Information theoretical algorithm based on statistical models for blind identification of nonstationary dynamical systems

Abstract

This paper presents an effective blind statistical identification technique for nonstationary nonlinear systems based on an information theoretical algorithm. This technique firstly extracts, from the output signals, the multivariate relationships in the Hilbert spaces by exploiting the separability properties of the signal outputs transformed by the Karhunen-Loeve transform (KLT). Then, the algorithm methodologically clusters the stochastic surfaces in the Hilbert spaces using the self-organizing maps (SOMs) and further develops their best statistical model under the fixed-rank condition. The resulting blind identification of the statistical system model is based on marginal probability density functions (PDFs), whose convergence to the statistical system model based on Monte Carlo simulations has also been demonstrated by asymptotically vanishing the Kullback-Leibler divergences. A large number of simulations on both synthetic and real systems demonstrated the validity and the excellent performances of this technique that is irrespective of the system order, the stochastic surface topology, the true marginal PDFs, and the knowledge of the statistics of the noise superimposed to the output signals. Finally, this approach could also represent a suitable and promising technique for the noninvasive diagnosis of a large class of medical pathologies originated by unknown physiological factors (nonlinear compositions of unknown input signals) and/or when they are difficult or unpractical to measure.