 3: Finding the distances Di between the estimated point E and L i for all i • the dot product of the tangent and Li is 0, thus (E - Ii) dot (Pi2 – Pi1) = 0 Solving this we have,

23. Substituting ui into the equation of Li gives the point of intersection Ii as • x = xi1 + ui (xi2 – xi1)y = yi1 + ui (yi2 – yi1) • Di is equal the distance between Ii and E

24. Step 4:check if Ii lies in the line segment Li • i.e. ui lies between 0 and 1 • Step 5: • Return Ii lying in Li and with smallest Di

26. Conclusion • Continuous Space Estimation solves the limitation in Discrete Space Estimation • Continuous Space Estimation improves the accuracy in determining position • Point Mapping overcome out of bound problem in CSE

27. THE END