Hello,

I'm not certain this is the appropriate newsgroup for this question,
but if it isn't, I'd appreciate any referrals to other forums.

In many posts dealing with "foxhunts" and radio tracking situations, I
hear directional antennas discussed, or triangulation via a moving
receiver. But what are the relevant parameters if the receiving
stations are fixed?

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.

-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

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

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

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:
Mike Andrews wrote:

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.

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...

While I do computer science now, rather than math, my degree is the
5-year Bachelor's in math, for what _that's_ worth. Every now and
again I get to actually use a bit of real math at work, generally to
the amazement of the in-juh-nears here at WeBuildHighways.

My point here is definitely not to wave my degree, as I'm quite sure
that others here have degrees more advanced than mine, or do math for
a living instead of as a hobby, etc., but to point out that having
a math background didn't make it any easier for me. It's still fun,
though.

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.

Seems to me that N+1 receivers gives you an unambiguous fix in
(min(N-1,3))-space: 2 receivers locate the transmitter on a line, 3
locate it on a plane, and 4 locate it in 3 dimensions. Since we only
get to sense 3 spatial dimensions, more than 4 receivers are useful
only to provide an overdetermined solution, which may permit more
precision.

Of course, the "closer" the receivers are to one another as seen by
the transmitter (think of the solid angle that the receiver array
subtends from the transmitter), the more ill-conditioned the matrix of
coefficients that one uses to determine the position.

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.

--
Mike Andrews

Tired old sysadmin

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

Tim Wescott wrote:
Mike Andrews wrote:

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.

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...

While I do computer science now, rather than math, my degree is the
5-year Bachelor's in math, for what _that's_ worth. Every now and
again I get to actually use a bit of real math at work, generally to
the amazement of the in-juh-nears here at WeBuildHighways.

My point here is definitely not to wave my degree, as I'm quite sure
that others here have degrees more advanced than mine, or do math for
a living instead of as a hobby, etc., but to point out that having
a math background didn't make it any easier for me. It's still fun,
though.

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.

Seems to me that N+1 receivers gives you an unambiguous fix in
(min(N-1,3))-space: 2 receivers locate the transmitter on a line, 3
locate it on a plane, and 4 locate it in 3 dimensions. Since we only
get to sense 3 spatial dimensions, more than 4 receivers are useful
only to provide an overdetermined solution, which may permit more
precision.

Of course, the "closer" the receivers are to one another as seen by
the transmitter (think of the solid angle that the receiver array
subtends from the transmitter), the more ill-conditioned the matrix of
coefficients that one uses to determine the position.

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.

--
Mike Andrews

Tired old sysadmin