  This paper studies the remote state estimation problem of linear
time-invariant systems with stochastic event-triggered sensor schedules in the
presence of packet drops between the sensor and the estimator. It is shown that
the system state conditioned on the available information at the estimator side
is Gaussian mixture distributed. Minimum mean square error (MMSE) estimators
are subsequently derived for both open-loop and closed-loop schedules. Since
the optimal estimators require exponentially increasing computation and memory,
sub-optimal estimators to reduce the computational complexities are further
provided. In the end, simulations are conducted to illustrate the performance
of the optimal and sub-optimal estimators.
