A Novel Volterra High-Order Kernels Algorithm Based on Linear Space Projection

In this paper, a novel estimation method on Volterra series high-order kernels to nonlinear dynamic system to arbitrary approximation is proposed. On the theoretical basis of kernel function, by the construction of linear space, the issue of solving the Volterra series order kernels is converted to solving the projection of the output of the observation vector in the a sub-space of Hilbert space, which makes the original complex approximation problem of Volterra series in nonlinear systems to be solved in the way of vector inner product. Compared with other time or frequency domain methods to estimate the Volterra kernels, the advantages of the algorithm is strictly theoretical, that the amount of calculation does not increase with the order in a geometric growth and high recognition accuracy. Simulation results prove the effectiveness of the method.