Back in April, I discussed how applying L5 phase-bias corrections allowed for triple-frequency ambiguity resolution in PPP solutions. I demonstrated how the third frequency could potentially improve convergence times, but did not put too much focus on the estimated L5 biases. In this post, we examine the intra-day time variation of the L5 biases for the 12 block IIF satellites in orbit.

The line bias between the L1/L2 and L5 signals of the GPS IIF satellites has been identified shortly after SVN62 was launched on 28 May 2010. As thoroughly explained by Montenbruck et al. (2012), this bias originates from temperature-dependent effects that manifest themselves as periodic variations of the signals. Depending on the elevation of the Sun above the orbital plane of the satellite (the beta angle), the illumination of the satellite varies and the observed periodicities of the signals therefore change over time. With a large beta angle, the line-bias fluctuations are greatly attenuated, while they are accentuated during eclipse seasons (small beta angle).

A potential solution proposed by Montenbruck et al. was to model the time variation of the line bias of SVN62 with a linear-plus-periodic model function. They showed that, over an 8-month period, this model could describe the bias variation with an accuracy of 1 cm RMS. The motivation behind this model was to be able to derive L1/L5 satellite clocks that are compatible with clocks derived from the L1/L2 observables. At the user end, applying the same model corrections would allow for (float) triple-frequency PPP solutions.

The situation is slightly different for PPP with ambiguity resolution (PPP-AR). Assuming that satellite clocks are based on the L1/L2 observables, a L5 phase bias must be estimated by the network to allow ambiguity fixing on L5. If such bias must already be estimated, applying the proposed corrections would only affect how the time variation of the biases are modeled. For obtaining the utmost precision, my own preference is to make no assumption on bias variability and estimate them as completely independent between epochs.

The global network of GNSS stations tracking the L5 signal is still expanding, and the current coverage (at least from data files available at CDDIS on a given day) is shown on the figure below. While it is possible to continuously track all satellites with this station distribution, there are clear gaps in the network. Canada is one such region with few stations contributing to the MGEX initiative, although four additional sites from NRCan are included in the network below.

**Fig.1 Network of stations tracking the GPS L5 signals**

These approximately 50 stations were used to estimate the L5 biases. To be rigorous, I should state that the estimated quantities are rather “biases to be applied to the L5 signal” since a true S-Basis analysis would reveal that the estimated quantities are in fact a combination of biases and datum ambiguities. Thus, the “L5 biases” estimated from the global network of stations for 8 August 2016 are displayed below. No assumptions were made regarding their temporal variations.

**Fig.2 Estimated L5 biases on 8 August 2016**

We can clearly see the periodic variations described in previous literature, which have different amplitude for different satellites. Although it would have to be confirmed, this could be correlated with the beta angle, as discussed above. The worst peak-to-peak variation on this day exceeds 10 cm. Such a fluctuation obviously has to be considered when processing L5 data in PPP, even when ambiguity resolution is not being attempted. The impact of network configuration can also be observed, with slightly noisier estimates being associated with less stations tracking the satellite during these periods.

In a near future, analysis centers of the IGS will most likely start disseminating such biases, paving the way for routine L5 processing.

**Reference**

Montenbruck O, Hugentobler U, Dach R, Steigenberger P, Hauschild A (2012) Apparent clock variations of the Block IIF-1 (SVN62) GPS satellite. GPS Solutions 16(3):303-313 doi:10.1007/s10291-011-0232-x

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4#1Michele Bavaro(Thursday, 22 September 2016 04:21)May I kindly ask you how you obtained such a smooth trend over multiple arcs? Did you apply a large elevation mask and matched the end of an arc with the beginning of another? Also, some biases are not zero mean.. could you please shed some light?

#2Simon Banville(Thursday, 22 September 2016 12:19)@Michele I am not sure why you are expecting several arcs. Using the global network of stations shown above, continuous tracking of the satellites can be achieved and, therefore, an estimate of the L5 bias is available for all epochs.

The L5 biases are not zero mean because they contain a fractional part of the satellite bias needed for L5 ambiguity resolution. They can also be offset by an integer number of L5 cycles (25 cm) without affecting the solution.

I hope this answers your questions.

#3stavros(Thursday, 07 September 2017 23:18)Hi Simon

got a question on your statement "Such a fluctuation obviously has to be considered when processing L5 data in PPP, even when ambiguity resolution is not being attempted". Wouldn't a lumped quantity of float ambiguities and biases absorb this effect when estimating only the satellite phase clocks of an iono-free L1/L5 combination ?

#4Simon Banville(Friday, 08 September 2017 14:55)@Stavros Yes, you are right: if you estimate satellite clocks using L1/L5, then the satellite clock parameters will absorb any fluctuations between L1 and L5.

My comment referred to estimating L1/L2 satellite clocks and using L5 at the user end. For the user to obtain a consistent system, a L5 bias would be needed to account for the time-variation of the L5 signal.