Method and system for determining a position of a communication satellite utilizing two-way ranging

• US 6,229,477 B1
• Filed: 10/16/1998
• Issued: 05/08/2001
• Est. Priority Date: 10/16/1998
• Status: Expired due to Term

• Current Assignee: Hughes Electronics Corporation (Rtx Corporation)
• Original Assignee: Hughes Electronics Corporation (Rtx Corporation)
• Inventors: Chang, Donald C. D., Yung, Kar W., Nunan, William J., Cheng, David C., Shuman, Bruce E.
• Primary Examiner(s): Blum, Theodore M.
• Application Number:
  US09/174,182
• Time in Patent Office: 935 Days
• Field of Search: 342/357.01, 342/357.16, 342/352
• US Class Current: 342/357.21
• CPC Class Codes: G01S 5/12 by co-ordinating position lines of different shape, e.g. hyperbolic, circular, elliptical or radial
• CPC Class Codes: G01S 5/14 Determining absolute distances from a plurality of spaced points of known location

Abstract

A method and system for determining a position of an orbiting transceiver in a communications network includes at least a first and second transceiver at a first and second known location, respectively, on Earth. The first and second transceivers are adapted to transmit and receive communications signals to and from the orbiting transceiver. A processor coupled to one of the first and second transceivers determines a first and second range measurement between each of the first and second transceivers and the orbiting transceiver, respectively, as well as corresponding first and second range rates representative of a time rate of change of the first and second range measurements. The processor then determines a circle of intersection representative of the set of possible positions for the orbiting transceiver based on the first range measurement and the first range rate wherein the circle of intersection includes a specific orientation in space, a specific radius and a center in a specific, three-dimensional position relative to the known position of the first transceiver. An angular position of the orbiting transceiver is then determined along the circle of intersection based on the known position of the second transceiver and the second range measurement. Finally, the position of the orbiting transceiver is determined based on the circle of intersection and the angular position.

Claims

1. A method for determining a position of an orbiting transceiver in a communications network including at least a first and second transceiver at a first and second known location, respectively, on Earth, the first and second transceivers adapted to transmit and receive communications signals to and from the orbiting transceiver, the method comprising:

determining a first and second range measurement between each of the first and second transceivers and the orbiting transceiver, respectively;

determining a first and second range rate corresponding to a time rate of change of the first and second range measurements, respectively;

determining a circle of intersection representative of the set of possible positions for the orbiting transceiver based on the first range measurement and the first range rate, the circle of intersection having a specific orientation in space, a specific radius and a center in a specific, three dimensional position relative to the known position of the first transceiver;

determining an angular position of the orbiting transceiver along the circle of intersection based on the known position of the second transceiver and the second range measurement; and

determining the position of the orbiting transceiver based on the circle of intersection and the angular position.

2. The method as recited in claim 1 wherein the orbiting transceiver is not stationary with respect to Earth.

3. The method as recited in claim 1 wherein determining the first and second range measurements includes determining the first and second range measurements utilizing two-way ranging.

4. The method as recited in claim 3 wherein one of the first and second transceivers is a primary transceiver and wherein determining the first and second range measurements includes:

transmitting a ranging signal at a known initial time from the primary transceiver to the orbiting transceiver;

transmitting the ranging signal from the orbiting transceiver to the primary transceiver and the other one of the first and second transceivers;

transmitting a reply signal from the other one of the first and second transceivers to the orbiting transceiver;

transmitting the reply signal from the orbiting transceiver to the primary transceiver;

receiving the ranging signal relayed back from the orbiting transceiver and reply signal at the primary transceiver at first and second time instants, respectively;

determining a time interval between the initial time instant and each of the first and second time instants;

determining a first and second signal path length between each of the primary transceiver and the other one of the first and second transceivers and the orbiting transceiver based on the time intervals; and

determining the first and second range measurements based on the first and second signal path lengths.

5. The method as recited in claim 4 wherein transmitting the ranging signal further includes transmitting the ranging signal at a known initial carrier frequency, and wherein receiving the ranging signal relayed back from the orbiting transceiver and the reply signal at the primary transceiver further includes receiving the ranging signal relayed back from the orbiting transceiver and the reply signal at first and second carrier frequencies, respectively, and wherein determining the time intervals further includes determining a frequency difference between the initial carrier frequency and each of the first and second carrier frequencies, and wherein determining the first and second signal path lengths further includes determining a rate of change of the signal path lengths based on the frequency differences and the time intervals.

