An Iterative Algorithm for Optimal Event-Triggered Estimation*

Abstract

This paper investigates the optimal design of event-triggered estimation for firstorder 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 eventtrigger. 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 via numerical simulations. 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.

Fundamental Limits of Remote Estimation of Autoregressive Markov Processes Under Communication Constraints

“…In addition, several variations of the remote estimation problem have been considered in the literature. The most closely related models are [1], [15]- [18], [20], which are summarized below. Other related work includes censoring sensors [21], [22] (where a sensor takes a measurement and decides whether to transmit it or not; in the context of sequential hypothesis testing), estimation with measurement cost [23]- [25] (where the receiver decides when the sensor should transmit), sensor sleep scheduling [26]- [29] (where the sensor is allowed to sleep for a pre-specified amount of time); and event-based communication [30]- [32] (where the sensor transmits when a certain event takes place).…”

“…In [1], [18], [20], optimal remote estimation of autoregressive Markov processes is investigated when there is a cost associated with each transmission. It is assumed that the autoregressive process is driven by a symmetric and unimodal noise process but no assumption is imposed on the structure of the transmitter or the receiver.…”

“…It is assumed that the autoregressive process is driven by a symmetric and unimodal noise process but no assumption is imposed on the structure of the transmitter or the receiver. Using different solution approaches ( [1], [18] use majorization theory while [20] uses person-by-person optimality), it is shown that the optimal transmission strategy is threshold-based and the optimal estimation strategy is Kalman-like (the precise form of these strategies is stated in Theorem 8). Thus, the optimal transmission and estimation strategies are easy to implement.…”

Consistency-preserving event-triggered estimation in sensor networks

“…The rule given in (6) has been shown to be optimal for certain event-triggered problems for first-order systems penalizing transmissions [1], [2]. For higher-order dynamics, optimal solutions turn out to be a threshold function ofx j k|k −x j k|k whose threshold manifolds have no closed-form solution in general.…”

Optimal self-driven sampling for estimation based on value of information

“…Rabi et al [9] study optimal sampling as a stopping time problem for a scalar system under a finite transmission budget constraint. Molin and Hirche [10] investigate the optimal design for sampling in a scalar system with a communication cost by considering a two-player problem. Moreover, Sijs and Lazar [11] study event-driven sampling for the estimation problem with an asymptotic bound on the estimation error covariance.…”