System and method for validating GNSS ambiguities

1. A method for determining a mobile receiver position comprising:

receiving a first and a second set of satellite observations;

determining a first fixed ambiguity set associated with the first set of satellite observations and a second fixed ambiguity set associated with the second set of satellite observations, wherein the first fixed ambiguity set is associated with a first transformation and the second fixed ambiguity set is associated with a second transformation;

determining a first and a second intersection transformation from the first and second transformations, wherein the first and second intersection transformations transform the first and second fixed ambiguity sets to a shared intersection space;

determining cross-validated ambiguities from the first and second fixed ambiguity sets, wherein a cross-validated ambiguity is identified when a number of differing ambiguities from the first and second fixed ambiguity sets in the shared intersection space is less than a threshold; and

determining the mobile receiver position based on at least one of the first or second fixed ambiguity sets.

2. The method of claim 1 , further comprising:

generating an augmented ambiguity set from the first and second fixed ambiguity sets;

determining augmented first and second transformations based on the augmented ambiguity set and the first and second transformation; and

wherein the first and second intersection transformation are determined based on the augmented first and second transformations.

3. The method of claim 2 , wherein the first and second fixed ambiguity sets comprise common fixed ambiguities, wherein the augmented ambiguity set includes the common fixed ambiguities.

4. The method of claim 3 , wherein the augmented ambiguity set includes the uncommon ambiguities from the first and second fixed ambiguity sets.

5. The method of claim 1 , further comprising determining a union of ambiguities between the first and second fixed ambiguity sets, wherein the union of ambiguities is used to determine the mobile receiver position.

6. The method of claim 1 , further comprising determining a position of an external system based on the mobile receiver position.

7. The method of claim 6 , further comprising operating the external system based on to the external system position.

8. The method of claim 1 , wherein the first and second transformations are distinct.

9. The method of claim 1 , wherein determining each of the first and second fixed ambiguity set comprises:

determining a set of integer phase ambiguity hypotheses associated with the respective set of satellite observations; and

internally-validating the set of integer phase ambiguities.

10. The method of claim 9 , wherein internally-validating the set of integer phase ambiguities comprises:

performing hypothesis testing on the set of integer phase ambiguity hypotheses, wherein the hypothesis testing comprises determining a ratio between likelihoods of two integer phase ambiguity hypotheses; and

ceasing hypothesis testing when the ratio exceeds a threshold value.

11. The method of claim 9 , wherein determining the set of integer phase ambiguity hypotheses for each of the first and second ambiguity set comprises:

determining a set of floating integer phase ambiguities using a Kalman filter; and

determining the set of integer phase ambiguity hypotheses using at least one of a LAMBDA or MLAMBDA search algorithm.

12. The method of claim 1 , further comprising correcting the first and second set of satellite observations using a set of corrections received from a correction service, wherein the corrected first and second set of satellite observations are used to determine the first and second fixed ambiguity sets.

13. A system comprising:

a receiver comprising a processing module configured to:

receive a first and a second set of satellite observations;

determine a first fixed ambiguity set associated with the first set of satellite observations and a second fixed ambiguity set associated with the second set of satellite observations, wherein the first fixed ambiguity set is associated with a first transformation and the second fixed ambiguity set is associated with a second transformation;

generate an augmented ambiguity set from the first and second fixed ambiguity sets;

determine augmented first and second transformations based on the augmented ambiguity set and the first and second transformation;

determine a first and a second intersection transformation that transforms the first and second fixed ambiguity sets, respectively, to a shared intersection space;

determine cross-validated ambiguities from the first and second fixed ambiguity sets, wherein a cross-validated ambiguity is identified when a number of differing ambiguities from the first and second fixed ambiguity sets in the shared intersection space is less than a threshold; and

determine the receiver position based on at least one of the first or second fixed ambiguity sets.

14. The system of claim 13 , wherein the processing module is further configured to:

generate an augmented ambiguity set from the first and second fixed ambiguity sets;

determine augmented first and second transformations based on the augmented ambiguity set and the first and second transformation; and

wherein the first and second intersection transformation are determined based on the augmented first and second transformations.

15. The system of claim 14 , wherein the processing module is further configured to determine a union of ambiguities between the first and second fixed ambiguity sets, wherein the union of ambiguities is used to determine the receiver position.

16. The system of claim 13 , further comprising a second receiver, wherein the receiver is configured to receive satellite observations of the first and second set of satellite observations associated with a first satellite constellation and the second receiver is configured to receive satellite observations of the first and second set of satellite observations associated with a second satellite constellation.

17. The system of claim 13 , further comprising a vehicle wherein the receiver is mounted to the vehicle, wherein the processing module is further configured to determine a location of the vehicle based on the receiver position.

18. The system of claim 17 , wherein the processing module is further configured to generate instructions for operation of the vehicle based on the vehicle location.

19. The system of claim 13 , wherein determining each of the first and second fixed ambiguity set comprises:

determining a set of integer phase ambiguity hypotheses associated with the respective set of satellite observations;

performing hypothesis testing on the set of integer phase ambiguity hypotheses, wherein the hypothesis testing comprises determining a ratio between likelihoods of two integer phase ambiguity hypotheses; and

ceasing hypothesis testing when the ratio exceeds a threshold value.

20. The system of claim 19 , wherein determining a set of integer phase ambiguity hypotheses for each of the first and second ambiguity set comprises:

determining a set of floating integer phase ambiguities using a Kalman filter; and

determining the set of integer phase ambiguity hypotheses using at least one of a LAMBDA or MLAMBDA search algorithm.