The JPL DESCANO book series is the absolute reference in precise orbit determination. It's free, and divided into separate chapters. It includes all of the calculations needed to understand and solve for orbit determination.
In short, OD achieves much better precision than GPS for the following reasons:
- The signal is at least a two-way signal (GPS is one-way).
- The signal is generated on the ground using extremely accurate clocks (GPS spacecraft have an atomic clock but it's far from being as accurate as the DSN atomic clocks).
- GPS relies on a single time of flight measurement and on expected ephemerides of the spacecraft. Ground antennas typically use both a range measurement (time of flight of the signal) and Doppler measurement (relative speed between the emitter and the receiver).
- Ground antennas also account for turn around time of the electronics onboard the spacecraft based on the emitting frequency.
- Ground OD integrates data over dozens of seconds or more (60 seconds is typical for Moon missions, but very distant spacecraft will require Very Long Baseline Interferometry (VLBI)) thereby filtering out a lot of noise. Then, an orbit determination arc is several hours (2-8 is common) and the output of the OD process is a reconstructed trajectory of the vehicle including position and velocity at the very least (as opposed to only an instantaneous position).