Identifying and partitioning legitimate GNSS satellite signals from illegitimate GNSS satellite signals using a contrario method
Provided are systems, methods, and devices for identifying correct satellite signals to improve the accuracy of a satellite navigation system. In some embodiments, identifying correct satellite signals may include receiving a plurality of satellite signals; demodulating the satellite signals to extract a first plurality of parameters; determining a first subset of parameters from the first plurality of parameters, wherein the first subset of parameters is based on a first geographic location; determining a second subset of parameters from a second plurality of parameters outside the first subset, the second plurality of parameters comprising one or more parameters of the first plurality of parameters outside the first subset, wherein the second subset of parameters is based on a second geographic location; and identifying an exemplary subset from the first subset and the second subset, wherein the exemplary subset comprises parameters corresponding to correct satellite signals.
1. A method of identifying correct satellite signals to improve the accuracy of a satellite navigation system comprising:
receiving a plurality of satellite signals;
demodulating the plurality of satellite signals to extract a first plurality of parameters;
determining one or more first subsets of parameters from the first plurality of parameters corresponding to the plurality of satellite signals;
identifying one or more second subsets of parameters for each first subset, comprising:
calculating one or more scores for one or more parameters of the first plurality of parameters outside the first subset;
identifying, based on the plurality of scores for one or more parameters of the plurality of parameters outside the first subset, one or more inlier parameters from one or more parameters of the first plurality of parameters outside the first subset;
forming a second subset based on the one or more identified inlier parameters;
identifying a third subset from the one or more first and one or more second subsets based on a plurality of scores for the one or more first subsets and the one or more second subsets, wherein the third subset comprises parameters corresponding to correct satellite signals.
2. The method of claim 1 , wherein the one or more first subsets are based on a single geographic location.
3. The method of claim 1 , wherein identifying one or more second subsets for each first subset further comprises:
aggregating a formed second subset to a first subset of the one or more first subsets to form an expanded first subset; and
recursively repeating the identification of one or more second subsets to identify further second subsets.
4. The method of claim 1 , wherein calculating one or more scores for one or more parameters of the first plurality of parameters outside the first subset comprises:
calculating an a contrario score; and
calculating a KL divergence score.
5. The method of claim 1 , wherein correct satellite signals comprise one or more of a multipath satellite signal or a line-of-sight satellite signal.
6. The method of claim 4 , wherein identifying one or more second subsets of parameters from the first plurality of parameters corresponding to the plurality of satellite signals comprises calculating a state vector based on the parameters of the first subset.
7. The method of claim 6 , wherein determining one or more first subsets of parameters from the first plurality of parameters corresponding to the plurality of satellite signals comprises:
identifying four parameters based on a single geographic location from the first plurality of parameters; and
verifying the state vectors based on the parameters of the first subsets using extrinsic information from one or more of an inertial measurement calculator, a clock, or a barometer.
8. The method of claim 6 , wherein determining one or more first subsets of parameters from the first plurality of parameters corresponding to the plurality of satellite signals comprises:
identifying four parameters based on a single geographic location from the first plurality of parameters; and
verifying the state vectors based on the parameters of the first subsets with a fifth measurement from the first plurality of parameters.
9. The method of claim 1 , wherein the first plurality of parameters comprises one or more of pseudo-range or pseudo-range-rate parameters.
10. The method of claim 2 , wherein the geographic location comprises one of a legitimate geographic location, a spoofed geographic location, or a faulted geographic location.
11. The method of claim 6 , wherein identifying a third subset from the one or more first subsets and the one or more second subsets based on a plurality of scores comprises:
identifying the third subset from the one or more first subsets and the one or more second subsets, the third subset having a lowest a contrario score and a highest KL divergence score; and
identifying one or more consensus inlier parameters from the first plurality of parameters based on the third subset having the lowest a contrario score and the highest KL divergence score.
12. The method of claim 6 , wherein identifying a third subset from the one or more first subsets and the one or more second subsets comprises identifying consensus inlier parameters from the first plurality of parameters, wherein the third subset and the consensus inlier parameters comprise parameters corresponding to correct satellite signals.
