Model-based Kalman filtering a noisy signal
I ended up with a quite satisfactory solution, not by using a Kalman filter, but by using the Savitzky-Golay differentiating filter.

The algorithm is described more or less like this:


In a for loop, apply a running window to get a segment of the unfiltered volume signal around a range of given time instants, as measured by the load cell;
For each segment, perform a polynomial interpolation. I am using quadratic;
Differentiate the found polynomial;
Evaluate the derivative at the given time instant;


This gives me a very natural-looking flow curve, based on the premise that the flow cannot physically contain high frequencies. So the "model" ended up being a well-chosen low-pass filter, with the bonus that I can differentiate a continuous function (the smoothing polynomial) instead of the discrete differentiation that tends to amplify the noise.