  This report investigates the optimal design of event-triggered estimation for
first-order linear stochastic systems. The problem is posed as a two-player
team problem with a partially nested information pattern. The two players are
given by an estimator and an event-trigger. The event-trigger has full state
information and decides, whether the estimator shall obtain the current state
information by transmitting it through a resource constrained channel. The
objective is to find an optimal trade-off between the mean squared estimation
error and the expected transmission rate. The proposed iterative algorithm
alternates between optimizing one player while fixing the other player. It is
shown that the solution of the algorithm converges to a linear predictor and a
symmetric threshold policy, if the densities of the initial state and the noise
variables are even and radially decreasing functions. The effectiveness of the
approach is illustrated on a numerical example. In case of a multimodal
distribution of the noise variables a significant performance improvement can
be achieved compared to a separate design that assumes a linear prediction and
a symmetric threshold policy.
