[time-nuts] getting accurate timing on RTL-SDR output

[Jim Lux]

I'm building a phased array receiver (actually, an interferometer) using 
RTL-SDR pods, where the elements are isolated from each other - there's 
a common WiFi network connection, and each node has a BeagleBone Green, 
a uBlox OEM-7M-C, and the RTL-SDR V3 (which works down to HF, since it 
has an internal bypass around the RF front end).

In general, I have the RTL-SDR set up to capture at 1 Megasample/second. 
I fire off a capture, record it to a file in the BeagleBone's flash, 
then retrieve it from my host computer using scp over the network.

What I'm trying to do is capture data from all the nodes at 
(approximately) the same time, then be able to line it all up in post 
processing. The GPS (or NTP) is good enough to get them all to start 
recording within a few tenths of a second.

So now the challenge is to "line em up".  An obvious approach is to 
transmit an inband pilot tone with some sync pattern, received by all, 
and I'm working on that too.

But right now, I have the idea of capacitively coupling the 1pps pulse 
from the GPS to the antenna input - the fast rising and falling edge are 
broad band and show up in the sampled data.

The attached pulses1.png shows the integrated power in 1 ms chunks (i.e. 
I sum the power from 1000 samples for each chunk) and it's easy to see 
the GPS edges.  And it's easy to create a estimate of the coarse timing 
(to 1 millisecond) - shown as the red trace.

But then, I want to get better.  So for the 20 edges in my 10 second 
example, I plotted  (drift1.png) the raw I/Q output of the RTL.  The 
pulse isn't too huge (maybe 10 DN out of the ADC's -128 to +128 range), 
but is visible. Bottom trace is the first, and they're stacked up
0, 0.1, 1.0, 1.1, 2.0, 2.1, etc.

And you can see, no surprise, that the sample clock in the RTL isn't 
dead on - over the 10 seconds, it looks like it drifts about 30- 50 
microseconds - that is, the RTL clock is slow by 3-5 ppm.

SO here's the question for the time-nuts hive-mind...
What's a good (or not so good) way to develop an estimator of the 
timing/frequency error. Post processing minutes of data is just fine..

I'm not sure what the actual "waveform" that is being sampled is (and it 
will be perturbed by the quantization of the ADC, and probably not be 
the same depending on where the RTL is tuned).  That is there's some 
sort of LPF in the front of the RTL, the edge is AC coupled, and then it 
goes into some sort of digital down converter in the RTL running at 28.8 
MHz sample rate.

But it seems that there might be some way to "stack" a series of samples 
and optimize some parameters to estimate the instantaneous time error- 
given that the frequency vs time varies fairly slowly (over a minute or 
so).  It's fairly obvious from the plot that if one looked at the 
"single" sample when the edge comes in, not only does the time shift 
with each pulse, but the phase rotates as well (totally expected)

this is one of those things where you could probably lay a ruler on it 
and estimate it by eye pretty well, but I'd like an automated algorithm.

It would be nice to be able to estimate the timing to, say, a few 
nanoseconds over a minute or so ( - that would allow a phase estimation 
of 1/10th of a wavelength of a 20 MHz signal (e.g. Jupiter's RF noise, 
or WWVH's transmissions)


Ideas???



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