# [time-nuts] Need advice for multilateration setup

Robert Watzlavick rocket at watzlavick.com
Wed Mar 25 22:27:35 EDT 2015

```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
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

```