M Nonparametric System Identification
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1 Introduction
System identification, as a particular process of statistical inference, exploits two types
of information. The first is experiment; the other, called a priori, is known before making
any measurements. In a wide sense, the a priori information concerns the system itself
and signals entering the system. Elements of the information are, for example:
the nature of the signals, which may be random or nonrandom, white or correlated,
stationary or not, their distributions can be known in full or partially (up to some
parameters) or completely unknown,
general information about the system, which can be, for example, continuous or
discrete in the time domain, stationary or not,
the structure of the system, which can be of the Hammerstein or Wiener type, or other,
the knowledge about subsystems, that is, about nonlinear characteristics and linear
dynamics.
In other words, the a priori information is related to the theory of the phenomena
taking place in the system (a real physical process) or can be interpreted as a hypothesis
(if so, results of the identification should be necessarily validated) or can be abstract in
nature.
This book deals with systems consisting of nonlinear memoryless and linear dynamic
subsystems, for example, Hammerstein and Wiener systems and other related structures. With respect to them, the a priori information is understood in a narrow sense
because it relates to the subsystems only and concerns the a priori knowledge about their
descript 内容过长，仅展示头部和尾部部分文字预览，全文请查看图片预览。 is bounded, that is,
that supn |an| < ∞. Writing an ～ bn, we mean that an/bn has a nonzero limit as n → ∞.
Throughout the book, “almost everywhere” means “almost everywhere with respect
to the Lebesgue measure,” whereas “almost everywhere (μ)” means “almost everywhere
with respect to the measure μ.
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