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electronics component - radio range finder

I'm looking for a base / mobile unit pair of electronic components that (via radio wave?) can determine their distance apart with high accuracy (1/4 inch).

Having this premade and attachable to an arduino or other microcontroler over rs-232 would be ideal. I think this could be built on the basis of the two units have a sync'd clock. The mobile unit could transmit its time and the base could receive the time and compare it to its own to figure out the distance. Obviously this would have to be very accurate.

Ultimately I want to combine 4+ of these units to determine the position of the mobile unit. The mobile unit will not always have line of sight of the base. The signal would need to pass through residential walls without much degradation.

There is a $500 budget per pair of units (set of at least 4 base / mobile unit pairs)

Any thoughts?
1 Solution
It is almost impossible without a very very very very high precision clock.
Radio waves propagates with about 30cm/ns speed, so to have a 1/4 inch = 0.65mm accuracy you would need a sub-ns accurate clock. GPS haves a 1m accuracy, and uses atomic clocks.
You could use a GPS + Internet access to transmit GPS positions, but you would have 15m approximations.

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