Single-Frequency PPP

The main challenge with single-frequency PPP is to mitigate ionospheric effects. Global ionospheric maps (GIM) can reduce the contribution of this error source to some extent but residual errors often lead to meter-level positioning accuracies. A popular option is to use the GRAPHIC combination, an average of code and phase observations that “eliminates” ionospheric errors. This formulation is, however, not always your best option.


Following a concept explained in a previous post, forming a linear combination to eliminate a parameter is usually equivalent to estimating this parameter unconstrained. Hence, explicitly forming the GRAPHIC combination implies that the temporal variation of slant ionospheric delays is modeled as white noise.

The ionospheric delay between a satellite and a receiver varies at a rate of a few millimeters to a few centimeters per second. This important piece of information can be exploited when using uncombined signals, i.e. using directly the code and phase observations. The main advantages of using uncombined signals are that:

  • Modeling slant ionospheric delays as a random walk process can reduce noise.
  • External information on the ionosphere can improve position estimates and possibly reduce convergence times.

The following plot shows three “kinematic” single-frequency PPP solutions computed from data collected at station UNB3 (Trimble NetR9) on 15 March 2015.

  1. The solution labeled ‘GIM’ does not estimate any parameters related to the ionosphere and simply uses corrections from a GIM. As expected, errors in the model and a poor temporal resolution lead to meter-level accuracies.
  2. A second solution labeled as 'GRAPHIC' uses uncombined signals but models the temporal variation of the ionospheric parameters as white noise. For this reason, it is expected to be equivalent to explicitly forming the GRAPHIC combination. This approach leads to a much better accuracy, but is quite noisy.
  3. The last solution also uses uncombined (UC) signals but models the temporal variation of the ionosphere as a random walk process. As a result, the noise is greatly reduced.

In the last two cases, the singularities of the systems are handled by constraining ionospheric parameters using the GIM for the first epoch when a satellite is observed only.

In conclusion, using uncombined signals allows adding extra information on the temporal variability of the ionosphere. Since single-frequency receivers typically have large code noise, this approach should be beneficial for improving the precision of the position estimates.

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Comments: 2
  • #1

    Ahmed El-Mowafy, Australia (Friday, 08 May 2015 12:25)

    - You used a single frequency data extracted from Trimble NetR9, which is a high geodetic-grade receiver. The code noise could be much larger if you used true single frequency receivers, e.g. U-blox.
    - How about the use of ionospheric correctional data received from satellite-based augmentation systems, such as WAAS or EGNOS, which seems more realistic for single-frequency users.

  • #2

    Simon Banville (Friday, 08 May 2015 21:01)

    Dear Ahmed,

    I agree with you that "true" single-frequency receivers have larger code noise than geodetic-grade receivers which, as a consequence, may lead to larger positioning errors. But even in this case, modeling slant ionospheric delays as a random walk process would reduce the noise significantly, which is the aspect I wanted to emphasize.

    The best source of ionospheric correction would be slant ionospheric delays from nearby stations of course. I'm also hoping that more agencies will broadcast ionospheric corrections (both VTEC and STEC) using the new RTCM-SSR messages.