TY - JOUR
T1 - Recursive Identification of Wiener-Hammerstein Systems with Nonparametric Nonlinearity
AU - Xiao-Li Hu & Yue-Ping Jiang
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 311
EP - 332
PY - 2018
DA - 2018/02
SN - 3
DO - http://doi.org/10.4208/eajam.290913.111113a
UR - https://global-sci.org/intro/article_detail/eajam/10860.html
KW - Wiener-Hammerstein system, nonparametric nonlinearity, recursive estimate, strong consistence.
AB - <p style="text-align: justify;">A recursive scheme is proposed for identifying a single input single output
(SISO) Wiener-Hammerstein system, which consists of two linear dynamic subsystems
and a sandwiched nonparametric static nonlinearity. The first linear block is assumed
to be a finite impulse response (FIR) filter and the second an infinite impulse response
(IIR) filter. By letting the input be a sequence of mutually independent Gaussian random
variables, the recursive estimates for coefficients of the two linear blocks and the value
of the static nonlinear function at any fixed given point are proven to converge to the
true values, with probability one as the data size tends to infinity. The static nonlinearity
is identified in a nonparametric way and no structural information is directly used. A
numerical example is presented that illustrates the theoretical results.</p>