Hi Jim,

On 04/13/2018 06:52 PM, Jim Lux wrote:
> 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???

Cross-correlate. Hug your Fourier transform as you do it.

Assume that you have a rough idea where the pulse occurs for each SDR.
FFT with a suitable window function each record.
Using one as reference, you then multiply the complex response with the
reference conjugated response.
Ether compare in the frequency domain or do inverse FFT and search the
time-domain for peak response.

This is how modern GPS receivers to quick lockup of phase, and it works
very well. Using an FFT library i could code it in relative little C
code and setup my classic channel decoder this way.

Now, use this to compare your SDR clocks compared to the reference. As
they drift over time the windown need to shift, but you can keep track
of the number of samples shifts to keep full track of it. This should
give you enough phase and frequency information. Toss in a least square
or Kalman if you think it would help.

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