How does a three-way doppler shift measurement work?

I was looking at this document who's name I can only speculate. Its title and designation includes:

810-005, Rev. E, 201, Rev. B, DSN Telecommunications Link, Design Handbook, 201, Rev. B, Frequency and Channel Assignments, Released December 15, 2009.

The following section caught my eye:

2.2 Spacecraft Transponder Turnaround Ratios

To measure two-way or three-way Doppler shift, the spacecraft must transmit a downlink signal that is phase coherent with the uplink signal. Table 1 provides the recommended spacecraft transponder turnaround ratios for various uplink and downlink frequency bands. The tracking equipment at the DSN 34-m and 70-m stations can accommodate other turnaround ratios but this support must be negotiated through the JPL Frequency Manager, who is resident in the Plans and Commitments Program Office.

Doppler shift is an essential technique for measuring the spacecraft trajectories. Along with absolute range from delay measurements, the rate of change of range provides a precise one-dimensional projection of the spacecraft's velocity. Combined with sophisticated orbital mechanics calculations, these can be used to locate a spacecraft in 3D within the solar system.

For two-way doppler shift measurements, A signal of known frequency is (usually) transmitted from Earth to a spacecraft. When it is received, the uplink frequency is shifted by a stable internally generated frequency or by a specific PLL-controlled divide-by ratio to shift it to a new, downlink frequency and transmitted back toward Earth. The spacecraft often (always?) uses two different bands so that it's sensitive receiver is not saturated by the simultaneous high-power broadcast of the shifted frequency.

While range-rate can be done on passive objects (e.g. NEO asteroids or very large planets) using standard radar techniques and picking up the weak, passively reflected signal, spacecraft at deep-space distances are too small to reflect a useful amount of power, so a boost in power by the spacecraft's sensitive receiver and powered retransmission is necessary.

Question: How does a three-way Doppler shift measurement work in practice? I'm looking for some level of technical specificity here, not just hypothesizing, generalizations, or hand-waving.

• I don't know if it was 2 or 3 way but the shuttle used doppler tracking between it and the TDRS it was talking through. It was a lot of trouble to get it to work right in the simulator. Commented Oct 11, 2017 at 3:41
• One ground station to spacecraft to another ground station. Read DESCANSO. Commented Oct 11, 2017 at 5:22
• @pericynthion Thanks; that might be the topology, but since initial and final destinations are physically separate, the initial transmitted and final received frequencies can not be compared locally. I'm interested in how this is done.
– uhoh
Commented Oct 11, 2017 at 5:37
• Primary frequency standards and time/frequency transfer by GPS and VLBI. It's all described clearly in the freely available DESCANSO book series, you could write a good answer based on that. Commented Oct 11, 2017 at 5:44
• @pericynthion ok if no answers are posted in a few days I will go read the book series.
– uhoh
Commented Oct 11, 2017 at 5:45

Three-way Doppler tracking was developed for when the spacecraft (specifically Voyager) is so danged far away, that by the time the round trip signal gets back to Earth the original transmitting complex has rotated out of view. Then the signal is being received at a different complex. Then there needs to be a third link between the two complexes for a phase reference.

Just to confuse things, I've seen the same term referring to something else entirely: two-way Doppler on one complex simultaneous with one-way Doppler to another complex, e.g. while handing off from one complex to another during the overlap.

• Thanks! Would GPS + local atomic clocks be one method for the synchronizing link?
– uhoh
Commented Oct 12, 2017 at 1:15
• I don't know how they do it. The DSN's atomic clocks are a lot better than a GPS atomic clock, so I'd guess they wouldn't want to do it that way. Commented Oct 12, 2017 at 2:27
• OK I'll do some due diligence on how atomic clocks are synchronized in general.
– uhoh
Commented Oct 12, 2017 at 2:32
• Is this edit OK?
– uhoh
Commented Oct 12, 2017 at 4:16