Post-processed accuracy prediction for GNSS positioning
Methods and apparatus for processing of data from GNSS receivers are presented. (1) A real-time GNSS rover-engine, a long distance multi baseline averaging (MBA) method, and a stochastic post-processed accuracy predictor are described. (2) The real-time GNSS rover-engine provides high accuracy position determination (decimeter-level) with short occupation time (2 Minutes) for GIS applications. The long distance multi baseline averaging (MBA) method improves differential-correction accuracy by averaging the position results from several different baselines. This technique provides a higher accuracy than any single baseline solution. It was found, that for long baselines (more than about 250 km), the usage of non-iono-free observables (e.g. L1-only or wide-lane) leads to a higher accuracy with MBA compared to the commonly used iono-free (LC) combination, because of the less noisy observables and the cancellation of the residual ionospheric errors. (3) The stochastic post-processed accuracy (SPPA) predictor calculates during data collection an estimate of the accuracy likely to be achieved after post-processing. This helps to optimize productivity when collecting GNSS data for which post-processed accuracy is important. The predictor examines the quality of carrier measurements and estimates how well the post-processed float solution will converge in the time since carrier lock was obtained.
1. A method of predicting post-processed accuracy of observations collected at a rover over multiple epochs from signals of GNSS satellites, comprising:
a. obtaining observations collected at the rover for a current epoch,
b. obtaining a current-epoch satellite position for each satellite,
c. obtaining an approximate current-epoch rover position,
d. obtaining a current-epoch error models,
e. determining a current-epoch error estimate from the current epoch error models and the approximate current-epoch rover position and the current-epoch satellite positions and a prior-epoch error estimate, the current-epoch error estimate representing an estimated rover position error to be expected upon subsequent differential post-processing of the observations of the plurality of epochs with reference data of a corresponding plurality of epochs, and
f. providing the current-epoch error estimate for use in determining whether observations of further epochs are needed to obtain a desired rover position error upon said subsequent differential post-processing.
2. The method of claim 1 , wherein the observations comprise at least one of (1) single-frequency combination observations prepared from single-frequency carrier-phase observations and single-frequency code-phase observations, and (2) multi-frequency observations prepared from carrier-phase observations of a plurality of frequencies.
3. The method of claim 1 , wherein obtaining the current-epoch satellite position for each satellite comprises at least one of: (1) deriving the current-epoch satellite position from a GNSS satellite navigation message, and (2) deriving the current-epoch satellite position from a source other than a GNSS satellite navigation message.
4. The method of claim 1 , wherein obtaining the approximate current-epoch rover position comprises at least one of: (1) computing the approximate current-epoch rover position from current-epoch observations, (2) retrieving a previously-stored rover position, and (3) obtaining the approximate current-epoch rover position from user input, and (4) deriving the approximate current-epoch rover position from another data source.
5. The method of claim 1 , wherein the current-epoch rover position is accurate to within some hundreds of meters.
6. The method of claim 1 , wherein obtaining the current-epoch error models comprises at least one of: (1) determining for each satellite a current-epoch satellite elevation relative to the current-epoch rover position, (2) determining for each satellite a current-epoch carrier-to-noise ratio of a signal received from the satellite, (3) obtaining a model based on atmospheric information, and (4) obtaining a model based on satellite orbit error information.
7. The method of claim 1 , wherein determining the current-epoch error estimate comprises:
i. computing a current-epoch time-update matrix from the current-epoch error models,
ii. computing a current-epoch process-noise matrix from the error models
iii. computing an current-epoch a priori error estimate from the current-epoch time-update matrix and the current-epoch process-noise matrix,
iv. computing a current-epoch design matrix from the current-epoch rover position and the current-epoch satellite positions,
v. computing a current-epoch measurement noise matrix from the current-epoch error models,
vi. computing a current-epoch filter gain from the current-epoch design matrix, the current-epoch a priori error estimate and the current-epoch measurement noise matrix, and
vii. computing a current-epoch a posteriori error estimate from the current-epoch a priori error estimate, the current-epoch filter gain, and the current-epoch design matrix.
8. The method of claim 7 , wherein computing the current-epoch design matrix comprises at least one of: (1) deriving the current-epoch satellite position from a GNSS satellite navigation message, and (2) deriving the current-epoch satellite position from a source other than a GNSS satellite navigation message.
9. The method of claim 1 , further comprising determining from the current-epoch error estimate whether observations of further epochs are needed to obtain a desired rover position error upon said subsequent differential post-processing.
