(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

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

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

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

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

Mike Andrews wrote:
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.


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?

--

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

Mike Andrews wrote:
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.


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?

--

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

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