Identification of Nonlinear Systems through Quasi-White Test Signals

The use of quasi-white test signals, i.e. physically realizable signals that approximate the statistical properties of ideal white noise, in nonlinear system identification through the crosscorrelation technique is comprehensively studied. Important theoretical aspects of the subject are illustrated (e. g. the mathematical mechanisms of kernel estimation through crosscorrelation, the role of the several orthogonal functional series, the meaning of the corresponding kernels, the accuracy of the obtained truncated models etc.), and useful tools for the actual application of the method are developed (e.g. analytical expressions for the kernel estimation errors, optimum test procedure etc.). In addition to the widely known and used band-limited gaussian white noise and pseudorandom signals based on m-sequences, a new family of quasi-white test signals is introduced and its properties are thoroughly studied. The various advantages and disadvantages of these three families of quasi-white signals are discussed independently as well as in a comparative perspective. The accuracy of the several estimated models is found to be comparable for all these families of quasi-white signals, with small differences pertaining to the specific system under study or random factors. The theoretical study is followed and confirmed by actual applications on computer simulated and physiological systems. The newly introduced family is simplifying, clarifying and unifying the concept of the quasi-white signal in connection with its use in the crosscorrelation technique. Some special purpose tests are also presented, with one of them (the "general nonlinearity test") possessing the potentiality of a totally different identification method aiming at the Volterra kernels of the system.