Of course it's impossible for us outsiders to know what the official USALS algorithm actually does, because to my knowledge it has not been published in the open literature. If they had done that we would be able to identify their error and presumably have them correct it. It would have also saved a lot of brain damage for receiver and software app developers, many of whom got the calculations wrong in a different manner.
What I did notice when comparing the deviations from a precise calculation was that the USALS errors fairly closely tracked the error caused by assuming the angle between the true south satellite and the desired satellite target (from the dish's perspective) is the motor angle. This approximation is fairly close at small to moderate motor angles, but breaks down at larger ones. I can see them wanting to make this approximation as calculating the inner product of these two vectors is child's play. But the approximation is such that one can run into meaningful pointing inaccuracies very easily.
What I did notice when comparing the deviations from a precise calculation was that the USALS errors fairly closely tracked the error caused by assuming the angle between the true south satellite and the desired satellite target (from the dish's perspective) is the motor angle. This approximation is fairly close at small to moderate motor angles, but breaks down at larger ones. I can see them wanting to make this approximation as calculating the inner product of these two vectors is child's play. But the approximation is such that one can run into meaningful pointing inaccuracies very easily.
