Machine and process for self localization using doppler
A system, method and apparatus is provided for calculating the position of a single receiver by receiving a signal from an emitter. Either the receiver or the emitter may be stationary relative to the surface of the Earth. The invention may use a particle filter to optimize the efficiency of the position calculation. The invention may further utilize a particle filter to estimate the frequency drift and bias of the emitter and/or receiver, and use the estimated frequency drift to improve the position calculation. In one embodiment, the invention may be used to calculate the position of a single GPS receiver given the position of, and a transmission from, a single GPS satellite.
1. A method of determining a location of a radio frequency (RF) receiver using an RF emitter located on a single moving platform, the method comprising:
A. receiving, by the receiver, an RF signal transmitted by the emitter over a period of time;
B. measuring, by the receiver, frequency of arrival (FOA) data of the RF signal over the period of time, the FOA data comprising a Doppler-shifted frequency of the emitter, a location of the emitter, and a velocity of the emitter;
C. determining an estimate of a frequency measurement bias of the receiver based on the measured FOA data and an estimate of the location of the receiver, wherein the estimated frequency measurement bias of the receiver includes an estimate of a frequency drift; and
D. determining an updated estimate of the location of the receiver based on the estimate of the frequency measurement bias of the receiver.
2. A method according to claim 1 further comprising measuring initial FOA data over an initial time period and calculating the estimate of the location of the receiver by modeling a region of interest with a plurality of particles.
3. A method according to claim 2 , wherein each particle represents a possible location of the receiver and is associated with a frequency drift conditioned on the location and the initial FOA data.
4. A method according to claim 2 , wherein each particle represents a possible frequency measurement bias estimate and is associated with a location of the receiver conditioned on the frequency measurement bias estimate, initial FOA data, and the observed signal frequency of the beacon.
5. A method according to claim 2 , wherein the estimate of the location of the receiver is based on a priori information or spread uniformly out in a grid-like fashion.
6. A method according to claim 1 , wherein the estimate of the frequency measurement bias of the receiver is calculated with a particle filter.
7. A method according to claim 6 , wherein the particle filter weights particles having a frequency drift that best corresponds to a model of an expected receiver frequency measurement bias drift.
8. A method according to claim 7 , wherein the model is a process model of a localized extended Kalman filter.
9. A method according to claim 7 , wherein the model is a parametric fit to the estimated frequency drift.
10. A method according to claim 7 , further comprising resampling the weighted particles.
11. A method according to claim 10 , wherein the updated estimate of the location of the receiver is determined based on a covariance of the resampled particles.
12. A method according to claim 1 comprising:
receiving, by the receiver, a second RF signal transmitted by the emitter over a second period of time;
repeating step C with the updated estimate of particle location to calculate an updated estimate of a frequency; and
repeating step D with the updated estimate of the frequency measurement bias of the receiver.
13. The method of claim 1 , wherein the emitter is an orbiting satellite or aerial vehicle.
14. The method of claim 1 , wherein the one or more of the group consisting of FOA-DOT, FOA-DOT-DOT, FDOA, and D-FDOA are used to calculate the updated estimate of the location of the receiver.
15. A system for determining a location of a radio frequency (RF) receiver comprising:
a receiver located on a platform, the receiver adapted to receive an RF signal transmitted by an emitter over a period of time; and
a processor in communication with the receiver adapted to:
measure frequency of arrival (FOA) data of the received RF signal over the period of time, the FOA data comprising a Doppler-shifted frequency of the emitter, a location of the emitter, and a velocity of the emitter;
determine an estimate of a frequency measurement bias of the receiver based on the measured FOA data and an estimate of the location of the receiver, wherein the estimated frequency measurement bias of the receiver includes an estimate of a frequency drift; and
determine an updated estimate of the location of the receiver based on the estimate of the frequency measurement bias of the receiver.
16. A system according to claim 15 wherein the processor is further adapted to measure initial FOA data over an initial time period and calculate the estimate of the location of the receiver by modeling a region of interest with a plurality of particles.
17. A system according to claim 16 , wherein each particle represents a possible location of the receiver and is associated with a frequency drift conditioned on the location and the initial FOA data.
18. A system according to claim 16 , wherein each particle represents a possible frequency measurement bias estimate and is associated with a location of the receiver conditioned on the frequency measurement bias estimate and initial FOA data.
19. A system according to claim 16 , wherein the estimate of the location of the receiver is based on a priori information or spread uniformly out in a grid-like fashion.
20. A system according to claim 15 , wherein the estimate of the frequency drift is calculated with a particle filter.
21. A system according to claim 20 , wherein the particle filter weights particles having a frequency measurement bias drift that best corresponds to a model of an expected frequency measurement bias drift.
22. A system according to claim 21 , wherein the model is a process model of a localized extended Kalman filter.
23. A system according to claim 21 , wherein the model is a parametric fit to the estimated frequency drift.
24. A system according to claim 21 , wherein the processor is further adapted to resample the weighted particles.
25. A system according to claim 24 , wherein the updated estimate of the location of the receiver is determined based on a covariance of the resampled particles.
26. The system of claim 15 , wherein one of the group consisting of the emitter or the platform is an aerial vehicle or orbiting satellite.
27. The system of claim 15 , wherein the processor employs one or more of the group consisting of FOA-DOT, FOA-DOT-DOT, FDOA, and D-FDOA to calculate the updated estimate of the location of the receiver.
28. A system according to claim 15 further comprising the RF emitter.
29. A system according to claim 15 , wherein the processor is located on-board the platform.
30. A system according to claim 15 , wherein the processor is located external to the platform and is in communication with the receiver via a network.