System and method for determining GNSS positioning corrections
A system or method for generating GNSS corrections can include receiving satellite observations associated with a set of satellites at a reference station, determining atmospheric corrections valid within a geographical area; wherein geographical areas associated with different atmospheric corrections can be overlapping, and wherein the atmospheric corrections can be provided to a GNSS receiver when the locality of the GNSS receiver is within a transmission region of the geographical area.
1. A method for generating satellite corrections comprising:
a) receiving satellite observations associated with a set of satellites at a reference station;
b) modelling at least one of ionospheric or tropospheric effects as a function of least one of a pierce point or a pierce angle for satellite rays for each satellite of the set of satellites;
c) fitting the at least one of ionospheric or tropospheric effects to a plurality of polynomial functions, wherein each polynomial function is valid within a unique geographic region, wherein adjacent unique geographic regions are overlapping;
d) determining a set of grid points comprising residuals of the polynomial fit to the at least one of ionospheric or tropospheric effects model;
e) determining a locality of the GNSS receiver; and
f) determining the satellite corrections from:
a polynomial function, of the plurality of polynomial functions, associated with a geographic region matching the locality of the GNSS receiver; and
an interpolated residual determined from grid points proximal the locality of the GNSS receiver.
2. The method of claim 1 , wherein adjacent unique geographic regions overlap by at least 1° latitude or 1° longitude.
3. The method of claim 1 , wherein each unique geographic region comprises an approximately 5° latitude by 5° longitude geographic region.
4. The method of claim 3 , wherein each unique geographic region is associated with 25 grid points.
5. The method of claim 1 , wherein the at least one of ionospheric or tropospheric effects are modelled using a Gaussian process.
6. The method of claim 1 , wherein steps a) through d) are performed at a cloud computing server, wherein only the polynomial function, of the plurality of polynomial functions, associated with the geographic region matching the locality of the GNSS receiver is transmitted from the cloud computing server to the GNSS receiver.
7. The method of claim 1 , further comprising correcting satellite observations used to determine a position of the GNSS receiver with the satellite corrections.
8. The method of claim 1 , further comprising determining operation instructions for a vehicle, wherein the GNSS receiver is mounted to the vehicle.
9. A method for generating GNSS corrections comprising:
a) receiving satellite observations associated with a set of satellites at a reference station;
b) determining atmospheric corrections comprising:
a set of fitting functions, wherein each fitting function is valid within a unique geographical area, wherein adjacent unique geographic areas overlap by at least 0.1° latitude or 0.1° longitude; and
a set of grid points comprising residual corrections to the set of fitting functions;
c) determining a locality of the GNSS receiver; and
d) determining the satellite corrections from:
a fitting function, of the plurality of fitting functions, associated with a geographic region matching the locality of the GNSS receiver, wherein the fitting function is only provided to the GNSS receiver when the locality of the GNSS receiver is within a transmission region of the associated unique geographical area; and
a residual determined from residual corrections associated with grid points proximal the locality of the GNSS receiver.
10. The method of claim 9 , wherein each unique geographical area is an approximately 5° latitude by approximately 5° longitude geographic area.
11. The method of claim 10 , wherein the transmission region of the unique geographical area is an approximately 3° latitude by approximately 3° longitude geographic area.
12. The method of claim 9 , wherein transmission regions for adjacent unique geographic areas do not overlap.
13. The method of claim 9 , wherein each unique geographic area is associated with at most 25 grid points.
14. The method of claim 9 , wherein determining the atmospheric corrections comprises:
a) modelling atmospheric effects as a function of least one of a pierce point or a pierce angle for satellite rays for each satellite of the set of satellites;
b) fitting the atmospheric effects model using the set of fitting functions; and
c) determining residuals of the fit to the atmospheric effects model.
15. The method of claim 14 , wherein each fitting function of the set of fitting functions is a bivariate polynomial function of at most second degree.
16. The method of claim 14 , wherein the atmospheric effects are modelled using a Gaussian process.
17. The method of claim 9 , wherein the residual is determined by interpolating the residual corrections between 2, 3, or 4 grid points proximal the locality of the receiver.
18. The method of claim 9 , further comprising correcting satellite observations used to determine a position of the GNSS receiver with the satellite corrections.
19. The method of claim 18 , further comprising determining operation instructions for a vehicle, wherein the GNSS receiver is mounted to the vehicle.
20. A method for generating GNSS corrections comprising:
a) receiving satellite observations associated with a set of satellites at a reference station;
b) determining atmospheric corrections comprising:
a set of fitting functions, wherein each fitting function is valid within a unique geographical area, wherein adjacent unique geographic areas overlap by at least 0.1° latitude or 0.1° longitude; and
a set of grid points comprising residual corrections to the set of fitting functions;
c) determining a locality of the GNSS receiver; and
d) determining the satellite corrections from:
a fitting function, of the plurality of fitting functions, associated with a geographic region matching the locality of the GNSS receiver, wherein the fitting function is only provided to the GNSS receiver when the locality of the GNSS receiver is within a transmission region of the associated unique geographical area; and
a residual determined from residual corrections associated with grid points proximal the locality of the GNSS receiver;
wherein determining the atmospheric corrections comprises:
modelling atmospheric effects as a function of least one of a pierce point or a pierce angle for satellite rays for each satellite of the set of satellites;
fitting the atmospheric effects model using the set of fitting functions; and
determining residuals of the fit to the atmospheric effects model.
21. The method of claim 20 , wherein each fitting function of the set of fitting functions is a bivariate polynomial function of at most second degree.
22. The method of claim 20 , wherein the atmospheric effects are modelled using a Gaussian process.