KL-divergence kernel regression for non-gaussian fingerprint based localization
View Patent ↗Embodiments are directed to mobile localization, and more specifically, but not exclusively, to tracking mobile devices. Embodiments include methods that consider probability kernels with distance-like metrics between distributions. Also described are probabilistic kernels that can be used for a regression of location, which can achieve up to about inn accuracy in an office environment.
1. A method of estimating the location of a device, comprising:
sampling a measurement distribution p of a parameter of the device for a predetermined duration, by a processor;
comparing the sampled measurement distribution p to a database of distributions q 1 to L using a symmetrized Kullback-Leibler (K-L) divergence D;
constructing a kernel function k(p, q) using the K-L divergence D between the measured sample distribution p and a database distribution q i component across all q 1 to L ;
performing a weighted regression using the constructed kernel function; and
estimating the location of the device based on the performed weighted regression of the constructed kernel function.
2. The method of claim 1 , wherein the sampling a measurement distribution is repeated at different locations, p x,y .
3. The method of claim 2 , wherein for each p x,y the comparing, constructing, performing, and estimating steps are performed.
4. The method of claim 1 , wherein the measurement parameter is signal strength.
5. The method of claim 1 , wherein the measurement parameter is access point presence.
6. The method of claim 1 , wherein the predetermined duration ranges from approximately 1 second to approximately 20 seconds.
7. The method of claim 1 , wherein the symmetrized KL divergence D is defined as:
D ( p,q )= KL ( p∥q )+ KL ( q∥p ).
8. The method of claim 1 , wherein the constructing the kernel, further comprises:
exponentiating the symmetrized KL divergence D.
9. The method of claim 1 , wherein the performing a weighted regression uses K nearest neighbors.
10. The method of claim 1 , wherein the database comprises a set of previously mapped measurement distributions for the device parameter.
11. A tangible computer readable medium embodying programmed instructions which, when executed on a processor, are configured for performing a method, the method comprising:
sampling a measurement distribution p of a parameter of the device for a predetermined duration, by a processor;
comparing the sampled measurement distribution p to a database of distributions q 1 to L using a symmetrized Kullback-Leibler (K-L) divergence D;
constructing a kernel function k(p, q) using the K-L divergence D between the measured sample distribution p and a database distribution q i component across all q 1 to L ;
performing a weighted regression using the constructed kernel function; and
estimating the location of the device based on the performed weighted regression of the constructed kernel function.
12. The tangible computer readable medium of claim 11 , wherein the sampling a measurement distribution is repeated at different locations, p x,y .
13. The tangible computer readable medium of claim 12 , wherein for each p x,y the comparing, constructing, performing, and estimating steps are performed.
14. The tangible computer readable medium of claim 11 , wherein the measurement parameter is signal strength.
15. The tangible computer readable medium of claim 11 , wherein the measurement parameter is access point presence.
16. The tangible computer readable medium of claim 11 , wherein the predetermined duration ranges from approximately 1 second to approximately 10 seconds.
17. The tangible computer readable medium of claim 11 , wherein the symmetrized KL divergence D is defined as:
D ( p,q )= KL ( p∥q )+ KL ( q∥p ).
18. The tangible computer readable medium of claim 11 , wherein the constructing the kernel, further comprises:
exponentiating the symmetrized KL divergence D.
19. The tangible computer readable medium of claim 11 , wherein the performing a weighted regression uses K nearest neighbors.
20. The tangible computer readable medium of claim 11 , wherein the database comprises a set of previously mapped measurement distributions for the device parameter.