With ongoing work at NRCan aiming at offering an online PPP service supporting ambiguity resolution, we performed a validation exercise consisting of processing nearly 40 permanent GPS stations in eastern Canada over a 10-year period. As a by-product of this analysis, we computed station velocities and compared them with the values derived from the Bernese network solutions done at NRCan. The results were published last week in Survey Review and I am offering a short summary of the main conclusions here.
The idea behind processing data over a long period of time was twofold: first, to detect any mismodeled error sources in the software; second, to validate the performance of ambiguity-fixed solutions using the GR2 products. In order to do this, we selected 37 continuously-operating GPS stations located mainly in eastern Canada-US, as shown on Fig 1.
Fig 1 The 37 stations processed in the study
We processed daily observations of the selected stations in static mode using the PPP method with satellite orbits, clocks and earth orientation parameters products provided by the Centre National d’Études Spatiales (CNES) of France as a part of the ‘repro2’ initiative (GR2 products). These products were selected because the satellite clock corrections are provided with widelane biases and allow for ambiguity resolution. This feature is enabled starting 2 May 2000, after selective availability was turned off. The a priori tropospheric delay was obtained using pressure values and mapping function coefficients from the Vienna Mapping Function 1 grids. The latest IERS conventions were implemented to model various error sources such as earth tides, ocean loading, pole tides and relativistic effects, except for the second-order ionospheric effects which were neglected. Uncombined observations on both frequencies were processed to estimate the following parameters: station position, receiver clock offset, uncalibrated signal delays, residual tropospheric zenith delay and two orthogonal gradients, stochastic slant ionospheric delays and carrier-phase ambiguities.
An example of the performance of PPP and PPP-AR is presented in Fig 2 for station GODE. We see that ambiguity resolution offers a significant reduction in the longitude scatter, although the impact is less perceptible for the other components.
Fig 2 Position time series for station GODE
This performance is quite representative of all the stations processed. For instance, Fig 3 below shows the repeatabilities of the PPP and PPP-AR solutions after removing a linear drift as well as annual and semi-annual signals. This detrending may remove unmodeled error sources such as atmospheric loading and could therefore offer a slightly optimistic view of the precision of daily PPP solutions. Nevertheless, these results were quite encouraging and confirm that ambiguity resolution can improve the longitude (east) component by nearly 40% on average.
Fig 3 Position repeatabilities from PPP and PPP-AR
In terms of velocities, the RMS of the velocity differences between the PPP-AR and the NRCan solutions was 0.28 mm/yr and 0.59 mm/yr for the horizontal and vertical components, respectively. However, I learned that computing velocities is not as simple as it seems, mainly due to the handling of discontinuities in the time series.
When using data at a 5-minute sampling interval, the whole network of Fig 1 for a period of 10 years, including 123 722 daily observation files, was processed in approximately 76.4 hours on a desktop computer. This is equivalent to an average duration of 2.2 seconds per station, which is notably faster than traditional processing based on double-differenced network solutions. Therefore, considering the precision attained and the computational efficiency of the PPP-AR solution, it seems like a good alternative to differential solutions for the determination of station velocities and for Earth deformation studies in general.
I would like to thank Mohammad Ali Goudarzi who wrote all of the scripts, and did all the number crunching and data analysis for this project. While he was still completing his PhD degree at Laval University when doing this work, he did such a good job that he is now a part of our team at NRCan!