Nonlinear filter design

TLDR: In this article, a technique for identifying nonlinear systems was introduced, beginning with a single input-single output system, and the first kernel (first convolution integral in the continuous case or first convolution sum in the discrete case) was calculated.

Abstract: A technique for identifying nonlinear systems was introduced, beginning with a single input-single output system. Assuming the system is initially at rest, the first kernel (first convolution integral in the continuous case or first convolution sum in the discrete case) was calculated. A controllable and observable linear realization was then obtained in a particular canonical form. The actual nonlinear system was probed with an appropriate input (or inputs) and the output (or outputs) determined. For the linear system, the input was computed that produces the same output. In the difference between the inputs to the nonlinear and linear systems, basic information was found about the nonlinear system. There is an interesting class of nonlinear systems for which this type of identification scheme should prove to be accurate.