A new cross correlation algorithm for 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, due to the presence of higher order Volterra kernels. A new algorithm is developed to identify the parameter matrix which characterizes the nonlinear part of a bilinear system. The estimation of the second-order kernel is significantly improved.