Triple-Frequency PPP-AR

The L5 signals transmitted by the block IIF GPS satellites caught the IGS by surprise. The time-varying inter-frequency phase bias that exists between L1/L2 and L5, also called “line bias”, is significant enough that it requires dissemination to users. Besides the lack of an adequate format, I believe that this initiative has been delayed because the benefits of a third frequency on float PPP are not substantial. To realize the benefits of L5, the IGS needs to embrace PPP with ambiguity resolution.

 

The proposed Bias-SINEX format is a step forward in that direction. The format expands on the conventional differential bias (i.e., DCB) concept, and allows for observable-specific signal biases (OSBs) to be specified. This formulation is similar to the RTCM state-space representation (SSR), in which one bias is specified for each signal, for example: L1C, L2W, C1C, C1W, C2C, C2W, etc. The main benefit of this approach is that users do not need to know the underlying functional model used by an analysis center in the computation of their clocks and biases. As explained by Laurichesse [2015], corrections enabling PPP-AR can be converted into such a representation and users can either form the linear combinations of their choice or process uncombined observations.

 

To gain more insights into triple-frequency PPP-AR, I decided to try it for myself. My methodology differs slightly from a “conventional” approach where the extra-widelane is first fixed, along with other widelane combinations. Since I already know how to fix ambiguities on L1 and L2, I introduced these integer ambiguities into a triple-frequency geometry-free and ionosphere-free phase combination, allowing to isolate the L5 ambiguity with a full wavelength of 25 cm. It is thus very easy, using a network of receivers, to fix the L5 ambiguities and estimate the L5 line bias. I then saved those biases in the Bias-SINEX format at an interval of 5 minutes.

 

On the user side, I processed data from station UNB3 collected on 2 January 2016. As inputs, I used NRCan's DCM orbits and clocks containing code biases allowing for dual-frequency PPP-AR, as well as the L5 biases that I computed. I processed uncombined signals in static mode, and attempted ambiguity resolution at each epoch using the BIE method. The following figure compares four solutions: dual- and triple-frequency PPP in float mode (labeled as DF-Float and TF-Float, respectively), as well as two solutions with ambiguity resolution (AR). I am showing here an hour in which 5 block IIF satellites were tracked at an elevation angle of 7 degrees or higher.

Triple-Frequency PPP-AR convergence at station UNB3 on 2 January 2016

Figure 1: Triple-frequency PPP-AR convergence for station UNB3

 

As we can see, the triple-frequency PPP-AR converges the fastest, although the gain over the dual-frequency case is not that spectacular. Although these results seem to contradict the ones presented in Figure 12 of Laurichesse [2015], my interpretation is that the bootstrapping algorithm used in his work for ambiguity resolution might not be as efficient as BIE in the dual-frequency case. Processing more data would also be required to obtain a more realistic picture. Nevertheless, I'm quite excited by the prospects of PPP convergence in a multi-GNSS scenario with triple-frequency PPP-AR capabilities and I hope that the IGS will put more efforts in this direction in the future.

 

Reference

Laurichesse, D. (2015). "Handling the biases for improved triple-frequency PPP convergence," GPS World, accessed online.



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