PARAMETER-ESTIMATION IN SUPERPOSITION OF DECAYING EXPONENTIALS

This note is devoted to the problem of determining the amplitudes and decay rates in a superposition of decaying exponentials. We develop se veral complementary ways of dealing with this problem which allow us t o treat the case in which there is noise in the observations and we al low 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 t here 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 t here is noise in the observations, we use filtering theory to eliminat e the noise before determining the amplitudes and decay rates with a g enetic algorithm. When the amplitudes are not random but there is obse rvational noise we propose a simple chi(2)-minimization procedure. (C) 1998 Published by Elsevier Science Inc. All rights reserved.