Peak detection of measured signal

There are lots and lots of classic peak detection methods, any of which might work. You’ll have to see what, in particular, bounds the quality of your data. Here are basic descriptions:

1. Between any two points in your data, (x(0), y(0)) and (x(n), y(n)), add up y(i + 1) - y(i) for 0 <= i < n and call this T (“travel”) and set R (“rise”) to y(n) - y(0) + k for suitably small k. T/R > 1 indicates a peak. This works OK if large travel due to noise is unlikely or if noise distributes symmetrically around a base curve shape. For your application, accept the earliest peak with a score above a given threshold, or analyze the curve of travel per rise values for more interesting properties.

2. Use matched filters to score similarity to a standard peak shape (essentially, use a normalized dot-product against some shape to get a cosine-metric of similarity)

3. Deconvolve against a standard peak shape and check for high values (though I often find 2 to be less sensitive to noise for simple instrumentation output).

4. Smooth the data and check for triplets of equally spaced points where, if x0 < x1 < x2, y1 > 0.5 * (y0 + y2), or check Euclidean distances like this: D((x0, y0), (x1, y1)) + D((x1, y1), (x2, y2)) > D((x0, y0),(x2, y2)), which relies on the triangle inequality. Using simple ratios will again provide you a scoring mechanism.

5. Fit a very simple 2-gaussian mixture model to your data (for example, Numerical Recipes has a nice ready-made chunk of code). Take the earlier peak. This will deal correctly with overlapping peaks.

6. Find the best match in the data to a simple Gaussian, Cauchy, Poisson, or what-have-you curve. Evaluate this curve over a broad range and subtract it from a copy of the data after noting it’s peak location. Repeat. Take the earliest peak whose model parameters (standard deviation probably, but some applications might care about kurtosis or other features) meet some criterion. Watch out for artifacts left behind when peaks are subtracted from the data.
   Best match might be determined by the kind of match scoring suggested in #2 above.

I’ve done what you’re doing before: finding peaks in DNA sequence data, finding peaks in derivatives estimated from measured curves, and finding peaks in histograms.

I encourage you to attend carefully to proper baselining. Wiener filtering or other filtering or simple histogram analysis is often an easy way to baseline in the presence of noise.

Finally, if your data is typically noisy and you’re getting data off the card as unreferenced single-ended output (or even referenced, just not differential), and if you’re averaging lots of observations into each data point, try sorting those observations and throwing away the first and last quartile and averaging what remains. There are a host of such outlier elimination tactics that can be really useful.