13. The method of claim 6 , wherein calculating an a contrario score for one or more parameters of the first plurality of parameters outside the first subset comprises generating a chi-squared distribution based upon error measurements between the one or more parameters of the first plurality of parameters outside the first subset and predicted parameters based on the state vector corresponding to the first subset.
14. The method of claim 6 , wherein the KL divergence score for one or more parameters of the first plurality of parameters outside the first subset is based on a distribution of the one or more parameters of the first plurality of parameters outside the first subset and a distribution of predicted parameters based on the state vector corresponding to the first subset.
15. A system for identifying correct satellite signals to improve the accuracy of a satellite navigation system comprising:
one or more processors and memory storing one or more programs that when executed by the one or more processors cause the one or more processors to:
receive a plurality of satellite signals;
demodulate the plurality of satellite signals to extract a first plurality of parameters;
determine one or more first subsets of parameters from the first plurality of parameters corresponding to the plurality of satellite signals;
identify one or more second subsets of parameters for each first subset, comprising:
calculate one or more scores for one or more parameters of the first plurality of parameters outside the first subset;
identify, based on the plurality of scores for one or more parameters of the plurality of parameters outside the first subset, one or more inlier parameters from one or more parameters of the first plurality of parameters outside the first subset;
form a second subset based on the one or more identified inlier parameters;
identify a third subset from the one or more first and one or more second subsets based on a plurality of scores for the one or more first subset and the one or more second subsets, wherein the third subset comprises parameters corresponding to correct satellite signals.
16. The system of claim 15 , wherein the one or more first subsets are based on a single geographic location.
17. The system of claim 15 , wherein identify one or more second subsets for each first subset further comprises:
aggregate a formed second subset to a first subset of the one or more first subsets to form an expanded first subset; and
recursively repeat the identification of one or more second subsets to identify further second subsets.
18. The system of claim 15 , wherein calculate one or more scores for one or more parameters of the first plurality of parameters outside the first subset comprises:
calculate an a contrario score; and
calculate a KL divergence score.
19. The system of claim 15 , wherein correct satellite signals comprise one or more of a multipath satellite signal or a line-of-sight satellite signal.
20. The system of claim 18 , wherein identify one or more second subsets of parameters from the first plurality of parameters corresponding to the plurality of satellite signals comprises calculate a state vector based on the parameters of the first subset.
21. The system of claim 20 , wherein determine one or more first subsets of parameters from the first plurality of parameters corresponding to the plurality of satellite signals comprises:
identify four parameters based on a single geographic location from the first plurality of parameters; and
verify the state vectors based on the parameters of the first subsets using extrinsic information from one or more of an inertial measurement calculator, a clock, or a barometer.
22. The system of claim 20 , wherein determine one or more first subsets of parameters from the first plurality of parameters corresponding to the plurality of satellite signals comprises:
identify four parameters based on a single geographic location from the first plurality of parameters; and
verify the state vectors based on the parameters of the first subsets with a fifth measurement from the first plurality of parameters.
23. The system of claim 15 , wherein the first plurality of parameters comprises one or more of pseudo-range or pseudo-range-rate parameters.
24. The system of claim 16 , wherein the geographic location comprises one of a legitimate geographic location, a spoofed geographic location, or a faulted geographic location.
25. The system of claim 20 , wherein identify a third subset from the one or more first subsets and the one or more second subsets based on a plurality of scores comprises:
identify the third subset from the one or more first subsets and the one or more second subsets, the third subset having a lowest a contrario score and a highest KL divergence score; and
identify one or more consensus inlier parameters from the first plurality of parameters based on the third subset having the lowest a contrario score and the highest KL divergence score.
26. The system of claim 20 , wherein identify a third subset from the one or more first subsets and the one or more second subsets comprises identify consensus inlier parameters from the first plurality of parameters, wherein the third subset and the consensus inlier parameters comprise parameters corresponding to correct satellite signals.
27. The system of claim 20 , wherein calculate an a contrario score for one or more parameters of the first plurality of parameters outside the first subset comprises generate a chi-squared distribution based upon error measurements between the one or more parameters of the first plurality of parameters outside the first subset and predicted parameters based on the state vector corresponding to the first subset.
