Monte Carlo Least-Squares Fitting of Experimental Signal Waveforms

This paper focuses on why the regular least{squares ¯tting technique is unstable when used to ¯t exponential functions to signal waveforms, since such functions are highly correlated. It talks about alternative approaches, such as the search method, which has a slow convergence rate of 1=N1=M, for M parameters, where N is the number of computations performed. We have used the Monte Carlo method, utilizing both search and random walk, to devise a stable least{squares ¯tting algorithm that converges rapidly at a rate 1=N1=2, regardless of the number of parameters used in ¯tting the waveforms. The Monte Carlo approach has been tested for computed data|with and without noise, and by ¯tting actual experimental signal waveforms associated with optogalvanic transitions recorded with a hollow cathode discharge tube containing a mixture of neon (Ne) and carbon monoxide (CO) gases, and has yielded excellent results, making the developed algorithm both stable and fast for today's personal computers.