The rest of the quote you were having trouble with is just referece to Wiki and a disclaimer. Above is the only significant portion.
Just before the portion above the article includes the statement, "
the relativistic corrections (which amount to 38 microseconds/day)". Keeping that in mind all the above quote is saying is that,
The sattelite pistons are not determined by the differences between the sattelite clock and the ground clock. Instead they are triangulated between two or more sattelite clocks.
I did not read through the whole link, but I agree that the way that first part is worded may be awkward, especially when trying to translate to Russian.
One note I would add, is that the sattelite computers do not make any relativistic corrections. There are pre-launch corrections made, and then inflight corrections made, based on computers, clocks and calculations made on the ground. When in these GPS articles they use the word, " receiver" they are referring to a ground based GPS unit.., or sometimes one in a airplane.
I hope the above helps the translation more than confusing it...