  We propose an open-loop and a closed-loop stochastic event-triggered sensor
schedule for remote state estimation. Both schedules overcome the essential
difficulties of existing schedules in recent literature works where, through
introducing a deterministic event-triggering mechanism, the Gaussian property
of the innovation process is destroyed which produces a challenging nonlinear
filtering problem that cannot be solved unless approximation techniques are
adopted. The proposed stochastic event-triggered sensor schedules eliminate
such approximations. Under these two schedules, the MMSE estimator and its
estimation error covariance matrix at the remote estimator are given in a
closed-form. Simulation studies demonstrate that the proposed schedules have
better performance than periodic ones with the same sensor-to-estimator
communication rate.
