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Peak finding

I have a set of 3-D data, where a single peak should occur for each Z
value. I wish to know where this peak is.

Currently, I've been using a gaussian fit with 5 parameters, and using
the centre of the gaussian as the peak location. This fails when the
peak is very near the edge of the dataset, but the results in the centre
are good. I can easily differentiate between good values and noise from

However, I tried running a different dataset and the gaussian fit just
hung completely. On experimentation, I discovered that the good data
hung if I tried a gaussian fit with 4 parameters (which I'd prefer) or
with 6 parameters.

I'm looking for a simple, but stable, way of detecting where these peaks
occur. I'd like to avoid functions that are dependant on only a few
points (like simply using MAX). It doesn't have to work in all
situations, but should be happy when both edges of the peak are present.

Any ideas?