GPS attitude determination system and method using optimal search space identification for integer cycle ambiguity resolution

• US 6,256,583 B1
• Filed: 09/16/1998
• Issued: 07/03/2001
• Est. Priority Date: 09/16/1998
• Status: Expired due to Term

• Current Assignee: Rockwell Collins, Inc. (Raytheon Technologies Corporation d/b/a RTX)
• Original Assignee: Rockwell Collins, Inc. (Raytheon Technologies Corporation d/b/a RTX)
• Inventors: Sutton, Eric
• Primary Examiner(s): Cuchlinski, Jr., William A.
• Assistant Examiner(s): PIPALA, EDWARD J
• Application Number:
  US09/154,378
• Time in Patent Office: 1,021 Days
• Field of Search: 701/4, 701/13, 701/207, 701/213-215, 342/352, 342/357.02, 342/357.03, 342/357.04, 342/357.06, 342/357.11, 342/357.12
• US Class Current: 701/215
• CPC Class Codes: G01S 19/55 Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method

Abstract

Disclosed are an integer cycle ambiguity resolution method, and attitude determining systems and apparatus using the same. In the method of determining a solution to an integer cycle ambiguity, four primary satellites out of a GPS satellite constellation are selected such that a number of false solutions for the integer cycle ambiguity is optimized. Next, a search space is defined such that the probability of rejecting a correct solution for the integer cycle ambiguity is guaranteed-to be below a predetermined value. Next, intervals in the defined search space are searched to determine a solution to the integer cycle ambiguity. Then, attitude is determined as a function of the determined solution to the integer cycle ambiguity.

Claims

1. A method of determining a solution to an integer cycle ambiguity in a global positioning system (GPS) attitude determination system, the method comprising:

selecting four primary satellites out of a plurality of satellites in a GPS satellite constellation such that a number of false solutions for the integer cycle ambiguity is optimized;

defining a search space such that the probability of rejecting a correct solution for the integer cycle ambiguity is guaranteed to be below a predetermined value;

searching through intervals in the defined search space to determine a solution to the integer cycle ambiguity; and

determining attitude as a function of the determined solution to the integer cycle ambiguity.

2. The method of claim 1, wherein selecting the four primary satellites out of the plurality of satellites in the GPS satellite constellation further includes selecting the four primary satellites out of the plurality of satellites which minimize the ratio:

$\frac{<br><br>\det <br><br>\text{\hspace{1em}<br><br>}<br><br>L<br><br>}{{\mathrm{\sigma <br><br>}}_3}.$

3. The method of claim 1, wherein selecting the four primary satellites out of the plurality of satellites in the GPS satellite constellation further includes:

generating a target value for the determinant of the line of sight vector L; and

selecting the four primary satellites, out of the plurality of satellites, which cause the determinant of L to be closest to the generated target value.

4. The method of claim 1, wherein defining the search space such that the probability of rejecting the correct solution for the integer cycle ambiguity is guaranteed to be below a predetermined value further includes:

comparing an estimated baseline length with an actual baseline length; and

determining an interval around the actual baseline length as a function of the comparison.

5. The method of claim 4, wherein determining the interval around the actual baseline length further includes determining a feasible interval for a first component of an integer ambiguity vector as a function of an upper limit on the feasible interval.

6. The method of claim 5, wherein determining the interval around the actual baseline length further includes determining a feasible interval for a second component of the integer ambiguity vector.

8. The method of claim 4, wherein searching through intervals in the defined search space to determine the solution to the integer cycle ambiguity further includes accepting any solution to the integer cycle ambiguity which is within the determined interval.

9. The method of claim 4, wherein the interval is determined as a function of satellite geometry of the four primary satellites relative to the GPS attitude determination system.

10. The method of claim 9, wherein the interval is further determined as a function of a measurement noise variance σ

_m².

11. The method of claim 10, wherein the interval is further determined as a function of a maximum probability of rejecting the correct solution for the integer cycle ambiguity defined by the predetermined value.

7. The method of clam 6, wherein determining the interval around the actual baseline length further includes determining a feasible interval for a third component N_s of the integer ambiguity vector as a function of a lower limit on the feasible interval.

12. An attitude determining system adapted to determine a solution to an integer cycle ambiguity, attitude determining system comprising:

satellite selection means for selecting four primary satellites out of a plurality of satellites in a GPS satellite constellation such that a number of false solutions for the integer cycle ambiguity is optimized;

search space definition means for defining a search space such that the probability of rejecting a correct solution for the integer cycle ambiguity is guaranteed to be below a predetermined value;

searching means for searching through intervals in the defined search space to determine a solution to the integer cycle ambiguity; and

attitude determining means for determining attitude as a function of the determined solution to the integer cycle ambiguity.

13. An attitude determining system comprising:

a first antenna for receiving satellite positioning signals from a plurality of global positioning system satellites;

a second antenna for receiving the satellite positioning signals from the plurality of global positioning system satellites;

signal receive circuitry coupled to the first and second antennas and receiving the satellite positioning signals, the signal receive circuitry providing as an output signals indicative of information contained within the global positioning signals; and

processing circuitry coupled to the signal receive circuitry and adapted to determine a solution to an integer cycle ambiguity as a function of the output signals, wherein the processing circuitry is adapted to select four primary satellites out of the plurality of satellites such that a number of false solutions for the integer cycle ambiguity is optimized, to define a search space such that the probability of rejecting a correct solution for the integer cycle ambiguity is guaranteed to be below a predetermined value, to search through intervals in the defined search space to determine a solution to the integer cycle ambiguity, and to determine attitude as a function of the determined solution to the integer cycle ambiguity.

14. The attitude determining system of claim 13, wherein the processing circuitry selects the four primary satellites, out of the plurality of satellites, which minimize the ratio:

$\frac{<br><br>\det <br><br>\text{\hspace{1em}<br><br>}<br><br>L<br><br>}{{\mathrm{\sigma <br><br>}}_3}.$

15. The attitude determining system of claim 13, wherein the processing circuitry is adapted to select the four primary satellites by generating a target value for the determinant of the line of sight vector L, and by selecting the four primary satellites which cause the determinant of L to be closest to the generated target value.

16. The attitude determining system of claim 13, wherein the processing circuitry is adapted to define the search space such that the probability of rejecting the correct solution for the integer cycle ambiguity is guaranteed to be below a predetermined value by comparing an estimated baseline length with an actual baseline length, and by determining an interval around the actual baseline length as a function of the comparison.

17. The attitude determining system of claim 16, wherein the processing circuitry is adapted to determine the interval around the actual baseline length by determining a feasible interval for a first component of an integer ambiguity vector as a function of an upper limit on the feasible interval.

18. The attitude determining system of claim 17, wherein the processing circuitry is further adapted to determine the interval around the actual baseline length by determining a feasible interval for a second component of the integer ambiguity vector.

20. The attitude determining system of claim 16, wherein the processing circuitry is further adapted to determine the interval as a function of satellite geometry of the four primary satellites relative to a position of the attitude determination system.

19. The attitude determining system of clam 18, wherein the processing circuitry is further adapted to determine the interval around the actual baseline length by determining a feasible interval for a third component N_s of the integer ambiguity vector as a function of a lower limit on the feasible interval.