6. The method as recited in claim 5 wherein the known position of the first transceiver includes a first position vector and wherein determining the center of the circle of intersection includes:

determining a first sphere centered about the first transceiver and having a first radius corresponding to the first range measurement;

determining a first angular velocity vector of the orbiting transceiver relative to the center of the Earth;

determining a second angular velocity vector of the first transceiver relative to the center of the Earth;

determining a difference between the first and second angular velocity vectors to obtain a difference angular velocity vector;

determining an x-unit vector corresponding to the normalized cross product of the difference angular velocity vector with first position vector;

determining an x-axis corresponding to a line passing through the center of the first sphere and being parallel to the x-unit vector;

defining a range rate cone having a vertex located at the center of the first sphere, the cone being oriented symmetrically about the x-axis and having its surface at a specific angle relative to the x-axis, the specific angle being determined by the rate of change of the signal path length between the primary transceiver and the orbiting transceiver; and

determining the center as lying on the x-axis at the specific distance and in the specific direction from the position of the first transceiver.

7. The method as recited in claim 6 wherein determining the angular position includes:

determining a y-axis and a z-axis which are perpendicular to each other and each of the y-axis and the z-axis further being perpendicular to the x-axis;

determining a second sphere centered about the second transceiver and having a second radius corresponding to the second range measurement;

defining two solution points located at the intersection between the circle of intersection and the second sphere;

defining an h-axis containing the two solution points and being parallel to the z-axis; and

determining the second intermediate point at the intersection between the h-axis and the x-y plane.

8. The method as recited in claim 7 wherein determining the y-axis and the z-axis further includes:

determining the y-axis intersecting the x-axis at the center of the circle of intersection and oriented such that the known position of one of the second transceiver and the third transceiver lies in an x-y plane containing the x-axis and the y-axis; and

determining the z-axis as being perpendicular to the x-y plane and intersecting the x-y plane at the center of the circle of intersection.

9. The method as recited in claim 1 further comprising a third transceiver wherein determining the first and second range measurement further includes determining a third range measurement, and wherein determining the circle of intersection further includes determining the circle of intersection relative to the first and second transceivers based on the first and second range measurements, and wherein determining the angular position further includes determining the angular position based on the circle of intersection, the known position of the third transceiver and the third range measurement.

10. The method as recited in claim 9 wherein determining the center of the circle of intersection includes:

determining a first sphere centered about the first transceiver and having a first radius corresponding to the first range measurement;

determining a second sphere centered about the second transceiver and having a second radius corresponding to the second range measurement;

determining an x-axis corresponding to a line containing the centers of the first and second spheres;

defining a second circle of intersection between the first and second spheres;

defining a first plane containing the second circle of intersection and being perpendicular to the x-axis; and

determining the center of the circle of intersection between the first and second spheres at an intersection of the x-axis with the first plane.

11. The method as recited in claim 10 wherein determining the angular position includes:

determining a y-axis and a z-axis which are perpendicular to each other and each of the y-axis and the z-axis further being perpendicular to the x-axis;

determining a third sphere centered about the third transceiver and having a third radius corresponding to the third range measurement;

defining two solution points located at the intersection between the second circle of intersection and the third sphere;

defining an h-axis containing the two solution points and being parallel to the z-axis;

determining a second intermediate point at the intersection between the h-axis and the x-y plane; and

determining two angular positions of the two solution points based on the position of the second intermediate point.

12. A system for determining a position of an orbiting transceiver in a communications network, the system comprising:

at least a first and second transceiver at a first and second known location, respectively, on Earth, the first and second transceivers adapted to transmit and receive communications signals to and from the orbiting transceiver; and

a processor coupled to one of the first and second transceivers operative to determine a first and second range measurement between each of the first and second transceivers and the orbiting transceiver, respectively, determine a first and second range rate corresponding to a time rate of change of the first and second range measurements, respectively, determine a circle of intersection representative of the set of possible positions for the orbiting transceiver based on the first range measurement and the first range rate, wherein the circle of intersection includes a specific orientation in space, a specific radius, and a center in a specific, three dimensional position relative to the known position of the first transceiver, determine an angular position of the orbiting transceiver along the circle of intersection based on the known position of the second transceiver and the second range measurement, and determine the position of the orbiting transceiver based on the circle of intersection and the angular position.

13. The system as recited in claim 12 wherein the orbiting transceiver is not stationary with respect to Earth.

14. The system as recited in claim 12 wherein the processor, in determining the first and second range measurements, is further operative to determine the first and second range measurements utilizing two-way ranging.

