Please read FAQ240-1032.
Your experiment is impossible. The movable point won't move without additional oblects ( arm, belt, cable, etc)
neither can a point (dimensionless... ) have the ability
to move. No point can have existence... etc.

We are engineers and not sorcerers... We can solve only
practical -- i.e. solvable -- problems.

Can U use light ?

<nbucska@pcperipherals DOT com> subj: eng-tips

Zzman,
    I am sorry you got such a rude answer from nbucska. I think he may have misunderstood your problem. Reading between the lines it seem that since you are a bioengineer the experiment has all sorts of wet and gooey stuff in it, moving around "under its own steam", possibly with fixed organic material as well. This precludes any (visible) optical sensing.

I think the problem is this, as you decrease the frequency of the electromagnetic wave you increase the wavelength. Trying to measure positions using "low frequency" electromagnetic fields is like trying to do watch repairs whilst wearing boxing gloves.

Light is a nice high frequency electromagnetic wave, giving plenty of resolution. Radio waves at say 300MHz have a wavelength of 1m and are therefore somewhat coarse for your experiment. The trouble with higher frequency waves, which have a higher photon energy, is that they may just pass right through your target objects. Xrays for example would go through organic material to a greater or lesser degree. Thus the first thing you would want to do would be to "tag" the items in question with a piece of metal or a miniature transponder of some sort. If the movement required is only 2mm I have to guess that the object is small as well.

If you can fill in some blanks and let us know what you are trying to do more explicitly we may be able to help, or at least advise definitely that the idea is not going to be very workable. Mostly it is a question of cost. It might mean you need a Terawave imaging system for example, and this would be beyond the financial reach of most users. Maybe you need a small radio-isotope system, but this might be beyond the safety limitations inside cities. There are often solutions, they just may be prohibitively expensive.

If all the obstacles are non metal, and you don't need exactly a one meter sphere, then try using an MRI machine at a hospital. MRI's can image with approximately that fidelity.
If this is to be an antenna problem, it sounds difficult.
If the movable object transmitted a signal to the other three locations, depending on the media and the reflections, you could easily see position changing by monitoring the signal transmitted from the moving unit to the other three locations.
Finding the direction of motion accurately would be difficult.
Analysis by computer may also help if the radiating frequency of the antennas is low enough.
kch (antennas)
Please add more detail regarding the setup, materials, antenna use, etc.

From a pulsed system radar range resolution standpoint, you will need 150GHz of signal bandwidth. Not something you will be able to cob together with spare parts.
 

I apologize for not presenting my planned experiment in a clearer fashion.  To simplify my problem: I would like to be able to attach two devices to a human and by interaction between the two devices record the distance between them.  (The full experiment I initially mentioned would only be an extension of this process.)  Since body parts could lie between the two devices, I don’t believe optical or acoustic methods are applicable and use of an external sensing device such as a MRI scanner is not feasible.  Ideally, the two devices would not have a hard-wired connection between them, but one of the devices could be connected to an external processor such as a computer.  Hopefully this will not confuse the situation further.  
Thank you for your time and attention

zzman:
Brevity was intentional, rudeness wasn't -- and I am sorry.
If the two devices are connected to the same person, can't
you have position/angle/ etc. transducers connected between
them? Let me mention that the two devices will be interconnected anyway by the same body (skin-muscle-skeleton-muscle-skin).

About using microwaves: the propagation speed in the body
is different so time/phase measurement becomes much more difficult.

<nbucska@pcperipherals DOT com> subj: eng-tips

That sounds much more feasible, though still difficult.

The US government is developing transmitters that a person swallows which measures body temp, etc. and sends data through the human to an external receiver. Normally the receiver just records digital ones and zero data sent from the transmitter.

The measurement of change in location would be difficult to get the resolution you require. You may be able to see just change small versus change larger over a multi-second time period, but measuring very accurately would require a system similar to "Differential GPS Tracking" at much lower frequency (to penetrate the skin).

What is the purpose to track so closely? digestive track viewing?

kch.