Identification of nonlinear biological systems using Laguerre expansions of kernels

Identification of nonlinear dynamic systems using the Volterra-Wiener approach requires the estimation of system kernels from input-output data. A kernel estimation technique, originally proposed by Wiener (1958) and recently studied by Ogura (1986), employs Laguerre expansions of the kernels and estimates the unknown expansion coefficients via time-averaging of covariance samples. This paper presents another implementation of the technique which utilizes least-squares fitting instead of covariance time-averaging and provides for the proper selection of the intrinsic Laguerre parameter "alpha". Results from simulation examples demonstrate that this implementation can yield accurate kernel estimates up to 3rd-order from short input-output data records. Furthermore, it is shown that this implementation remains effective in the presence of noise and when the spectral characteristics of the input signal deviate somewhat from the theoretical requirements of whiteness. The computational requirements and the overall performance of this technique compare favorably to existing methods, especially in cases where the system kernels can be represented with a relatively small number of Laguerre basis functions.