Position validation

1. A method comprising:

receiving, at a central processing system, versions of a message from a first satellite-based receiver and a second satellite-based receiver that both received a radio frequency (“RF”) transmission of the message, the message comprising a self-reported position of a transmitter of the message;

wherein the respective versions of the message from the first satellite-based receiver and the second satellite-based receiver include a first arrival time of the RF transmission of the message at the first satellite-based receiver and a second arrival time of the RF transmission of the message at the second satellite-based receiver;

determining, at the central processing system, a time difference between the first arrival time of the RF transmission of the message at the first satellite-based receiver and the second arrival time of the RF transmission of the message at the second satellite-based receiver;

determining, at the central processing system, a measure of the likelihood that the self-reported position of the transmitter is valid based on the time difference between the first and second arrival times and an expected time difference between the first and second arrival times based upon respective positions of the first and second satellite-based receivers and the self-reported position; and

transmitting, to an aircraft surveillance system, the self-reported position and an indication of the measure of the likelihood that the self-reported position is valid for use in air traffic control.

2. The method of claim 1 , wherein the respective versions of the message include information regarding the respective positions of the first satellite-based receiver and the second satellite-based receiver and wherein determining the measure of the likelihood comprises:

determining a three dimensional surface comprising potential positions of the transmitter based on the time difference between the first and second arrival times.

3. The method of claim 2 , wherein determining the measure of the likelihood further comprises:

determining a distance between the self-reported position and a point on the surface that is closest to the self-reported position; and

determining if the distance is within a defined range.

4. The method of claim 2 , wherein determining the measure of the likelihood further comprises:

determining an other three-dimensional surface based on an altitude component of the self-reported position; and

determining a curve defined by an intersection of the three-dimensional surface and the other three-dimensional surface, the curve comprising potential positions of the transmitter.

5. The method of claim 4 , wherein determining the measure of the likelihood further comprises:

determining a distance between the self-reported position and a point on the curve that is closest to the self-reported position; and

determining if the distance is within a defined range.

6. The method of claim 2 , wherein the three dimensional surface is a hyperboloid.

7. The method of claim 1 , wherein the transmitter is hosted on an in-flight aircraft, and wherein the time difference is determined by comparing the first arrival time and the second arrival time received in the first message.

8. The method of claim 7 , wherein the message is an automatic dependent surveillance-broadcast (“ADS-B”) message transmitted by the transmitter on the aircraft.

9. The method of claim 1 , wherein determining the measure of the likelihood comprises:

determining a three dimensional surface comprising potential positions of the transmitter based on:

the time difference between the first and second arrival times, and

respective positions of the first and second satellite-based receivers.

10. The method of claim 9 , wherein the locations of the first and second satellite-based receivers are defined according to predetermined orbits of the first and second satellite-based receivers.

11. The method of claim 1 , wherein determining a measure of the likelihood that the self-reported position of the transmitter is valid based on the time difference between the first and second arrival times comprises:

determining an expected time difference between the first and second arrival times based on positions of the first and second satellite-based receivers and the self-reported position; and

comparing the time difference between the first and second arrival times to the expected time difference between the first and second arrival times.

12. A method comprising:

receiving versions of a first message from a first satellite-based receiver and a second satellite-based receiver that both received a radio frequency (“RF”) transmission of the message, the message comprising a first self-reported position of a transmitter of the message;

wherein the respective versions of the first message from the first satellite-based receiver and the second satellite-based receiver include a first arrival time of the RF transmission of the message at the first satellite-based receiver and a second arrival time of the RF transmission of the message at the second satellite-based receiver;

determining a time difference between the first arrival time of the RF transmission of the first message at the first satellite-based receiver and the second arrival time of the RF transmission of the first message at the second satellite-based receiver;

receiving a second message from the first satellite-based receiver, the second message comprising a second self-reported position of the transmitter, wherein an RF transmission of the second message is received on a first beam of the first satellite-based receiver;

wherein the first satellite-based receiver comprises an antenna array forming multiple beams of the first satellite-based receiver;

determining a set of beams of the first satellite-based receiver expected to receive the RF transmission of the second message based on measuring the respective gain of each of the multiple beams of the first satellite-based receiver with respect to the second self-reported position of the transmitter, and comparing the respective gain of each of the multiple beams to a respective threshold value;

determining a number of the beams of the set that received the RF transmission of the second message;

determining a measure of the likelihood that the self-reported positions of the transmitter are valid based on (i) the time difference between the first and second arrival times and (ii) number of the beams of the set that received the RF transmission of the second message; and

transmitting, to an aircraft surveillance system, the self-reported position and an indication of the likelihood that the self-reported positions are valid, for use in air traffic control.

13. The method of claim 12 , wherein determining a set of beams of the first satellite-based receiver is performed in response to determining that the transmitter is outside of a coverage area, for the second message, associated with the second satellite-based receiver.

14. The method of claim 12 , wherein the transmitter is hosted on an in-flight aircraft.

15. The method of claim 14 , wherein the message is an automatic dependent surveillance-broadcast (“ADS-B”) message transmitted by the transmitter on the aircraft.

16. The method of claim 12 , wherein the indication of the measure of the likelihood that the self-reported position of the transmitter is valid is determined based on a state machine that is updated after the message is received.

17. The method of claim 13 , wherein the transmitter is hosted on an aircraft and transmits automatic dependent surveillance-broadcast (“ADS-B”) messages.

18. The method of claim 12 , wherein the satellite-based receiver is hosted on a satellite that is part of a satellite constellation, wherein the transmitter is out of range of other satellites in the satellite constellation, and wherein the measure of the likelihood that the self-reported position of the transmitter is valid is used to validate self-reported position data transmitted by the transmitter after previous self-reported position data was validated using time difference of arrival (“TDOA”) based on differences in times of arrival of RF transmissions transmitted by the transmitter at two or more satellites of the satellite constellation.

19. The method of claim 12 , wherein determining a set of beams of the first satellite-based receiver is performed in response to determining that the transmitter is outside of a coverage area, associated with the second satellite-based receiver.

20. The method of claim 15 , wherein determining a set of beams of the first satellite-based receiver is performed in response to determining that the transmitter is outside of a coverage area, for the second message, associated with the second satellite-based receiver.