Convolution, correlation and maximization

Hi,

I have a load of mass spec (maldi-tof) data that I need some help 
working with.  At any time index t, there is a corresponding mass as 
determined by the coefficients from a quadratic.

I would like to try to maximize my correlation by convolving my actual 
spectra with the expected signals.

The problem is that I dont know how to adjust my coefficients in a 
coordinated fashion with my convolution to ensure that I get the best 
possible coefficients possible.

Currently, I use a simplex method to bump my coeffs around and at each 
simplex step use a levenberg-marquardt fit until to test the 
correlation, or fit of the data sets.

This seems to work alright, but local maxima are a problem since they 
may be many signals, as well as the time taken to iterate through the 
simplex algorithm.  I am basically using the simplex to zone in on the 
coeffs, and convolving/correlation as a test to identify best fits.

I am not a math guy nor a dsp guy, Im just a software engineer trying to 
  fix a problem with our expected signals not matching our detected 
signals because our coefficients are off.

Can anyone offer any alternative approaches to this problem? 
Suggestions?  Critiques?

Thanks,
Bryan