[time-nuts] Need advice for multilateration setup

[Robert Watzlavick]

Budget is a concern but not an overriding concern. I'd like to keep the whole system around $1k.  I was planning on making it as portable as possible with each ground station being self contained and sending their data to the launch site over a serial RF modem at 9600 baud. I agree though - fiber connections would make it a lot easier. 

-Bob


> On Mar 26, 2015, at 08:41, Anders Wallin <anders.e.e.wallin at gmail.com> wrote:
> 
> 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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