ON ESTIMATION OF A CLASS OF NONLINEAR-SYSTEMS BY THE KERNEL REGRESSION ESTIMATE

The estimation of multi-input single-output discrete Hammerstein system is studied. Such a system contains a nonlinear memoryless subsystem followed by a dynamic linear subsystem. We obtain the impulse response of the dynamic linear subsystem by the correlation method. The main results concern the estimation of the nonlinear memoryless subsystem. We impose no conditions on the functional form of the nonlinear subsystem, recovering the nonlinearity using the kernel regression estimate. We prove the distribution-free pointwise and global convergence of the estimate; that is, no conditions are imposed on the input distribution, and convergence is proven for virtually all nonlinearities. The rates of pointwise as well as global convergence are obtained for all input distributions and for nonlinearities of Lipschitz type. © 1990 IEEE