Originally Posted by slang

Well, I don't quite see how these questions can be answered in detail without insight into the technology used, but.. if you want to know the exact calculations done to steer the craft and to predict its positions, you're probably best off contacting the project team. Send them an email with specific questions, and ask nicely who would be the best person to ask these questions. Then email that person, or request the original email to be forwarded.

There is a general Johns Hopkins University contact form here, and a New Horizons contact page here.

Or, even better, ask them to answer the questions here on the forum