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

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.

--

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

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?

--
Mike Andrews

Tired old sysadmin

Do you have any frequency ranges in mind? A VHF system would be vastly
different in size than shortwave for example.

jw
K9RZZ

Zack Lau wrote:

(Washed Phenom) wrote in message om...


Partly for the fun of it, and also for practical uses, I'd like to
design a receiving system whereby a small transmitter could be
located. This would not technically be a "tracking" situation, since
the transmitter would not always be on. I'm imagining something like
a garage door opener, where pushing the button can send a brief (but
very strong if necessary - this may have power implications?) signal.

The reason I ask about the non-directional solution is because I have
access to a plot of land approx. 300 x 300 feet square, with no
restrictions on building antennas on the four corners of the property.
I'm guessing such a system could be more accurate than a directional
system at a given power level, but the technical aspects of the
situation are beyond me.

I am a mathematician by trade, but know a smattering of electronics.
It would seem, at least in theory, that the relevant parameters here
are the distances between the 3-4 antennas (would a 4th help?), and
the strength and frequency of the signal. I also realize that some
processing of the signal would need to be done at the receiving end.
Perhaps the triangulation can be handled by software?

Any advice, direction, URLs, or discussion is much appreciated.


Accurate signal strength measurements are surprisingly difficult.
Ground reflections can combine to to double the signal strength,
or nearly cancel it out. Hams and broadcasters often use the term
"picket fencing" to describe the rapid fluctuations in signal strength
that occurs with fixed to mobile signal paths.

Not that your task is impossible, just hard. Perhaps a sufficient number
of signals can be simultaneously processed to statistically reduce the
signal combination/cancellation effect to an acceptable error.

Zack Lau W1VT

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.

The higher the carrier the better the measurement, but with a lot 100
meters on a side you probably also want to send some sort of time
reference (you do get to design the transmitter as well, right?).

--

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

(Washed Phenom) wrote in message om...


Any advice, direction, URLs, or discussion is much appreciated.


Thanks for the replies so far. They've been helpful, and have sent me
on some interesting Google searches learning a lot about RDF in
general. Some more specifics:

I have no preferred frequency ranges, but that is more out of
ignorance than flexibility! In terms of transmitter power, in my
first post I mentioned that a continuous signal wasn't necessary if
that would help matters. It seemed plausable to me that a transmitter
which used its power to transmit a short, strong signal could be
detected at a much longer range than a weaker signal.

The reply regarding carrier phase was interesting, and sent me on a
tour of GPS basics. Half the fun of this project is going to be
learning new stuff. As I understand it, the reason you called this a
"reverse GPS" is because the multiple receivers are in known locations
instead of multiple transmitters. It would be feasible to build a
second transmitter (a time reference?) and place it somewhere in the
100 yard square. There is a house roughly in the center of the
property which would be where the "guts" of the processing equipment
would be anyway. How does the carrier phase solution compare to VHF
and shortwave in terms of power requirements, size of transmitter,
etc?

Just to get a better sense of whether the range and resolutions I'm
looking at are feasible, suppose you wanted to locate your local
college radio station's transmitter. I just googled a few college
stations and found two FM stations that transmit at 300 and 400 watts.
The 300 watt station claims to cover 700 square miles. Of course I
realize that: 1) "covering an area" may not be equivalent to "area
within which their location can be pinpointed", and 2) Even if I could
generate such power in a portable transmitter, I would need to choose
bands so as not to run afoul of the FCC. (Just how much transmitting
power can be generated from a garage door sized unit is another issue,
and another reason the brief "burst" signal sounded preferable).
Anyway, I was sidetracked there. To get back to the main question, if
you had antennas at 4 corners of a 300 x 300 ft square lot, are there
any good thumbnail estimates of how accurate you could be at locating
the 300 watt college station, and how this accuracy varied as a
function of the distance to the station?

In addition to being a fun way to learn new things and tinker with
electronics, this project is also motivated by someone I care a great
deal about who often works in isolated outdoor locations and doesn't
own a cell phone or GPS. I know when she is at these sites, but worry
she will be unable to call for help if something happens. Can she be
located by her pushing a button and at what range?

She's already suggested building a Bat-Signal, but that is beyond by
technical expertise. Also, she said that buying her a cell phone and
GPS would be cheaper than building this monstrosity, but I like
intellectual challenges and need to keep my mad scientist reputation
well-exercised.

Thank you again, and please continue the excellent discussion.

-wp

Washed Phenom wrote:
Partly for the fun of it, and also for practical uses, I'd like to
design a receiving system whereby a small transmitter could be
located. This would not technically be a "tracking" situation, since
the transmitter would not always be on. I'm imagining something like
a garage door opener, where pushing the button can send a brief (but
very strong if necessary - this may have power implications?) signal.

Try this one:
http://members.aol.com/BmgEngInc/Adcock.html

73, Markus HB9BRJ

(Washed Phenom) wrote in message om...

Partly for the fun of it, and also for practical uses, I'd like to
design a receiving system whereby a small transmitter could be
located. This would not technically be a "tracking" situation, since
the transmitter would not always be on. I'm imagining something like
a garage door opener, where pushing the button can send a brief (but
very strong if necessary - this may have power implications?) signal.

The reason I ask about the non-directional solution is because I have
access to a plot of land approx. 300 x 300 feet square, with no
restrictions on building antennas on the four corners of the property.
I'm guessing such a system could be more accurate than a directional
system at a given power level, but the technical aspects of the
situation are beyond me.

I am a mathematician by trade, but know a smattering of electronics.
It would seem, at least in theory, that the relevant parameters here
are the distances between the 3-4 antennas (would a 4th help?), and
the strength and frequency of the signal. I also realize that some
processing of the signal would need to be done at the receiving end.
Perhaps the triangulation can be handled by software?

Any advice, direction, URLs, or discussion is much appreciated.

Accurate signal strength measurements are surprisingly difficult.
Ground reflections can combine to to double the signal strength,
or nearly cancel it out. Hams and broadcasters often use the term
"picket fencing" to describe the rapid fluctuations in signal strength
that occurs with fixed to mobile signal paths.

Not that your task is impossible, just hard. Perhaps a sufficient number
of signals can be simultaneously processed to statistically reduce the
signal combination/cancellation effect to an acceptable error.

Zack Lau W1VT

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.

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