Systems and methods for compressive sensing ranging evaluation

1. An RFID system comprising:

at least one exciter comprising at least one transmit antenna configured to transmit an activation signal to activate an RFID tag;

a phased antenna array comprising a plurality of receive antennas configured to receive a backscattered response signal from the activated RFID tag;

an RFID receiver system configured to communicate with the at least one exciter and connected to the phased antenna array, the RFID receiver system is configured to locate an RFID tag by:

performing reads of the RFID tag at multiple frequencies using the at least one exciter and the plurality of receive antennas of the phased antenna array;

generating a measurement matrix for each of the plurality of receive antennas using the phase of the backscattered response signals from the activated RFID tag at each of the multiple frequencies; and

determining a line of sight (LOS) distance between the activated RFID tag and each of the plurality of receive antennas by eliminating bases from the measurement matrix.

2. The RFID system of claim 1 , wherein performing reads of the RFID tag at multiple frequencies further comprises:

selecting a new transmit carrier frequency for the activation signal; and

instructing the at least one exciter to send the activation signal at the new transmit carrier frequency.

3. The RFID system of claim 2 , wherein performing reads of the RFID tag at multiple frequencies further comprises:

receiving the backscattered response signal from the activated RFID tag using each of the plurality of receive antennas of the phased antenna array; and

measuring at least a phase associated with the received backscattered response signal.

4. The RFID system of claim 3 , wherein generating a measurement matrix further comprises selecting a basis function representing the distance travelled from the exciter to the RFID tag to each of the plurality of receive antennas of the phased antenna array.

5. The RFID system of claim 1 , wherein eliminating bases from the measurement matrix further comprises:

deconvolving the measurement matrix;

sequentially eliminating a basis from the basis function corresponding to distance outward from the RFID receiver system;

calculating and minimizing error after elimination of each successive basis; and

determining if the calculated error is greater than a threshold value.

6. The RFID system of claim 5 , wherein the threshold value can be determined using a stopping rule.

7. The RFID system of claim 6 , wherein sequentially eliminating a basis further comprises eliminating the shortest remaining basis by a predetermined distance each time.

8. The RFID system of claim 7 , wherein calculating and minimizing error after elimination of each successive basis further comprises forcing a convex optimization process to fit with the remaining basis.

9. The RFID system of claim 1 , wherein eliminating bases from the measurement matrix further comprises placing an upper limit on the estimate of the line of sight distance.

10. The RFID system of claim 1 , wherein the RFID receiver system is further configured to locate an RFID tag by defining a plurality of elliptical representations using the at least one exciter, the RFID tag, and each of the plurality of receive antennas of the phased antenna array.

11. The RFID system of claim 10 , wherein the RFID receiver system is further configured to locate an RFID tag using the determined line of sight distance and the plurality of elliptical representations to locate the RFID tag as the intersection of a first ellipse and a second ellipse.

12. A method of determining location of RFID tags comprising:

activating an RFID tag at multiple frequencies using at least one exciter comprising at least one transmit antenna;

reading the RFID tag at the multiple frequencies using an RFID receiver comprising a phased antenna array and an RFID receiver system, phased antenna array comprising a plurality of receive antennas configured to receive a backscattered response signal from the activated RFID tag and the RFID receiver system configured to communicate with the at least one exciter and connected to the phased antenna array;

generating a measurement matrix for each of the plurality of receive antennas using the phase of the backscattered response signals from the activated RFID tag at each of the multiple frequencies using the RFID receiver system; and

determining a line of sight (LOS) distance between the activated RFID tag and each of the plurality of receive antennas by eliminating bases from the measurement matrix using the RFID receiver system.

13. The method of claim 12 , wherein activating an RFID tag at multiple frequencies further comprises:

selecting a new transmit carrier frequency for the activation signal using the RFID receiver system;

instructing the at least one exciter to send the activation signal at the new transmit carrier frequency using the RFID receiver system; and

activating the RFID tag using the activation signal at the new transmit carrier frequency using the exciter.

14. The method of claim 13 , wherein reading the RFID tag at the multiple frequencies further comprises:

receiving the backscattered response signal from the activated RFID tag using each of the plurality of receive antennas of the phased antenna array; and

measuring at least a phase associated with the received backscattered response signal using the RFID receiver system.

15. The method of claim 14 , wherein generating a measurement matrix for each of the plurality of receive antennas further comprises selecting a basis function representing the distance travelled from the exciter to the RFID tag to each of the plurality of receive antennas of the phased antenna array.

16. The method of claim 12 , wherein eliminating bases from the measurement matrix using the RFID receiver system further comprises:

deconvolving the measurement matrix;

sequentially eliminating a basis from the basis function corresponding to distance outward from the RFID receiver system;

calculating and minimizing error after elimination of each successive basis; and

determining if the calculated error is greater than a threshold value.

17. The method of claim 16 , wherein the threshold value can be determined using a stopping rule.

18. The method of claim 17 , wherein sequentially eliminating a basis further comprises eliminating the shortest remaining basis by a predetermined distance each time.

19. The method of claim 17 , wherein calculating and minimizing error after elimination of each successive basis further comprises forcing a convex optimization process to fit with the remaining basis.

20. The method of claim 13 , wherein eliminating bases from the measurement matrix further comprises placing an upper limit on the estimate of the line of sight distance.

21. The method of claim 13 , further comprising locating the RFID tag by defining a plurality of elliptical representations using the at least one exciter, the RFID tag, and each of the plurality of receive antennas of the phased antenna array.

22. The method of claim 21 , wherein locating an RFID tag further comprises using the determined line of sight distance and the plurality of elliptical representations to locate the RFID tag as the intersection of a first ellipse and a second ellipse.