How does a third DSN station serves as a “relay” to tie-together observations by two other stations doing VLBI?

Question

Section 2.1 of the DESCANSO document 211 Wideband Very-Long Baseline Interferometry (from here, found here) says:

The precision of a VLBI measurement improves with the length of the baseline. The location of the DSN stations provides baselines of 66% (Goldstone to Madrid) and 83% (Goldstone to Canberra) of the Earth’s diameter. The third baseline, Canberra to Madrid, is 98% of the Earth’s diameter but provides very limited mutual visibility (see module 301). To mitigate mutual visibility effects, additional antennas are often involved in VLBI measurements allowing a station between DSN locations to serve as a “relay” to tie-together observations made in different portions of the sky during an observation session.

I don't understand what function the third station performs. If A and B are the two DSN stations and I is the intermediate station, I can imagine AI and IB could collect additional data leading and trailing in time, when B or A are missing (no mutual visibility to AB) but I am not sure if that's what's happening here. It seems like waiting for the third DSN station C to appear would be an alternative.

Image Source

Answer 1

Very-Long Baseline Interferometry is interferometry with telescopes that physically distant. The observation data is recorded locally, and post-observation the data is combined at a central location to produce the measurement result.

In order to do the combination post-observation, you need a common reference. They use very accurate atomic clocks for this, but unknowns in the telescope locations, local atmospheric effects, etc. require that you move the signals a bit backwards or forwards in time (order of nanoseconds at most) in order to get a good results (this is why in VBLI measurements there is always some uncertainty in the result: moving a signal 0.1 nanosecond backwards or forward in time may both give a reasonable result, but which one is correct is open to interpretation; see e.g. the various versions of the black hole images).

This moving around of signals in time is only possible if there is an overlap in the signal contents. If you have two telescopes A and B, one observing at $t=1,2,3,4$ and one at $t=6,7,8,9$ (e.g. because they are on opposite sides of the Earth), then you can only go by your atomic clock and there's no way to improve your observation.

However, if you had an intermediate telescope C that observed the same source at $t=3,4,5,6,7$, you can use this to tie it together: first correlate the signals of A and C and then correlate that with B.