28. The system of claim 20 , wherein the KL divergence score for one or more parameters of the first plurality of parameters outside the first subset is based on a distribution of the one or more parameters of the first plurality of parameters outside the first subset and a distribution of predicted parameters based on the state vector corresponding to the first subset.
29. A device for identifying correct satellite signals to improve the accuracy of a satellite navigation system comprising:
a receiver configured to receive a plurality of satellite signals;
a processor configured to:
demodulate the plurality of satellite signals to extract a first plurality of parameters;
determine one or more first subsets of parameters from the first plurality of parameters corresponding to the plurality of satellite signals;
identify one or more second subsets of parameters for each first subset, comprising:
calculate one or more scores for one or more parameters of the first plurality of parameters outside the first subset;
identify, based on the plurality of scores for one or more parameters of the plurality of parameters outside the first subset, one or more inlier parameters from one or more parameters of the first plurality of parameters outside the first subset;
form a second subset based on the one or more identified inlier parameters;
identify a third subset from the one or more first and one or more second subsets based on a plurality of scores for the one or more first subsets and the one or more second subsets, wherein the third subset comprises parameters corresponding to correct satellite signals.
30. The device of claim 29 , wherein the one or more first subsets are based on a single geographic location.
31. The device of claim 29 , wherein identify one or more second subsets for each first subset further comprises:
aggregate a formed second subset to a first subset of the one or more first subsets to form an expanded first subset; and
recursively repeat the identification of one or more second subsets to identify further second subsets.
32. The device of claim 29 , wherein calculate one or more scores for one or more parameters of the first plurality of parameters outside the first subset comprises:
calculate an a contrario score; and
calculate a KL divergence score.
33. The device of claim 29 , wherein correct satellite signals comprise one or more of a multipath satellite signal or a line-of-sight satellite signal.
34. The device of claim 32 , wherein identify one or more second subsets of parameters from the first plurality of parameters corresponding to the plurality of satellite signals comprises calculate a state vector based on the parameters of the first subset.
35. The device of claim 34 , wherein determine one or more first subsets of parameters from the first plurality of parameters corresponding to the plurality of satellite signals comprises:
identify four parameters based on a single geographic location from the first plurality of parameters; and
verify the state vectors based on the parameters of the first subsets using extrinsic information from one or more of an inertial measurement calculator, a clock, or a barometer.
36. The device of claim 34 , wherein determine one or more first subsets of parameters from the first plurality of parameters corresponding to the plurality of satellite signals comprises:
identify four parameters based on a single geographic location from the first plurality of parameters; and
verify the state vectors based on the parameters of the first subsets with a fifth measurement from the first plurality of parameters.
37. The device of claim 29 , wherein the first plurality of parameters comprises one or more of pseudo-range or pseudo-range-rate parameters.
38. The device of claim 30 , wherein the geographic location comprises one of a legitimate geographic location, a spoofed geographic location, or a faulted geographic location.
39. The device of claim 34 , wherein identify a third subset from the one or more first subsets and the one or more second subsets based on a plurality of scores comprises:
identify the third subset from the one or more first subsets and the one or more second subsets, the third subset having a lowest a contrario score and a highest KL divergence score; and
identify one or more consensus inlier parameters from the first plurality of parameters based on the third subset having the lowest a contrario score and the highest KL divergence score.
40. The device of claim 34 , wherein identify a third subset from the one or more first subsets and the one or more second subsets comprises identify consensus inlier parameters from the first plurality of parameters, wherein the third subset and the consensus inlier parameters comprise parameters corresponding to correct satellite signals.
41. The device of claim 34 , wherein calculate an a contrario score for one or more parameters of the first plurality of parameters outside the first subset comprises generate a chi-squared distribution based upon error measurements between the one or more parameters of the first plurality of parameters outside the first subset and predicted parameters based on the state vector corresponding to the first subsets.
42. The device of claim 34 , wherein the KL divergence score for one or more parameters of the first plurality of parameters outside the first subset is based on a distribution of the one or more parameters of the first plurality of parameters outside the first subset and a distribution of predicted parameters based on the state vector corresponding to the first subset.