Tim Wescott wrote:
Mike Andrews wrote:

[snip]

An interesting variation on the problem would be one in which the
receivers also received or derived some precise time signal, such as
GPS time, and the transmitter to be located transmitted a signal which
contained a precise time referenced to the same standard.

This turns out to provide a good location for the transmitter, I
believe.

But if you put GPS into the transmitter for the time signal why not just
have it get it's own position and transmit it, ala APRS locators?

(Shhhhhh! Pay no attention to the man behind the curtain.)

That, of course, is an elegant solution to the problem, but I didn't
consider it because it appeared to be outside the postulates given.

--
Mike Andrews

Tired old sysadmin

If you want to build something that will locate the roving transmitter on
your plot of land that is 300 foot by 300 foot it might not be too hard to
do if you can get your four receivers to do a little bit of timing
computations for you.

Set the roving unit up to send a pulse on a regular basis. It doesn't have
to carry any data or anything like that and it wouldn't have to be too
powerful either.

There are a few assumptions that can be made that are pretty definate.

1. The distance from two diagonal corners of the square is the maximum
distance the transmitter can be from the receiver and still be in the area
that is designated as home.

2. The transmitter should be home. If the calculations are coming out wrong
then the transmitter has violated the bondary of home.

3. All four of the receivers must be set to a very accurate clock so that
they are all using the same reference.


I don't have a calculator with me that will let me do the calculation to
find the diagonal distance across the square so I will use 450 feet as the
rough number for the maximum distance from any receiver.

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.

The nice thing about doing it this way is that there is nothing mechanical
and with todays computing power that is available a solution can be had
within milliseconds of the transmitter putting out a pulse.

An idea for the accurate clock could be to use a receiver at each receiver
in the square to receive a local TV station and use the synch pulses as a
reference. Just don't forget the propagation delay is from one side of the
square to the other and figure that in.

Another option would be to put a GPS receiver at each corner and use the
clock from these as your reference.

Or you could use a common receiver site and one clock feeds all four
detectors. Just remember that there will need to be four receiver
antennas and corresponding feed lines to take care of.

If you want to build something that will locate the roving transmitter on
your plot of land that is 300 foot by 300 foot it might not be too hard to
do if you can get your four receivers to do a little bit of timing
computations for you.

Set the roving unit up to send a pulse on a regular basis. It doesn't have
to carry any data or anything like that and it wouldn't have to be too
powerful either.

There are a few assumptions that can be made that are pretty definate.

1. The distance from two diagonal corners of the square is the maximum
distance the transmitter can be from the receiver and still be in the area
that is designated as home.

2. The transmitter should be home. If the calculations are coming out wrong
then the transmitter has violated the bondary of home.

3. All four of the receivers must be set to a very accurate clock so that
they are all using the same reference.


I don't have a calculator with me that will let me do the calculation to
find the diagonal distance across the square so I will use 450 feet as the
rough number for the maximum distance from any receiver.

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.

The nice thing about doing it this way is that there is nothing mechanical
and with todays computing power that is available a solution can be had
within milliseconds of the transmitter putting out a pulse.

An idea for the accurate clock could be to use a receiver at each receiver
in the square to receive a local TV station and use the synch pulses as a
reference. Just don't forget the propagation delay is from one side of the
square to the other and figure that in.

Another option would be to put a GPS receiver at each corner and use the
clock from these as your reference.

Or you could use a common receiver site and one clock feeds all four
detectors. Just remember that there will need to be four receiver
antennas and corresponding feed lines to take care of.

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

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

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.

--
Mike Andrews

Tired old sysadmin

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.

--
Mike Andrews

Tired old sysadmin

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

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

"Tim Wescott" wrote in message
...
Mike Andrews wrote:

Allan Butler wrote:

[snip preconditions]


Withoug the previous parts of the thread this may be duplication since I
don't know the original constraints...but

I have always wanted to build a model rocket altitude transponder using this
concept:

On-board the rocket we have a "transponder"... a one transistor superregen
Rx on, say 10 or 6 Meters. I hae a schematic around here somewhere for a
one tranny FM broadcast receiver from Pop Tronics. Have it's demodulated
signal modulate a 2 meter TX. This can be a 9 or 12 Mhz. xtal osc and 2
meter tuned circuit (gets you a few miles on the ground from a tower
receiver).
On the ground you have the "Ground Station" 10 or 6 meter mobile. Since
you can have lots of power, the crummy Rx onboard the rocket is no problem.
From the mobile, transmit a tone. Measure the time delay of a zero crossing
of the transponded tone. A simple freq counter can be made to do this if it
had (I forget the official name--triggered event counter maybe??) the
ability to start counting on the TX tone's edge and stop on the RX tone's
edge. Just a few chips for this.
You pick the frequency that the counter is counting to display feet or
whatever units you like.
What's-it, something like a nano second per foot?
You also need a delay in the proper place to account for the "zero distance"
delay of the receivers & transmitters.
Seems like one other "Ground" receiver is all that's needed to triangulate
the location horizontally...

There was an article in QST within the last year or so where some fellas
measured the delay through a, I think, 2M repeater versus distance...same
concept, 'cept they just used a dual trace scope..

--
Steve N, K,9;d, c. i My email has no u's..