[time-nuts] Need advice for multilateration setup

[Chris Albertson]

Your second method is by far the best.  But it can be simplified.  All you
need is two very stable oscillators, one in the rocket and one some known
fixed location.  Then you ground stations can be just dumb recorders that
record both signals.  In post processing you compare the relative phases.

Likely the rock has a transmitter already so all you need is a very good
oscillator on the ground. This one transmits to all you ground stations

This technique has. Even been used to analyze serious failures of large
rockets.  Transmitters are packed with batteries and continue after the
explosion.  They have recovered spin rates and so on of falling derbies.

On Wednesday, March 25, 2015, Robert Watzlavick <rocket at watzlavick.com>
wrote:

> I'm working on a project that I could use some advice on and also might be
> of interest to the list.   If it's not appropriate for the list, my
> apologies.
>
> I want to develop a tracking system for an amateur rocket that can allow
> me to track the rocket even if onboard GPS is lost (as is typical during
> ascent and sometimes during descent) or if telemetry is lost.  The idea is
> to use a transmitter in the rocket and have 4 or more ground stations about
> a mile apart each receive the signal. Multilateration based on TDOA (time
> difference of arrival) measurements would then be used to determine x, y,
> z, and t.  With at least 4 ground stations, you don't need to know the time
> the pulse was transmitted.  The main problem I'm running into is that most
> of the algorithms I've come across are very sensitive to the expected
> uncertainty in the time measurements.  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.  My
> desired position accuracy is around 100 ft up to a range of 100k ft.
>
> There were two different methods I thought of.  The first method would
> transmit a pulse from the rocket and then use a counter or TDC on the
> ground to measure the time difference between a GPS PPS and the pulse
> arrival.  This is the most straightforward method but I'm worried about the
> timing accuracy of the pulse measurement.  I should be able to find a
> timing GPS that has a PPS output with about +/- 30-40 ns of jitter (2
> sigma) so that portion is in the ballpark.  There also seem to be TDCs that
> have accuracy and resolution in the tens of picosecond range but they also
> have a maximum interval in the millisecond range.   I'm not sure I can
> ensure the pulse sent from the rocket will be within a few miilliseconds of
> the 1 PPS value on the ground.  I will have onboard GPS before launch so in
> theory I could initialize a counter to align the transmit pulse within a
> millisecond or so to the onboard PPS. But, once GPS is lost on ascent,
> unless I put an OCXO onboard that pulse may drift too far away (due to
> temperature, acceleration, etc.) for the TDC on the ground to pick it up.
> Plus an OCXO will add weight and require extra power for the heater.
> Another idea would be to send pulses at a very fast rate, say 1 kHz to stay
> within the TDC window.  But then I need to worry about what happens if the
> pulses get too close to the edge of the TDC window.  One other variable is
> the delay through the RF chain on the receive end but I figure I could
> calibrate that out.
>
> The other idea, and I'm not sure exactly how to implement it, would be to
> transmit a continuous tone (1 kHz for example) and perform some kind of
> phase measurement at each ground station against a reference.  I could use
> a GPSDO to divide down the 10 MHz to 1 kHz to compare with the received
> signal but how can I assure the divided down 1 kHz clocks are synchronized
> between ground stations?  Are the 10 MHz outputs from GPSDOs necessarily
> aligned to each other?  I let two Thunderbolts sit for a couple of hours
> and the 10 MHz outputs seemed to stabilize with an offset of about 1/4 of a
> cycle, too much for this application.  Another related idea would be to use
> the 10 MHz output to clock an ADC and then sample several thousand points
> using curve fitting, interpolation, and averaging to get a more accurate
> zero crossing than you could get based on the sample rate alone.  Adding a
> TDC would allow the use of RIS (random interleaved sampling) for repetitive
> signals which could generate an effective sample rate of 1 GS/s.
>
> Does anybody have advice or practical experience on which method would
> work better?
>
> Thanks,
> -Bob
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-- 

Chris Albertson
Redondo Beach, California