My understanding is part of GPS is knowing the precise location of the satellite[0]. Is this knowable within any useful precision?
I naively imagine this is the largest degree of uncertainty in the whole system?
[0] https://en.wikipedia.org/wiki/GPS_signals#Navigation_message
The technique used in the article is quite powerful and general, but it does have certain drawbacks too. One advantage is that it is relatively insensitive to errors in the ephemeris. The path we are exploring relies more heavily on the ephemeris, as you speculate; but these can be really quite excellent, even in the sub-meter range. Actually the bigger source of uncertainty for absolute positioning using non-Doppler techniques will probably be clock errors. For Doppler, integration time/time-to-first-fix is a sticking point, unless you have 8+ satellite signals, IIRC.
We think accuracy in the low single digit meters is not too much of a stretch (note that I am making a claim about a rather different technique than the one in the article... nothing worth doing is ever totally straightforward!).
[0] https://conference.sdo.esoc.esa.int/proceedings/sdc6/paper/4...