A method for informed selection of memory-length and nonlinearity-order parameters in Volterra---Wiener systems from exponential sweep excitations

Blanco-Murillo, J.L.; Yagüe-Jiménez, V.
Multidimensional Systems and Signal Processing, vol. 29, pp. 1861-1893, n.º 4, Kluwer Academic Publishers.

We prove that through the analysis of the static, nonlinear system output to an exponential sweep excitation, it is possible to make an easy and informed estimation of memory-length and nonlinearity order parameters, prior to complete identification. The selection of these parameters has been a matter of discussion for many years since most identification techniques require early estimates of those. This work extends the results of previous contributions concerning a constrained set of memory- and order-fading nonlinear systems with diagonal kernels, onto the more general case of memory- and order-fading nonlinear systems that admit a Volterra series representation. A full mathematical formulation of the system output is provided, based on the input. Estimates on the parameters may be obtained by simple inspection on a single, filtered, output to the exponential sweep excitation. This happens to be a projection of the multidimensional, order kernels, as we prove. Examples are provided to evidence the simplicity and reliability of the proposed method.

This work is partially supported by the Spanish Ministry of Economy and Competitivity, Grant No. TEC2012-38402-C04-01.