  This paper aims to study the state estimation problem under the stochastic
event-triggered (SET) schedule. A posterior-based SET mechanism is proposed,
which determines whether to transmit data by the effect of the measurement on
the posterior estimate. Since this SET mechanism considers the whole posterior
probability density function, it has better information screening capability
and utilization than the existing SET mechanisms that only consider the
first-order moment information of measurement and prior estimate. Then, based
on the proposed SET mechanism, the corresponding exact minimum mean square
error estimator is derived by Bayes rule. Moreover, the prediction error
covariance of the estimator is proved to be bounded under moderate conditions.
Meanwhile, the upper and lower bounds on the average communication rate are
also analyzed. Finally, two different systems are employed to show the
effectiveness and advantages of the proposed methods.