15. The system as recited in claim 14 wherein one of the first and second transceivers is a primary transceiver and the system further comprising:

the primary transceiver for transmitting a ranging signal at a known initial time to the orbiting transceiver;

the orbiting transceiver for transmitting the ranging signal to the primary transceiver and the other one of the first and second transceivers;

the other one of the first and second transceivers for transmitting a reply signal to the orbiting transceiver;

the orbiting transceiver for transmitting the reply signal to the primary transceiver;

the primary transceiver for receiving the ranging signal relayed back from the orbiting transceiver and reply signal at first and second time instants, respectively; and

the processor further operative to determine a time interval between the initial time instant and each of the first and second time instants, determine a first and second signal path length between each of the primary transceiver and the other one of the first and second transceivers and the orbiting transceiver based on the time intervals, and determine the first and second range measurements based on the first and second signal path lengths.

16. The system as recited in claim 15 wherein the primary transceiver, in transmitting the ranging signal is further operative to transmit the ranging signal at a known initial carrier frequency, and wherein the primary transceiver, in receiving the ranging signal relayed back from the orbiting transceiver and the reply signal is further operative to receive the ranging signal relayed back from the orbiting transceiver and the reply signal at first and second carrier frequencies, respectively, and wherein the processor, in determining the time intervals further includes determining a frequency difference between the initial carrier frequency and each of the first and second carrier frequencies, and, in determining the first and second signal path lengths, is further operative to determine a rate of change of the signal path lengths based on the frequency differences and the time intervals.

17. The system as recited in claim 16 wherein the known position of the first transceiver includes a first position vector and wherein the processor, in determining the center of the circle of intersection, is further operative to determine a first sphere centered about the first transceiver and having a first radius corresponding to the first range measurement, determine a first angular velocity vector of the orbiting transceiver relative to the center of the Earth, determine a second angular velocity vector of the first transceiver relative to the center of the Earth, determine a difference between the first and second angular velocity vectors to obtain a difference angular velocity vector, determine an x-unit vector corresponding to the normalized cross product of the difference angular velocity vector with first position vector, determine an x-axis corresponding to a line passing through the center of the first sphere and being parallel to the x-unit vector, define a range rate cone having a vertex located at the center of the first sphere, the cone being oriented symmetrically about the x-axis and having its surface at a specific angle relative to the x-axis, the specific angle being determined by the rate of change of the signal path length between the primary transceiver and the orbiting transceiver, and determine the center as lying on the x-axis at the specific distance and in the specific direction from the position of the first transceiver.

18. The system as recited in claim 17 wherein the processor, in determining the angular position, is further operative to determine a y-axis and a z-axis which are perpendicular to each other and each of the y-axis and the z-axis further being perpendicular to the x-axis, determine a second sphere centered about the second transceiver and having a second radius corresponding to the second range measurement, define two solution points located at the intersection between the circle of intersection and the second sphere, define an h-axis containing the two solution points and being parallel to the z-axis, and determine the second intermediate point at the intersection between the h-axis and the x-y plane.

19. The system as recited in claim 18 wherein the processor, in determining the y-axis and the z-axis, is further operative to determine the y-axis intersecting the x-axis at the center of the circle of intersection and oriented such that the known position of one of the second transceiver and the third transceiver lies in an x-y plane containing the x-axis and the y-axis, and determine the z-axis as being perpendicular to the x-y plane and intersecting the x-y plane at the center of the circle of intersection.

20. The system as recited in claim 12 further comprising a third transceiver and wherein the orbiting transceiver is stationary with respect to Earth, wherein the processor, in determining the first and second range measurement, is further to determine a third range measurement, and, in determining the circle of intersection, is further operative to determine the circle of intersection relative to the first and second transceivers based on the first and second range measurements, and, in determining the angular position, is further operative to determine the angular position based on the circle of intersection, the known position of the third transceiver and the third range measurement.

21. The system as recited in claim 20 wherein the processor, in determining the center of the circle of intersection, is further operative to determine a first sphere centered about the first transceiver and having a first radius corresponding to the first range measurement, determine a second sphere centered about the second transceiver and having a second radius corresponding to the second range measurement, determine an x-axis corresponding to a line containing the centers of the first and second spheres, define a second circle of intersection between the first and second spheres, define a first plane containing the second circle of intersection and being perpendicular to the x-axis, and determine the center of the circle of intersection between the first and second spheres at an intersection of the x-axis with the first plane.

22. The system as recited in claim 21 wherein the processor, in determining the angular position, is further operative to determine a y-axis and a z-axis which are perpendicular to each other and each of the y-axis and the z-axis further being perpendicular to the x-axis, determine a third sphere centered about the third transceiver and having a third radius corresponding to the third range measurement, define two solution points located at the intersection between the second circle of intersection and the third sphere, define an h-axis containing the two solution points and being parallel to the z-axis, determine a second intermediate point at the intersection between the h-axis and the x-y plane, and determine two angular positions of the two solution points based on the position of the second intermediate point.