How to measure the agreement between to curves?

I have values (plotted below) of expected RSSI values over time that I would like to compare with my measured RSSI values. What I was looking for was a way to quantify it so I can change parameters and be able to compare/contrast different approaches.

It is a hard problem in my mind because I don't know how to compare the signals and yet take into account the large-scale (overall shape) and small-scale (individual fluctuations) of signal.

For instance, here is a plot of one set of signals:

In the image I can see that the red measure signal roughly follows the model, but it also does an OK job of simulating some of the sinusoidal qualities of the model (in some places). Any thoughts?

<> In response to pichenettes' comments (which seem reasonable), I took a diff of the two values and plotted the abs(fft(diff)) and got this:

I am not sure what to make of that though. Since we don't have any actual freqs, I am not sure how to scale the axis, and then if I did, what metric would you use?

• What about computing something like the square error in different frequency ranges (or breaking down the different into different frequency bands)? In the lower frequency range it'll measure the overall tracking abilities - irrespective of fast bumps. In the higher frequency, it'll measure the ability to track abrupt changes irrespectively of larger DC errors. – pichenettes Apr 10 '13 at 14:22
• OK, I added a new plot to the original post (as an edit) to show the fft(real(diff)), but I am not quite sure what to make of it. – toozie21 Apr 10 '13 at 17:48
• I would smooth both of them first; then you get a very good agreement (assuming that's the result you want). P.S. I always recommend sharing the data you used to make your plots so we can help more easily. – Emre Apr 10 '13 at 18:37
• How much do you care about matching the phase at higher frequencies? The sense I get is that you might want to compare the time-domain signal directly (after a low-pass filter), then compare frequency-domain for higher frequencies, possibly looking only at magnitude and ignoring the phase. – Dan Bryant May 16 '13 at 22:48
• @toozie21 do you already know the time locations at which the signal properties change? e.g. 8 ms, 17ms .. so on. – user13107 Aug 12 '13 at 2:20