10. The method of claim 1 , further comprising at least one of: (1) displaying the current-epoch error estimate, (2) comparing the current-epoch error estimate with a value representing a desired rover position error upon said subsequent differential post-processing, (3) signaling that observations of enough epochs have been collected to obtain a desired rover position error upon said subsequent differential post-processing, and (4) terminating collection of observations when the current-epoch error estimate reaches a desired value.
11. Apparatus for predicting post-processed accuracy of observations collected at a rover over multiple epochs from signals of GNSS satellites, comprising,
a. a first element to obtain observations collected at the rover for a current epoch,
b. a second element to obtain a current-epoch satellite position for each satellite,
c. a third element to obtain a current-epoch rover position,
d. a fourth element to obtain current-epoch error models,
e. a fifth element to determine a current-epoch error estimate from the current epoch error models and the current-epoch rover position and the current-epoch satellite positions and a prior-epoch error estimate, the current-epoch error estimate representing an estimated rover position error to be expected upon subsequent differential post-processing of the observations of the plurality of epochs with reference data of a corresponding plurality of epochs, and
f. a sixth element to provide the current-epoch error estimate for use in determining whether observations of further epochs are needed to obtain a desired rover position error upon said subsequent differential post-processing.
12. The apparatus of claim 11 , wherein the observations comprise at least one of (1) single-frequency combination observations prepared from single-frequency carrier-phase observations and single-frequency code-phase observations, and (2) multi-frequency minimum-error combination observations prepared from carrier-phase observations of a plurality of frequencies.
13. The apparatus of claim 11 , wherein the second element is operative to determine the approximate current-epoch satellite position for each satellite by at least one of: (1) deriving the approximate current-epoch satellite position from a GNSS satellite navigation message, and (2) deriving the approximate current-epoch satellite position from satellite a source other than a GNSS satellite navigation message.
14. The apparatus of claim 11 , wherein the third element is operative to determine the approximate current-epoch rover position by at least one of: (1) computing the approximate current-epoch rover position from current-epoch observations, (2) retrieving a previously-stored rover position, and (3) obtaining the approximate current-epoch rover position from user input, and (4) deriving a current-epoch rover position from a data source.
15. The apparatus of claim 11 , wherein the third element is operative to determine the current-epoch rover position with an accuracy of about 100 meters.
16. The apparatus of claim 11 , wherein the fifth element is operative to obtain the current-epoch error models by at least one of: (1) determining for each satellite a current-epoch satellite elevation relative to the current-epoch rover position, (2) determining for each satellite a current-epoch carrier-to-noise ratio of a signal received from the satellite, (3) obtaining a model based on atmospheric information, and (4) obtaining a model based on satellite orbit error information.
17. The apparatus of claim 11 , wherein the fifth element to determine a current-epoch error estimate is operative to:
i. compute a current-epoch time-update matrix from the current-epoch error models,
ii. compute a current-epoch process-noise matrix from the error models
iii. compute an current-epoch a priori error estimate from the current-epoch time-update matrix and the current-epoch process-noise matrix,
iv. compute a current-epoch design matrix from the current-epoch rover position and the current-epoch satellite positions,
v. compute a current-epoch measurement noise matrix from the current-epoch error models,
vi. compute a current-epoch filter gain from the current-epoch design matrix, the current-epoch a priori error estimate and the current-epoch measurement noise matrix, and
vii. compute a current-epoch a posteriori error estimate from the current-epoch a priori error estimate, the current-epoch filter gain, and the current-epoch design matrix.
18. The apparatus of claim 17 , wherein the fifth element is operative to compute the current-epoch design matrix by at least one of: (1) deriving the current-epoch satellite position from a GNSS satellite navigation message, and (2) deriving the current-epoch satellite position from a source other than a GNSS satellite navigation message.
19. The apparatus of claim 11 , further comprising an element operative to determine from the current-epoch error estimate whether observations of further epochs are needed to obtain a desired rover position error upon said subsequent differential post-processing.
20. The apparatus of claim 11 , further comprising a element operative to perform at least one of: (1) displaying the current-epoch error estimate, (2) comparing the current-epoch error estimate with a value representing a desired rover position error upon said subsequent differential post-processing, (3) signaling that observations of enough epochs have been collected to obtain a desired rover position error upon said subsequent differential post-processing, and (4) terminating collection of observations when the current-epoch error estimate reaches a desired value.
21. The apparatus of claim 11 , wherein the first element comprises a GNSS receiver.
22. An article of manufacture comprising a computer-readable medium instructions stored therein for causing a machine to perform the method of claim 1 .