Parameter estimation in superposition of decaying exponentials

摘要

This note is devoted to the problem of determining the amplitudes and decay rates in a superposition of decaying exponentials. We develop several complementary ways of dealing with this problem which allow us to treat the case in which there is noise in the observations and we allow for randomness in the determination of the amplitudes as well. We propose a combination of genetic algorithms and filtering to deal with the various possible alternatives for the presence of noise: either there is no noise or there is noise in the observation process, and the amplitudes may be random or not. When the amplitudes are random and there is noise in the observations, we use filtering theory to eliminate the noise before determining the amplitudes and decay rates with a genetic algorithm. When the amplitudes are not random but there is observational noise we propose a simple χ2-minimization procedure.