Mike Andrews wrote:

Allan Butler wrote:

[snip preconditions]


The first receiver detects the transmit pulse and it is known that the
transmitter is within 450 feet of that receiver. That starts a clock. The
second receiver detects the transmit pulse and the time since the clock
started is noted. The third receiver detects the transmit pulse and the
time since the first receiver detected the signal is noted. With this much
information the position of the transmitter can be determined on a two
dimensional plot. The fourth receiver could be used for a sanity check to
make certain that the transmitter is in the expected location and it would
allow better coverage for when only three receivers can detect the signal.


The space between clock start and second receive detect is the difference in
distance between these two receivers. The next detect is the difference in
distance between the first receiver and the third. And lastly the fourth
detect sets the distance between the fourth receiver and the first. If the
math is done right there will be four circles drawn each has the center at
the corner of your property. When the drawings are made they will all cross
in only one place. There will be other places where two or three circles
cross.


But for this to work, as I pointed out in another post, you need to
know the true distance from the transmitter to any one or more of the
receivers already, or (equivalently) you need to know the exact time
of transmission relative to the receiver clock. Otherwise all you
have is the delta-Time Of Arrival (TOA) from the receiver that gets
the pulse first to the other receivers, and that's not sufficient to
locate the transmitter.

Even where the maximum distance is known, you still need the true
distance from the transmitter to any one receiver at a minimum. If
you don't have that, you can't draw any circles.

Or I'm missing something obvious. I really don't think I am, but if
someone can point out what I'm missing I _will_ be grateful.


If you know the positions of any two receivers, and the time delta
between the reception of the pulses from the transmitters, the set of
possible positions of the transmitter lies on a hyperbola that
intersects the line between the two receivers.

With two pairs of receivers you get two hyperbolas and two intersections
-- and three receivers gives you three pairings to calculate with.

So you don't need to know the absolute time of the transmitted pulse,
just the difference.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com