文档介绍：I
IEEE TRANSACTIONS ON IN€ORMAIlON IHEOKY, VOL. 36, NO. 1 JANUARY 1990 141
On Estimation of a Class of Nonlinear
Systems by the Kernel
Regression Estimate
ADAM KRZYZAK, MEMBER,IEEE
Ahstrrrct -The e\timation of multi-input single-output discrete Ham- Womack [28] and Chow and Chizeck [lo], to adaptive
merstein sjstem i\ ftudied. Such a system contains a nonlinear memoryless noise cancellation by Stapleton and Baas [40], and to the
subsystem followed by a dgnamic linear subsystem. We obtain the impulse design of nonlinear discrete-time predictors by McCannon
response of the dynamic linear subsystem by the correlation method. The
main results concern the estimation of the nonlinear memoryless subsys- et al. [32], [33]. Its application munication and radar
tem. We impose no conditions on the functional form of the nonlinear design is discussed by Mortensen [34]. All the authors
subsystem, recovering the nonlinearity using the kernel regression esti- mentioned consider single-input single-output system
mate. We prove the distribution-free pointwise and global convergence of (SISO) in which the nonlinearity is restricted to a polyno-
the estimate; that is, no conditions are imposed on the input distribution, mial of fixed degree. This restriction excludes discontinu-
and convergence is proven for virtually all nonlinearities. The rates of
pointwise as well as global convergence are obtained for all input distribu- ous characteristics, even such basic ones as ideal or dead-
tions and for nonlinearities of Lipschitz type. zone limiters. They do not estimate separately the
polynomial coefficients and those of the weighting func-
I. INTRODUCTION tion; they hold constant the parameters in the first subsys-
tem while determining the parameters in the other section.
ANY SCHEMES have been developed for nonlin-
M They also do not provide formal proofs of convergence.
ear systems estimation. These methods have usua