Fit data recorded with different internal clocks

I have 2 sets of data, A and B, that records a distance which fluctates ~2ft for 600 seconds. The two devices have a differing internal clocks. Data B time drifts slightly forwards and backwards compared to the time in Data A, which I'm using as the reference.

I am looking to finely match the data between the two, and ultimately create a vector to multiply the time in Data B by to bring the data to a better appoximation of Data A. Then I can apply this vector to adjust other data recorded by the device with the time drift.

I've tried peak fitting, and the part I am stuck on is producing a sequential 'best fit'.

My question is, would there a better way to produce the corrective time drift vector than peak fitting?

Answer 1

[Chad Greene]

This is an interesting problem. If you can identify a few peaks that occur throughout the 600 s measurement, and those peaks are present in both signals, I think it's actually easy to solve elegantly.

Say in signal A you find five peaks at times

ta_peaks = [51 90 200 306 510]; 

and you see those same peaks in signal B, but in signal B they appear to occur at

tb_peaks = [49 89 200 307 515]; 

Start by fitting a relationship between ta and tb:

plot(ta_peaks,tb_peaks,'o') 
hold on 
xlabel 'time a peaks'
ylabel 'time b peaks'

% Relate time b to time a: 
p = polyfit(ta_peaks,tb_peaks,2); % quadratic fit 
tb_fit = polyval(p,ta_peaks); 
plot(ta_peaks,tb_fit)

Now with the relationship between clock A and clock B, you can use interp1 to interpolate signal B to the timing of signal A's clock.

B_interp = interp1(tb,B,polyval(p,ta)); 

and now the peaks and overall timing of B_interp should align with the signal A.