  In this paper we propose a new identification scheme for Hammerstein systems,
which are dynamic systems consisting of a static nonlinearity and a linear
time-invariant dynamic system in cascade. We assume that the nonlinear function
can be described as a linear combination of $p$ basis functions. We reconstruct
the $p$ coefficients of the nonlinearity together with the first $n$ samples of
the impulse response of the linear system by estimating an $np$-dimensional
overparameterized vector, which contains all the combinations of the unknown
variables. To avoid high variance in these estimates, we adopt a regularized
kernel-based approach and, in particular, we introduce a new kernel tailored
for Hammerstein system identification. We show that the resulting scheme
provides an estimate of the overparameterized vector that can be uniquely
decomposed as the combination of an impulse response and $p$ coefficients of
the static nonlinearity. We also show, through several numerical experiments,
that the proposed method compares very favorably with two standard methods for
Hammerstein system identification.
