Real-time and post-processed orbit determination and positioning

1. A method comprising:

receiving, by one or more computers, measurements from at least one global navigation satellite system (GNSS) receiver;

analyzing, by the one or more computers, the measurements, thereby detecting and flagging anomalous measurements and phase breaks;

calculating, by the one or more computers, high-fidelity satellite and signal models that approximate the measurements, wherein the models comprise a plurality of model parameters having a priori values;

estimating, by the one or more computers, values for the plurality of model parameters affecting orbital and clock states of a GNSS satellite or affecting reception of said measurements by the at least one GNSS receiver, wherein the estimating is based on the measurements, thereby obtaining a plurality of estimated model parameters;

calculating, by the one or more computers, improved orbital and clock states based on the plurality of estimated model parameters and the measurements;

calculating, by the one or more computers, refined model parameters, additionally to the improved orbital and clock states, based on the plurality of estimated model parameters and the measurements; and

transmitting, by the one or more computers, the improved orbital and clock states and the refined model parameters to the at least one GNSS receiver.

2. The method of claim 1 , further comprising:

calculating, by a computer, a position of the at least one GNSS receiver.

3. The method of claim 1 , wherein the transmitting, by a computer, the improved orbit and clock states is within 6 seconds from the receiving, by a computer, the measurements from the at least one GNSS receiver.

4. The method of claim 1 , wherein the transmitting is streaming through an internet connection, cell network, satellite communications, or other radio communications.

5. The method of claim 1 , wherein the plurality of physical parameters is chosen from the group consisting of: solar pressure scale and Y-Bias, Earth radiation scale, satellite physical properties, constant accelerations, once-per-orbital-revolution accelerations satellite yaw angle and rate, state of troposphere, state of ionosphere, gravitational harmonics, Earth orientation, polar motion, polar motion rates, Earth hour angle, earth rotation rates, tropospheric delay, zenith delay and gradients, real-valued phase biases, and ionospheric delay.

6. The method of claim 1 , further comprising:

estimating, by a computer, inter-signal bias between pairs of signals transmitted by the GNSS satellite.

7. The method of claim 1 , further comprising:

receiving and processing, by a computer, measurements of doppler orbitography and radiopositioning integrated by satellite (DORIS) or satellite laser ranging (SLR).

8. The method of claim 1 , further comprising:

performing, by a computer, on-the-fly decoupling and recoupling of GNSS satellites states and/or GNSS stations states in a filter.

9. The method of claim 8 , further comprising estimating, by a computer, a position of the at least one GNSS receiver as a decoupled state within a network-based orbit-determination filter.

10. The method of claim 1 , further comprising:

performing, by a computer, integer GNSS phase bias ambiguity resolution during a network-based orbit determination.

11. The method of claim 1 , wherein the estimating further comprises implementing, by a computer, solar radiation force models for the GNSS satellite.

12. The method of claim 1 , wherein the analyzing is on the fly or in post-processing.

13. The method of claim 1 , further comprising:

producing data records at a specified time by a first filter; and

reading the data records at a time later than the specified time, by a second filter,

thereby continuing a filtering of the first filter without loss of accuracy.

14. The method of claim 1 , wherein the calculating, by a computer, high-fidelity satellite and signal models comprises modeling phase biases as time-varying stochastic processes.

15. The method of claim 1 , further comprising estimating inter-signal bias between pairs of signals transmitted by GNSS satellites.

16. The method of claim 1 , wherein the estimating, by a computer, values for the plurality of model parameters comprises estimating, by a computer, through a parameter estimation filter of square root information (SRI) type.

17. The method of claim 16 , wherein the estimating through the SRI filter comprises at least one of the following steps:

adding or removing parameters on the fly;

smoothing backward or forward;

filtering or smoothing multiple updates simultaneously;

computing sigmas and covariances by applying pseudo-measurements, or by rotating columns of the SRI matrix and re-upper-triangularizing;

applying phase bias ambiguity constraints;

assigning first order Gauss-Markov stochastic attributes to any estimable parameter;

using Householder transformations rather than Givens rotations, by temporarily breaking upper triangularity of the SRI matrix to estimate the required parameters.

