Precise Point Positioning (PPP) uses precise satellite orbit and clock corrections from global navigation satellite systems (GNSS) to provide users with accurate positioning capabilities with respect to a global reference frame. In recent years, some International GNSS Service (IGS) analysis centers (ACs) also started providing satellite clock correction sets that preserve the integer nature of carrier-phase ambiguities. Even though these “integer clocks” allow for a more rapid convergence of PPP solutions and improved stability of the position estimates, their integer properties are currently neglected in the IGS clock combination. For this reason, recent efforts at NRCan have focused on generating a satellite clock combination product allowing for PPP with ambiguity resolution.
The theoretical details of integer clock combination and a proof of concept were first presented at the ION GNSS+ 2016 meeting last September. Readers are referred to this publication for more details on the technical aspects of our approach:
Seepersad G, Banville S, Collins P, Bisnath S, Lahaye F (2016) Integer satellite clock combination for Precise Point Positioning with ambiguity resolution. In: Proceedings of the 29th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2016), Portland, Oregon, September 2016, pp. 2058-2068 (Download)
In a nutshell, this paper showed that simply realigning the combined IGS clocks using the GRG (CNES) and/or DCM (NRcan) clocks could benefit from both the low-noise and integer properties of the individual products. This is illustrated in the figure below which compares the mean repeatability of 24-hour static positions from 29 globally distributed IGS stations over a one-week period. The new combined clock product, labeled IGS-AR, clearly shows improved performance in the east component with respect to the original IGS clocks.
Fig 1 Repeatability of the PPP user solution in static mode utilizing different types of
clock products: IGS, IRC (CNES), DCM (NRCan) and IGS-AR (realigned IGS)
After these encouraging results, our intention was to reprocess historical data to create an archive of realigned IGS clocks dating back from the introduction of IGS08 in 2011. However, this process turned out to be more of a challenge than anticipated. As an example, the figure below shows the clock discrepancies on 29 Dec 2011 between the GRG and IGS clocks after accounting for radial orbit differences, timing offsets and a constant shift for each satellite. In this plot, quality checks were deliberately omitted to better emphasize problematic issues.
Fig 2 Clock discrepancies between the GRG and IGS clocks on 29 Dec 2011
The first problem originates from eclipsing satellites, an obvious case being satellite G03 (in blue) around 05:00 and 17:00 GPST. Several analysis centers adopt a different satellite orientation during yaw maneuvers which leads to important clock discrepancies caused mainly by the satellite wind-up effects. This situation can be easily identified in the clock combination process by monitoring eclipse seasons. Still, during these events, it only makes sense to combine clock products that adopt compatible yaw modeling. One solution would be for the IGS to follow the RTCM SSR standard in which the satellite yaw angle is provided along with clock estimates, which would allow to apply wind-up corrections to the clocks of each AC. Still, my preferred solution would be to improve agreement among ACs, either by adopting a standard or by estimating the satellite orientation via reverse precise point positioning.
Another obvious problem, particularly visible for satellites G03 and G06 is the seemingly two parallel time series for each satellite. An investigation revealed that the IGS combination has an offset between clock estimates at 30-sec and 5-min intervals for these satellites! Both of the problems stated above can be seen in PPP carrier-phase residuals, for example using satellite G06 tracked at IGS station ZECK (see figure below). We see the clear drift in the residuals when using the IGS products (about 5-6 cm over 4 hours) which matches the drift in the previous figure. Furthermore, even though measurements are noisy, we can still see that the residuals obtained using the IGS products have values sticking out every 5 minutes (clearly seen between 08:00 and 09:00).
Fig 3 Carrier-phase residuals from satellite G06 at station ZECK using the GRG and IGS clock products
These results revealed that simply realigning the IGS clocks to obtain improved PPP-AR products may not be the solution of choice. In order to benefit from ambiguity resolution in PPP, consistent modeling between an AC and PPP users is imperative. When combining clock products, modeling inconsistencies between ACs will propagate to the user which could impact position estimates when fixing ambiguity parameters to integer values. Perhaps that the integer clock combination process requires a whole new way of looking at clock combinations, with a focus on consistency rather than robustness.