https://web.archive.org/web/20120205022334/tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf (page 11)

"But it's the absence of any explicit acknowledgment of special relativistic effects due to the speed of light being the same whenever measured by an observer, leading to the relativity of simultaneity and the associated Lorentz transformation physics - there's nothing of that at all modeled in the current system."

So, if Niel Ashby or whathewer tries to claim GPS uses lorentz transformations, he is wrong. So, why do his papers "contain" lorentz transformations?

Ashby was using galilean transformations, not lorentz. But if he used them(galilean), it isn't longer relativity, and his paper fails

Again, I have gone over this before.

The first paper is discussing "The Operational Control System (OCS) of the Global Positioning System (GPS)" and not the entire system.

It's a paper suggesting that ONE PART of the GPS system does not use relativistic calculations, and if it did, accuracy would be improved. There is nothing controversial here, of course if you use more complex calculations you get better answers. As computers get faster, we can upgrade systems to use formulae that in the past were too slow and required using approximations.

The quote you have is from comments on the paper, and is describing "I would like to make another point. When one looks at differential GPS". Differential GPS is a ground based addition to GPS to give extra accuracy, so she is talking about yet another, even smaller part of the GPS system. Differential GPS is very rarely used and requires specialized equipment.

So again, let me make this clear. That paper is saying only ONE SMALL PART of the GPS system doesn't use those calculations.

Neil Ashby is discussing the system as a whole, and there are parts that do indeed require relaitivity. I showed actual calculations for the 10MHz frequency offset in other threads that prove this.