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The Volterra integral-functional series is the classic approach for nonlinearblack box dynamical systems modeling. It is widely employed in many domainsincluding radiophysics, aerodynamics, electronic and electrical engineering andmany other. Identifying the time-varying functional parameters, also known asVolterra kernels, poses a difficulty due to the curse of dimensionality. Thisrefers to the exponential growth in the number of model parameters as thecomplexity of the input-output response increases. The least squares method(LSM) is widely acknowledged as the standard approach for tackling the issue ofidentifying parameters. Unfortunately, the LSM suffers with many drawbacks suchas the sensitivity to outliers causing biased estimation, multicollinearity,overfitting and inefficiency with large datasets. This paper presentsalternative approach based on direct estimation of the Volterra kernels usingthe collocation method. Two model examples are studied. It is found that thecollocation method presents a promising alternative for optimization,surpassing the traditional least squares method when it comes to the Volterrakernels identification including the case when input and output signals sufferfrom considerable measurement errors.

Volterra black-box models identification methods: direct collocation vs least squares