18. The method of claim 17 , wherein the SRI filter can be configured to run as a current-state filter, or as a pseudo-epoch state filter.

19. The method of claim 1 , further comprising partitioning, by a computer, a filter into multiple processes, wherein the multiple processes run concurrently on multiple processing units and communicate with a message passing interface (MPI).

20. The method of claim 1 , further comprising partitioning, by a computer, a filter into multiple threads running concurrently on multiple processing cores on a same computer.

21. The method of claim 1 , further comprising estimating, by a filter, signal range biases between a GNSS transmitter and the at least one GNSS receiver pair.

22. The method of claim 1 , wherein the measurements are simulated or replayed from archive.

23. The method of claim 1 , wherein the measurements are read from shared memory or from files.

24. The method of claim 1 , further comprising integrating, by a computer, orbits by an Embedded Runge-Kutta method with adaptive step site, or a variable step Adams-type predictor corrector.

25. The method of claim 24 wherein the Embedded Runge-Kutta method comprises a general-purpose high-order interpolation algorithm.

26. The method of claim 24 wherein the Embedded Runge-Kutta method comprises an independent residual evaluator.

27. The method of claim 24 wherein the Embedded Runge-Kutta method comprises a global error bound for the integrated orbits.

28. The method of claim 24 wherein the integrating comprises interpolating by an algorithm to points at an interior of a step size.

29. The method of claim 24 wherein the integrating comprises accounting, by a computer, for various types of discontinuities in forces acting on a plurality of GNSS satellites, wherein the plurality of GNSS satellites comprise said GNSS satellite, wherein the discontinuities comprise discontinuities due to eclipses and due to maneuvers of the plurality of GNSS satellites, and wherein the integrating further accommodates user-specified discontinuous source functions.

30. The method of claim 1 , further comprising computing analytically partial derivatives of all satellite dynamics models and all signal propagation models relative to estimable model parameters.

31. The method of claim 1 , further comprising providing user input via a RTG-Tree interface, wherein the interface comprises inheritance attributes.

32. The method of claim 1 , further comprising providing formal errors for said plurality of model parameters.

33. The method of claim 11 , wherein the solar radiation force models comprise at least one of empirical models from the GPS solar pressure model (GPSM) family, tabulated models, Fourier expansions, or smoothed tabulated models via a Fourier series approximation.

34. The method of claim 1 , wherein the estimating, by a computer, values for the plurality of model parameters comprises estimating in real-time an inter-signal bias between pairs of signals transmitted by the at least one GNSS receiver.

35. The method of claim 34 , wherein the pairs of signals transmitted by the at least one GNSS receiver are L1P and L1CA.

36. The method of claim 35 , wherein the estimating in real-time an inter-signal bias comprises estimating and comparing two satellite clock states.

37. An apparatus for aiding global navigation satellite system positioning, the apparatus comprising:

a communication link from a global navigation satellite system (GNSS) satellite to a RTGx system;

a communication link from a GNSS receiver to the RTGx system;

a communication link from the GNSS satellite to the GNSS receiver;

wherein the RTGx system is configured to generate improved orbital and clock states according to the following steps:

receiving, by one or more computers, measurements from at least one global navigation satellite system (GNSS) receiver;

analyzing, by the one or more computers, the measurements, thereby detecting and flagging anomalous measurements and phase breaks;

calculating, by the one or more computers, high-fidelity satellite and signal models that approximate the measurements, wherein the models comprise a plurality of model parameters having a priori values;

estimating, by the one or more computers, values for the plurality of model parameters affecting orbital and clock states of a GNSS satellite or affecting reception of said measurements by the at least one GNSS receiver, wherein the estimating is based on the measurements, thereby obtaining a plurality of estimated model parameters;

calculating, by the one or more computers, improved orbital and clock states based on the plurality of estimated model parameters and the measurements;

calculating, by the one or more computers, refined model parameters, additionally to the improved orbital and clock states, based on the plurality of estimated model parameters and the measurements; and

transmitting, by the one or more computers, the improved orbital and clock states and the refined model parameters to the at least one GNSS receiver.