Relative Positioning

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Relative Positioning mattrapoport 05-05-2008
Posted by Peter Baltus on May 8, 2008, 3:04 pm
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Hi Matt,

in principle you are right, the time difference would represent the change
in distance divided by the speed of light. So 1mm difference would
correspond to approximately 3ps time difference.

There are several sources of inaccuracies:
- the speed of light depends on the medium. In air, it's close to vacuum but
not quite, and depends somewhat on temperature, moisture, pressure etc.
- the circuits/equipment you use to measure such small time differences will
not be perfectly accurate, depending on how much you would want to spend on
this. In addition to initial inaccuracy (which you could calibrate out) the
errors might also depend on temperature, supply voltage, etc.
- the phase shift in the cables that connect the antennas to the equipment
often depends on e.g. bends in the cable and so on (unless you want to spend
many hundreds of dollars per yard of cable). So moving the antennas (and
therefore the cables) around might influence the measurement results
- at short distances (in the order of one wavelength or less) the coupling
between the antennas becomes somewhat complicated and involves other modes
than TEM waves - which will result in other phase shifts/time differences
than you would expect based on simple radio wave propagation
- however, the most important source of inaccuracies is probably the
reflections of radio waves off other objects and so multiple copies of the
radio signal will reach the receive antenna along different paths (this is
called multipath) and with different delays - very similar to what happens
with echo's and sound.

So, in summary, yes it will work, but it is not quite so easy and/or
accurate as you might imagine - sorry...

Peter

> If I take an RF transmitter (A) and an RF receiver (B) and I precisely
> record the time it takes for the the signal to get from A to B, I
> wonder how accurate the distance measurement would be. If I moved A
> 1mm away from B, would the recorded time accurately represent the
> change in distance?
>
> Thanks,
>
> Matt
>



Posted by Deep Reset on May 8, 2008, 5:32 pm
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> If I take an RF transmitter (A) and an RF receiver (B) and I precisely
> record the time it takes for the the signal to get from A to B, I
> wonder how accurate the distance measurement would be. If I moved A
> 1mm away from B, would the recorded time accurately represent the
> change in distance?
>
> Thanks,
>
> Matt

Approximation:

At the speed of light (radio wave, infrared beam, gamma ray, whatever) , 1
foot (30cm) is 1 nano second. (10 ^ -9 seconds)
(I seem to remember 11.7 inches, but hey, who's counting?)

1mm is 1/300 of this distance.

You do the rest of the math(s).

How were you planning on measuring the propagation delay?

Deep.


Posted by Gordon McComb on May 8, 2008, 6:09 pm
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mattrapoport@gmail.com wrote:
>
> If I take an RF transmitter (A) and an RF receiver (B) and I precisely
> record the time it takes for the the signal to get from A to B, I
> wonder how accurate the distance measurement would be. If I moved A
> 1mm away from B, would the recorded time accurately represent the
> change in distance?

You'd probably want to use a modulated RF signal, and compare the phase
of the returned signal (from another sensor) with the original. This is
how some surveyors transits work. The circuitry is simpler, as you are
not measuring speed of light. You could probably achieve 1mm accuracy
depending on the frequencies used. How to make all this so that each
sensor is stand-alone and independent is another matter. If you use more
than two sensors you need a way of timing the pulses from each. There
will need to be some coordination between the sensors. There are other
problems to overcome that are left to the OP.

-- Gordon

Posted by John Nagle on May 9, 2008, 1:46 pm
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Gordon McComb wrote:
> mattrapoport@gmail.com wrote:
>> If I take an RF transmitter (A) and an RF receiver (B) and I precisely
>> record the time it takes for the the signal to get from A to B, I
>> wonder how accurate the distance measurement would be. If I moved A
>> 1mm away from B, would the recorded time accurately represent the
>> change in distance?
>
> You'd probably want to use a modulated RF signal, and compare the phase
> of the returned signal (from another sensor) with the original. This is
> how some surveyors transits work. The circuitry is simpler, as you are
> not measuring speed of light. You could probably achieve 1mm accuracy
> depending on the frequencies used. How to make all this so that each
> sensor is stand-alone and independent is another matter. If you use more
> than two sensors you need a way of timing the pulses from each. There
> will need to be some coordination between the sensors. There are other
> problems to overcome that are left to the OP.
>
> -- Gordon

I built a LIDAR that way once, around 1990. Surprisingly similar to
an FM radio, IF cans and all. But nobody does it that
way any more. (Well, the Swiss Ranger does, which allows them to use
LEDs as the light source). Today, you usually just count, really fast.
Here's a Bosch laser range finder for $129:
"http://www.amazon.com/Bosch-DLR165K-Laser-Rangefinder-Kit/dp/B000T7LISM".
Accuracy is 1-2 mm.

The main problem with working in this area is that while the
parts are cheap (they're derived from cell phone technology),
the test instruments required are expensive.

If you want to work in this area, you'll need shelves full
of RF engineering books, some really good RF test gear, and the
software for designing boards with gigahertz transmission lines.
There are advanced radio hams who do such things.

Look up "A UWB based Localization System for Indoor Robot Navigation"
for some hints on current (2007) thinking on the subject.

This is a basically good idea which takes significant engineering
effort to make work, but probably won't be expensive to replicate.

                                        John Nagle

Posted by on May 9, 2008, 1:27 pm
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> If I take an RF transmitter (A) and an RF receiver (B) and I precisely
> record the time it takes for the the signal to get from A to B, I
> wonder how accurate the distance measurement would be. If I moved A
> 1mm away from B, would the recorded time accurately represent the
> change in distance?


Lots more helpful responses. It sounds like it will be very difficult
to achieve. It seems strange that we can get accuracy to a meter with
transceivers flying 20,000 kilometers above the earth (GPS) but we
can't get accuracy to a millimeter in a system where the transceivers
are all a couple feet from each other.

Thank you for all the help,

Matt

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