Event-Triggered Estimation of Linear Systems: An Iterative Algorithm and Optimality Properties ∗

This report investigates the optimal design of event-trigg ered estimation for first- order linear stochastic systems. The problem is posed as a tw o-player team problem with a partially nested information pattern. The two players are g by an estimator and an event- trigger. The event-trigger has full state information and d ecides, whether the estimator shall obtain the current state information by transmitting it thr ough a resource constrained channel. The objective is to find an optimal trade-off between the meansquared estimation error and the expected transmission rate. The proposed iterative algori thm alternates between optimizing one player while fixing the other player. It is shown that the solu tion of the algorithm converges to a linear predictor and a symmetric threshold policy, if the d of the initial state and the noise variables are even and radially decreasing functions . This is achieved by considering the iterative algorithm as a dynamical system and apply Lyapuno v methods to show that it is globally asymptotically stable. The effectiveness of the approach i s illustrated on a numerical example. In case of a multimodal distribution of the noise variables a si gnificant performance improvement can be achieved compared to a separate design that assumes a l inear prediction and a symmetric threshold policy.