A genetic algorithm for the maximum likelihood estimation of the parameters of sinusoids in a noisy environment

An adaptive generic algorithm was developed to solve the optimization problem of the maximum likelihood estimation of the sum of sinusoids in a noisy environment. The algorithm is based on genetic concepts and is extended, with modifications, to this problem. Simulation results were performed to see the effect of different parameters such as permutation and crossover probabilities. The effects of the signal-to-noise ratio (SNR) were also studied. It was found that the key factor for accuracy is the probabilities of permutation and crossover. Thus, we developed an adaptive method to estimate these probabilities, on line, to reduce the error. This was accomplished by considering them as unknown parameters to be estimated with the signal parameters. The mean square error of the frequency estimates was compared favorably to the Cramér-Rao lower bound. Several simulations are shown for SNR values ranging between −7 dB and 20 dB.