[time-nuts] Need advice for multilateration setup

[Hal Murray]

> I want to develop a tracking system for an amateur rocket ...

Do you need the position in real time, or just after the rocket returns so 
you can find it?

> I had  thought 100 ns of timing accuracy in the received signals would be
> good  enough but I think I need to get down less than 40 ns to keep the
> algorithms from blowing up

40 ns is 25 MHz.  It shouldn't be hard to find a uP with counter/timer that 
runs faster than that.


I think you can get away without fancy oscillators.

I'm assuming you can use GPS to get the the initial position of the rocket 
and the receiving stations.  I'm also assuming that the rocket can start 
transmitting a few seconds/minutes before launch to calibrate things.

Suppose the receiver puts out a pulse.  Feed that to a uP with a 
counter/timer module that gives you a time stamp.  Feed all the time-stamps 
to a central PC that will sort things out.

If the pulses are far enough apart it will be easy to figure out which 
time-stamps go together. [1]  The clocks used to make the time stamps don't 
need to agree on a base time.  You can sort that out at the PC with data from 
before the rocket leaves the ground.

How accurate do the oscillators need to be?  If you can listen for a while 
before launch you can calibrate the individual oscillators.  So the question 
becomes how long does it take to do the calibration?

How stable do the oscillators need to be?  How long does the flight last?  
The calibration error and noise/wander from calibration is part of your error 
budget.

If a flight lasts 100 seconds (handy number for back of napkin calculations) 
and the calibration/drift is off by 1E9, that's 100 ns.  So you will need an 
oscillator that is stable to better than 1E10 over 100 seconds.  
Ballpark/handwave.

You can also calibrate the receiver oscillators again after the rocket lands. 
 Does the transmitter survive the landing?  Does the antenna survive well 
enough?


> measurements would then be used to determine x, y, z, and t

Is Z interesting?  I'm assuming you are firing rockets in flat desert 
terrain.  All the receivers will be in the same plane.  I'll bet the math has 
troubles if you try to calculate the Z when the rocket is near the plane of 
the receivers.  Have you looked into a different set of algorithms that 
assume the rocket is on the ground?

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1)  If you need more data, you can still sort things out if the transmitter 
sends pulses with non-uniform spacing.  I think there is a whole branch of 
math for that problem but I don't know the name/term.


-- 
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