In article , Tim Wescott
writes:

Mike Andrews wrote:

Tim Wescott wrote:

Doing it by carrier phase would be better, if you could arrange a phase
reference. With hard-mounted receivers (or with a 2nd transmitter in a
known location) you can broadcast a time reference and do a reverse-GPS
sorta thing.

I thought about the reverse-GPS approach, but couldn't figure out how
to determine absolute position. The most I could come up with was that
you'd know times-of-arrival at the various receivers, and that would
give you deltas from the earliest time-of-arrival. But until you know
the distance of the transmitter from any one of the receivers, you
can't determine position w.r.t. _any_ of them. As soon as you have
distance from one of the receivers and N deltas, you have a fix in
(min(N-1,3)) dimensions -- assuming that the processor knows where all
the receivers (or antennas, at least) is in that space.

So what am I missing?

OK, maybe reverse LORAN. If you know the difference in the times of
arrival between two stations you can plot the hyperbolic surface where
your transmitter must lie. With four stations you should have six
different surfaces. The intersections won't agree, but you can get a
maximum likelihood estimation of the transmitter's position in
three-dimensional space.

Being a mathematician by trade would make this easier, and more fun...

Actually three receivers would do it unambiguously most of the time, but
four would be more accurate at the cost of a bunch more math.

This sort of thing was attempted in 1960-1961 by Ramo-Wooldridge
Corporation (the corporation that spun off what was to become TRW)
on HF direction finding using "time of arrival."

Essentially that project failed due to a need of absolute group-delay
control in the receivers, specifically in the IF chain.

While the same local oscillator could feed the mixers and be well
isolated from one another to prevent signal coupling around the
wrong path, the group-delay or relative phase shift of the various
IF chains defeated the theoretical concept.

To stay within a 100m (or so) square, one has to work with the
phases of the wavefronts so a superheterodyne type of receiver
is not too swift unless each IF section is an absolute duplicate
of the others. It might be possible with a DC (Direct Conversion)
or "zero-IF" type, working with a specific audio tone (as an
example), but that's more stuff for analysis.

Group delay in tuned amplifiers is not normally measured, nor was
it a factor in the military R-391 receivers used for this project at
R-W. My body was involved to the extent of others' wants to
set up equal group delays but still others' wants had me on the
short list for what is now termed "downsizing." [R-W eventually
went kaput despite being the origin of STL and, eventually the
space factory of TRW] As far as I know the project never made
it to full promise.

Len Anderson
retired (from regular hours) electronic engineer person