Ionospheric delay estimation for global navigation satellite system signals

1. A method of determining a position of a mobile device, comprising:

obtaining, with the mobile device, a pseudorange measurements and carrier-phase measurements from a satellite at a first frequency band and a second frequency band;

determining, with the mobile device, a bias estimate for the satellite based on a plurality of pseudorange measurements and carrier-phase measurements, wherein the bias estimate is associated with a common bias in the mobile device and a clock bias for the satellite;

determining, with the mobile device, a delta carrier-phase measurement for the satellite based on a difference between the carrier-phase measurements at the first frequency band and the second frequency band;

determining, with the mobile device, an ionospheric delay estimate based at least on the bias estimate and the delta carrier-phase measurement; and

determining, with the mobile device, the position of the mobile device based at least in part on the ionospheric delay estimate and the pseudorange measurements, or the ionospheric delay estimate and the carrier-phase measurements, or the ionospheric delay estimate and both the pseudorange measurements and the carrier-phase measurements, wherein the ionospheric delay estimate is used with a slant factor corresponding to an elevation of the satellite.

2. The method of claim 1 wherein the plurality of pseudorange measurements and carrier-phase measurements are obtained in an epoch.

3. The method of claim 2 wherein the delta carrier-phase measurement at the epoch corresponds to the plurality of pseudorange measurements and carrier-phase measurements received in the epoch.

4. The method of claim 2 further comprising determining the bias estimate across multiple, continuous epochs and the delta carrier-phase measurement is determined at the epoch.

5. The method of claim 4 wherein determining the bias estimate includes determining a divergence-free, smoothed estimate based on the plurality of pseudorange measurements and carrier-phase measurements.

6. The method of claim 5 wherein the bias estimate is based on a weighted average of a plurality of delta-pseudorange measurements and a plurality of delta-carrier-phase measurements with the satellite based on the first frequency band and the second frequency band made over time.

7. The method of claim 1 wherein a first number of the pseudorange measurements and carrier-phase measurements received on the first frequency band is greater than a second number of the plurality of pseudorange measurements and carrier-phase measurements received on the second frequency band.

8. An apparatus, comprising:

a memory;

at least one receiver;

at least one processor communicatively coupled to the memory and the at least one receiver, the at least one processor configured to:

obtain, via the at least one receiver, a pseudorange measurements and carrier-phase measurements from a satellite at a first frequency band and a second frequency band;

determine a bias estimate for the satellite based on a plurality of pseudorange measurements and carrier-phase measurements, wherein the bias estimate is associated with a common bias in the the apparatus and a clock bias for the satellite;

determine a delta carrier-phase measurement for the satellite based on a difference between the carrier-phase measurements at the first frequency band and the second frequency band;

determine an ionospheric delay estimate based at least on the bias estimate and the delta carrier-phase measurement; and

determine a position of the apparatus based at least in part on the ionospheric delay estimate and the pseudorange measurements, or the ionospheric delay estimate and the carrier-phase measurements, or the ionospheric delay estimate and both the pseudorange measurements and the carrier-phase measurements, wherein the ionospheric delay estimate is used with a slant factor corresponding to an elevation of the satellite.

9. The apparatus of claim 8 wherein the plurality of pseudorange measurements and carrier-phase measurements are obtained in an epoch.

10. The apparatus of claim 9 wherein the at least one processor is further configured to determine the delta carrier-phase measurement based on the plurality of pseudorange measurements and carrier-phase measurements received in the epoch.

11. The apparatus of claim 9 wherein the at least one processor is further configured to determine the bias estimate across multiple, continuous epochs and determine the delta carrier-phase measurement in the epoch.

12. The apparatus of claim 11 wherein the at least one processor is further configured to determine a divergence-free, smoothed estimate based on the plurality of pseudorange measurements and carrier-phase measurements.

13. The apparatus of claim 12 wherein the at least one processor is further configured to compute a weighted average of a plurality of delta-pseudorange measurements and a plurality of delta-carrier-phase measurements with the satellite based on the first frequency band and the second frequency band made over time.

14. The apparatus of claim 8 wherein a first number of the pseudorange measurements and carrier-phase measurements received on the first frequency band is greater than a second number of the plurality of pseudorange measurements and carrier-phase measurements received on the second frequency band.

