Second order calculations use careful analysis of the signal pattern in telemetry data- IIRC you can see a slow stretch of the phase which can be used to estimate distance and velocity with high accuracy.
Voyager, along with Apollo, stand as the finest examples of human engineering done yet- we got a bunch of people to the moon and back, and built a probe that still operates 50 years later... farther than anything else humans have launched... I'd be lucky if I can deploy my web app once a week.