  This paper investigates the adaptive identification and prediction problems
for stochastic dynamical systems with saturated observations, which arise from
various fields in engineering and social systems, but up to now still lack
comprehensive theoretical studies including performance guarantees needed in
practical applications. With this impetus, the paper has made the following
main contributions: (i) To introduce a two-step Quasi-Newton (TSQN) algorithm
to improve the performance of the identification, which is applicable to a
typical class of nonlinear stochastic systems with outputs observed under
possibly varying saturation. (ii) To establish the global convergence of both
the parameter estimators and adaptive predictors and to prove the asymptotic
normality, under the weakest possible non-persistent excitation (PE) condition,
which can be applied to stochastic feedback systems with general non-stationary
and correlated system signals or data. (iii) To establish useful probabilistic
estimation error bounds for any given finite length of data, using either
martingale inequalities or Monte Carlo experiments. A numerical example is also
provided to illustrate the performance of the proposed identification
algorithm.
