Re: [time-nuts] Need advice for multilateration setup
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?
- 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.
--
These are my opinions. I hate spam.
On 03/26/2015 02:25 PM, Hal Murray wrote:
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?
Near real-time would be nice but I guess not an absolute requirement.
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.
Good idea - I hadn't thought about that. As long as they don't drift
too far, I can calibrate out the initial drift.
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.
Powered flight will be less than 30 seconds. Depending on when the
chute deploys, it may take a few minutes or tens minutes to make it all
the way down. If the chute doesn't open (a common occurrence), then it
will come down much faster :)
You can also calibrate the receiver oscillators again after the rocket lands.
Does the transmitter survive the landing? Does the antenna survive well
enough?
If I get the rocket back in a small number of pieces, it will be an
achievement. The recovery success rate with large amateur liquids isn't
that grea
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?
Altitude (z) is not too important for finding it but will be useful in
confirming the performance. From the multilateration simulations I've
done so far, there are some "bad" areas and yes, near the ground isn't
too good if all them are in the same plane. Maybe I can put one or more
of the ground stations on a big hill or something. Good point though -
if they're nearly in the same plane, the equations may be a bit simpler.
-Bob
NASA uses the Doppler effect for deep space navigation, by integrating
the velocity.
You'd need a very stable oscillator, but you don't need a powered oven,
due to the short duration of the flight.
You only need one receiver. In fact, if it's possible for the rocket to
hear a ground signal and return it at some offset or fractional
frequency, you don't need an oscillator on the rocket.
But if you do need a stable oscillator, consider enclosing it in
aerogel, as we were discussing a few months ago. Bring it up to temp
with ground power and let it go.
There is still the matter of acceleration. If the oscillator can be
calibrated, then the frequency versus acceleration is known and can be
used to get the rocket's acceleration during powered flight. Double
integration yields position. Taking the Doppler shift out of the
integral could be tricky.
Disclaimer: The last time I had anything to do with a rocket was 1959,
with an Aerobee-Hi launched from White Sands, NM. We used Doppler to get
altitude for upper air density measurement. The rocket went off course
horizontally (determined by radar) and was destroyed before it crossed
the border.
Bill Hawkins