  This paper deals with the problem of remote estimation of the state of a
discrete-time stochastic linear system observed by a sensor with computational
capacity to calculate local estimates. We design an event-triggered
communication (ETC) scheme and a remote state estimator to optimally calibrate
the tradeoff between system performance and limited communication resources.
The novel communication scheme is the time-varying thresholding version for the
cumulative innovation-driven communication scheme in [1], and its transmission
probability is given. We derive the corresponding remote minimum mean square
error (MMSE) estimator and present a tight upper bound for its MSE matrices. We
also show that by employing a couple of weak assumptions, the optimality
problem becomes (asymptotically) exact and can be addressed in an Markov
Decision Process (MDP) framework, which delivers optimal policy and cost in an
algorithmic procedure. The simulation results illustrate the effectiveness of
our approach.
