Maximum likelihood and Bayesian optimization based AFD identification algorithms

The adaptive Fourier decomposition (AFD) has been extensively researched within the domain of system identification, noted for its ability to expedite convergence through the adaptive selection of basis function poles. A pivotal aspect of this methodol-ogy entails the identification of poles pursuant to the maximum selection criterion, which often leads existing approaches into local optima. In this paper, new algorithms of global optimization and reduced complexity are introduced for the AFD method. The maximum likelihood and Bayesian estimation techniques are applied to the AFD identification. Numerical simulations substantiate the effectiveness of the proposed algorithms.