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Tips on reproducing “PPP-RTK with augmentation from a single reference station”

I have received some requests to reproduce the work published under the title PPP-RTK with Augmentation from a Single Reference Station Below, I have provided answers to some common questions and suggested procedures that may help facilitate the reproduction of this work.

Q&A

- Q: The float ambiguity N1,N2 on L1 and L2 frequencies that you calculated by non-differential non-composition. PB1 is the float ambiguity N1 minus the nearest integer value. In the rover station, is PB1 changed directly to the phase observation?
- Ans: PB1 is generated by the base station. In the Rover station, PB1 can be corrected directly from phase observation. Alternatively, you can also correct PB1 from the estimated N1 before AR process instead (then you have to add some extra processing noise for the estimated N1 as the iono/trop generated from prior-convergence satellite at the base station are still drifting, and such priror-convergence drifting will be propagated into the estimated N1 in the rover station).

- Q: In PPP-AR, you fixed the WL first and then fixed N1. Is the WL calculated from the float N1-N2 at the rover station? And then fix N1 on L1 after constraining the WL.
- Ans: While WL can be calculated directly from N1-N2, it does not significantly contribute to positioning accuracy. Therefore, it is recommended to focus on achieving a successful N1 fix to replicate the accuracy presented in the paper.

- Q: Is there a limit on the minimum number of satellites that can be fixed when the ambiguity is fixed, such as four satellites or more fixed before fixing the WL and N1.
- Ans: minimum number of satellites is set as 6 for N1 (5 double difference N1), no limitation for WL.

- Q: When I tried to reproduce your work, I found that the integer properties of my DF N1 values are not good and help less to improve the localization during the constraint process, but the WL has obvious integer properties. Have you encountered these problems during your testing?
- Ans: First make sure you are calculating the between-satellite single differenced N1. Other than that, this may happen if you are not correcting phase bias from observations, but from the estimated ambiguities. For example, if you are using PB1 from a prior-convergence satellite in the base station, and correcting PB1 from N1 instead of correcting PB1 fromL1 directly, the estimated N1 in the rover station is no longer constant in nature, this is because base station generated iono/trop are still driftting, and the unconverged bias will be propagated into N1 in the rover station. But when you are using fully coverged satellite generated PB1, assuming N1 to be constant will be ok.

- Q: Are the covariance for phase bias PB1 and PB2 used for setting up observation covariance in the user station end?
- Ans: The answer to this question is highly dependent on the specific use case. While the paper does not provide any information about the covariance for phase bias for any specific use, this covariance is typically representative of two factors: (1) the stage of phase bias convergence in the reference station, and (2) the quality of the reference station observations. In an ideal scenario where the reference station data is of high quality and the phase bias has already converged after a short period of time (e.g. 30 seconds as demonstrated in the paper), it may be possible to set an arbitrary integer constraint to the AR fixed ambiguity subset, as presented in the paper. However, if the phase bias is still in the fast-changing stage (i.e. convergence time is less than 30 seconds), setting a tight integer constraint to the estimated ambiguities in the rover station may result in a violation of the random constant assumption for the ambiguity parameters.

Some other ideas may help during development

  • Make sure you are looking for integer property from between-satellite N1 instead of undifferenced one
  • Check the quality of PB1, for example, reject the PB1 with too large std like 0.4m, it only takes a few seconds for the base end to converge into 0.4m, but a large drift in the beginning will mislead the N1 estimation in the rover end as it is assuming N1 to be random constant
  • Make sure you have properlly constraint iono in single differenced mode or add an extra parameter to absorb the bias.
  • When AR fail in the rover end, reject the N1 with the largest std and try again.
  • Setting a larger constraint covariance for the PB1 with large std, as a PB1 with large STD may have a quality issue if you have not handled it properly in the base end.
  • First try the reference station AR with the SSR corrections generated by itself to make sure you have the correct code implementation.