[time-nuts] Need advice for multilateration setup

[Peter Reilley]

Robert;

It seems that a Doppler system should work for you.

But first, you have a problem.   If you want to track your rocket
to 100K feet (20 miles) using some form of triangulation then you
need your receiving stations further apart than 1 mile.   Your
triangle is too extreme and any measurement error will be greatly
amplified.

Here is what I suggest.

Place a simple transmitter in the rocket of say 100 MHz.   It 
really should be a legal frequency, 2 meter ham band?   The 
transmitted frequency is not modulated and should be stable
for the duration of the flight.

The receiving stations should have a very narrow receive filter
on the front end and mix the signal with a local oscillator that is
5 KHz off from the rocket frequency.   For example: 100.005 MHz.
A narrow audio filter will help as well.   This is results in a 
very narrow bandwidth receiver which is very good in rejecting 
received noise.

Take the audio signal and feed it into a computer's audio input.
Sample the audio A/D converter as fast as you can and timestamp
each sample.   The computer's clock should be synchronized with
your GPS receiver's time.

This system measures velocity relative to your vantage point.
Because distance is the integral of velocity you can calculate
the distance during your flight.   Since the initial positions
are known you can calculate absolute position.

If we assume a 100 MHz transmitter and with the speed of light
at 300,000 KM/S you will see about 1/3 of a HZ shift for each 1 M/S
of velocity.

You do not need super stable oscillators.   They only need 
to be stable for the duration of the flight.

Here is how the flight will be tracked:

Before the flight, the ground stations will receive the 100 MHz
from the rocket and record the offset between the rocket's
oscillator and the local oscillator.   Any error will show up
as the 5 KHz being somewhat off.   This is not a problem if
it remains constant during the flight. 

Before the flight the computer logs the audio input data
with the timestamp.   This is the reference data.

When the rocket is launched the computer continues logging
but should notice the shift in frequency.   The entire set
of logged data should show the velocity profile for the entire
flight.   This can be converted to distance since all of the
initial positions of the ground stations and the rocket are
known.   Using the data from all the ground stations you can
calculate the absolute position of the rocket for the entire 
flight.

This setup should easily fit within your budget.   The crystal
oscillators do not need to be super precise or stable.
They only need to be stable for the duration of the flight
since the system calibrates itself immediately before launch.

Pete.
 

Robert Watzlavick 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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