The use of clipped input information in multidimensional cross-correlation for estimating Wiener-like kernels of non-linear systems

While the measurement of Wiener-like kernels by multidimensional input-output cross-correlation is a well-known non-parametric approach to non-linear system identification, we propose here a simplifying kernel estimation scheme; rather than using the white-noise signal that is actually applied to stimulate the system, the present method uses a clipped information (that is, two- or three-level quantization) of the continuous-level test input for computing the cross-correlation. This greatly reduces the computational requirement without disturbing the generality of actual test input which may be gaussian. The statistical variance of the kernel estimation is discussed in comparison with other algorithms. Certain non-statistical errors may be incurred using this approach, but are thought to be minor in most applications. A special emphasis is given to the problem of choosing optimal procedural parameters for ternary quantization in the case of white gaussian input.