A Simple Algorithm for Fitting a Gaussian Function
Hongwei Guo
IEEE Signal Processing Magazine
Volume 28, September 2011, page 134
This short article was a nice quick read which taught me a few new things and reminded me of several key points. 1) To curve fit data to a Gaussian function it is helpful if you first take the natural log of the data, then fit a quadratic to it. 2) The logarithm naturally weights the small values of noise much more than you want, so this approach has several drawbacks. What the authors did which was cools was instead of fitting to ln(data) then fitted to data*ln(data) which helped aliveiate the weighting issues. This also had some drawbacks so they introduced an interative process which was not dependent on the initial guess to quite persuasively fit the data well. It was a nice reminder of how to do least squares linear algebra with a Newton-Raphson iterative algorithm.
