A new approach to volterra-kernel estimation of bilinear systems

Correlation analysis is applied to estimate the first and second-order kernels in a Volterra series expansion of bilinear systems. The kernels are estimated for a simulation model of a nuclear fission process. The method yields good estimates of the first-order kernel under noisy input-output measurements. However, the estimation of the second-order kernel is not satisfactory. A new approach to the estimation of second-order kernel is developed. The input-output relation of bilinear system is represented by an integral equation. A Wiener-Hopf type equation is obtained by cross-correlation of the input and the output. The estimation of the second-order kernel is significantly improved.