15. An apparatus for determining a position of a mobile device, comprising:

means for obtaining a pseudorange measurements and carrier-phase measurements from a satellite at a first frequency band and a second frequency band;

means for determining a bias estimate for the satellite based on a plurality of pseudorange measurements and carrier-phase measurements, wherein the bias estimate is associated with a common bias in the mobile device and a clock bias for the satellite;

means for determining a delta carrier-phase measurement for the satellite based on a difference between the carrier-phase measurements at the first frequency band and the second frequency band;

means for determining an ionospheric delay estimate based at least on the bias estimate and the delta carrier-phase measurement; and

means for determining the position of the mobile device based at least in part on the ionospheric delay estimate and the pseudorange measurements, or the ionospheric delay estimate and the carrier-phase measurements, or the ionospheric delay estimate and both the pseudorange measurements and the carrier-phase measurements, wherein the ionospheric delay estimate is used with a slant factor corresponding to an elevation of the satellite.

16. The apparatus of claim 15 wherein the plurality of pseudorange measurements and carrier-phase measurements are obtained in an epoch.

17. The apparatus of claim 16 wherein the delta carrier-phase measurement at the epoch corresponds to the plurality of pseudorange measurements and carrier-phase measurements received in the epoch.

18. The apparatus of claim 16 further comprising means for determining the bias estimate across multiple, continuous epochs and the delta carrier-phase measurement is determined at the epoch.

19. The apparatus of claim 18 wherein the means for determining the bias estimate includes means for determining a divergence-free, smoothed estimate based on the plurality of pseudorange measurements and carrier-phase measurements.

20. The apparatus of claim 19 wherein the bias estimate is based on a weighted average of a plurality of delta-pseudorange measurements and a plurality of delta-carrier-phase measurements with the satellite based on the first frequency band and the second frequency band made over time.

21. The apparatus of claim 15 wherein a first number of the pseudorange measurements and carrier-phase measurements received on the first frequency band is greater than a second number of the plurality of pseudorange measurements and carrier-phase measurements received on the second frequency band.

22. A non-transitory processor-readable storage medium comprising processor-readable instructions configured to cause one or more processors to determine a position of a mobile device, comprising instructions for:

obtaining a pseudorange measurements and carrier-phase measurements from a satellite at a first frequency band and a second frequency band;

determining a bias estimate for the satellite based on a plurality of pseudorange measurements and carrier-phase measurements, wherein the bias estimate is associated with a common bias in the mobile device and a clock bias for the satellite;

determining a delta carrier-phase measurement for the satellite based on a difference between the carrier-phase measurements at the first frequency band and the second frequency band;

determining an ionospheric delay estimate based at least on the bias estimate and the delta carrier-phase measurement; and

determining the position of the mobile device based at least in part on the ionospheric delay estimate and the pseudorange measurements, or the ionospheric delay estimate and the carrier-phase measurements, or the ionospheric delay estimate and both the pseudorange measurements and the carrier-phase measurements, wherein the ionospheric delay estimate is used with a slant factor corresponding to an elevation of the satellite.

23. The non-transitory processor-readable storage medium of claim 22 wherein the plurality of pseudorange measurements and carrier-phase measurements are obtained in an epoch.

24. The non-transitory processor-readable storage medium of claim 23 wherein the delta carrier-phase measurement at the epoch corresponds to the plurality of pseudorange measurements and carrier-phase measurements received in the epoch.

25. The non-transitory processor-readable storage medium of claim 23 further comprising instructions for determining the bias estimate across multiple, continuous epochs and the delta carrier-phase measurement is determined at the epoch.

26. The non-transitory processor-readable storage medium of claim 25 wherein the instructions for determining the bias estimate includes instructions for determining a divergence-free, smoothed estimate based on the plurality of pseudorange measurements and carrier-phase measurements.

27. The non-transitory processor-readable storage medium of claim 26 wherein the bias estimate is based on a weighted average of a plurality of delta-pseudorange measurements and a plurality of delta-carrier-phase measurements with the satellite based on the first frequency band and the second frequency band made over time.

28. The non-transitory processor-readable storage medium of claim 22 wherein a first number of the pseudorange measurements and carrier-phase measurements received on the first frequency band is greater than a second number of the plurality of pseudorange measurements and carrier-phase measurements received on the second frequency band.