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I'm willing to spend a decent amount on a textbook, but please tell me about cheap or free sources as well.

Schlusstein
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    I'd recommend searching the terms that @ChrisR mentions "Statistical Orbit Determination" and "(spacecraft) Range Rate Measurement" and just getting a "flavor" of what the material looks like. Some will be rigorous mathematically, some may contain more explanations. The measurements only give partial information (distance and speed along the line of sight) and need to be combined with orbital mechanics and numerical integration to reconstruct motion in the transverse direction. This answer explains some of the principles. – uhoh Jun 05 '17 at 01:05
  • You can also look at the other questions and answers here that have the tracking or the navigation or the navigation tags which have dozens but not hundreds of hits each. – uhoh Jun 05 '17 at 01:09

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"Statistical Orbit Determination" by Tapley, Schultz, Born is probably what you'd want if trying to estimate spacecraft orbits in general. Most of what is taught in this book is specific to using range and range-rate measurements in Kalman filters. If you are willing to invest a significant amount of money, you may want to look into the Continuing Education program at CU Boulder and specifically take the "statistical orbital determination" classes.

ChrisR
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If you're willing to settle for "how it's done" instead of "how to do it", there's an article "Navigation between the Planets" by William G. Melbourne in the June 1976 Scientific American, pp. 58-74. The article discusses timekeeping, radiometric range and range-rate measurements, orbit determination, and trajectory-correction maneuvers. Charts show how accuracy had improved over the years.

Bob Werner
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