I have recently got my hands on a copy of the Springer Handbook of Global Navigation Satellite Systems, edited by Peter Teunissen and Oliver Montenbruck. I am quite impressed with the list of contributing authors, with many experts on GNSS sharing their knowledge on a wide variety of topics contained in 41 chapters. While I encourage anyone interested in learning more about GNSS to order a copy of this book, I also want to point out an erratum related to GLONASS RTK processing.

I have to confess: out of curiosity, I scanned the book for any references to my work. I was actually quite surprised to see, in Chapter 26 on Differential Positioning, a whole half-page discussing the NRCan paper on “GLONASS ambiguity resolution of mixed receiver types without external calibration,” published in 2013 in GPS Solutions. After explaining the proposed method, the authors concluded that (pp.767-768):

“However, it is stressed that this approach of GLONASS integer ambiguity resolution fully relies on the underlying assumption that the differential interchannel biases may be ignored, which only holds for identical receiver pairs. For mixed receivers still external calibrations are needed, despite the claims made by [Banville et al. 2013]”

Really???

I see two things that could have led the authors to make such a statement:

1) They did not recognize the true origin of the GLONASS inter-frequency phase biases (IFPBs). The IFPBs come from a misalignment of the code and the phase measurements within a receiver and, if you do not combine the phase and code measurements, there is no such thing as IFPBs. The method proposed by Banville et al. (2013) fully decouples the two types of observables which prevents the differential code-phase timing bias to propagate into the carrier-phase functional model.

2) As I have explained in a previous blog post, it is not exact to model the IFPBs as a linear function of the frequency channel number. The proper partial derivative is a multiple of the wavelength and the frequency channel number. Hence, if you start with the proper functional model, you would see that IFPBs (assuming here that they exist regardless of code measurements) get fully absorbed by the model parameters (I can back this up with equations, of course).

The figure below, extracted from the paper, shows the convergence of ambiguities between NovAtel and Javad receivers which are known to have interchannel biases exceeding 2 cm/channel:

**Fig 1 Estimated GLONASS ambiguities between a NovAtel and a Javad receiver. All ambiguities converge naturally to integers with the method proposed by Banville et al. (2013)**

My question is: why haven’t the authors of the chapter contacted us before accusing us of making false claims? I would have been very happy to provide further explanations!

I am thinking that there is a need for a follow-up paper on GLONASS inter-frequency biases. I have written a few additional blog posts about them, but I still have undisclosed knowledge about this topic that might be worth sharing.

**Reference**

Banville S, Collins P, Lahaye F (2013) GLONASS ambiguity resolution of mixed receiver types without external calibration. GPS Solut doi:10.1007/s10291-013-0319-7

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