[time-nuts] Need advice for multilateration setup

[Anders Wallin]

What's your budget?
Put a white-rabbit switch (3.5keur) in the middle, and install a mile of
single-mode fiber to each rx-station. Then use TDC or FDEL SPEC-cards
(1.5keur each) at the RX-stations to time-stamp the incoming pulse. <1 ns
systematic and <50 ps RMS random error should be doable. The systematic
constant error in time-stamp for each rx-station can maybe be calibrated
out in the TDOA-algorithm? The FDEL-card can time-stamp up to 100 kEdges/s
(that results in a ca  4 Mb/s datastream).

Anders


On Thu, Mar 26, 2015 at 4:27 AM, 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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