Stochastic Event-Triggered Sensor Schedule for Remote State Estimation

Abstract

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 minimum mean squared error (MMSE) estimator and its estimation error covariance matrix at the remote estimator are given in a closed-form. The stability in terms of the expected error covariance and the sample path of the error covariance for both schedules is studied. We also formulate and solve an optimization problem to obtain the minimum communication rate under some estimation quality constraint using the open-loop sensor schedule. A numerical comparison between the closed-loop MMSE estimator and a typical approximate MMSE estimator with deterministic eventtriggered sensor schedule, in a problem setting of target tracking, shows the superiority of the proposed sensor schedule.

Distributed State Estimation under State Inequality Constraints with Random Communication over Multi-Agent Networks

“…Since the agents only transmit valuable information, the event-triggered scheme may achieve better performance compared with the proposed RS scheme. In [17,18], the authors dealt with a centralized stochastic event-triggered estimation problem. Here we introduce a distributed stochastic event-triggered scheme by extending the algorithms described in [18].…”

“…As stated in [18], at each time instant, agent i generates an i.i.d random variable ϕ i,k and computes γ i,k as follows:…”

“…The local MMSE estimator (without consensus and projection) for agent i with incorporating the stochastic event-triggering (13) is given as follows (see Theorem 2 in [18]):…”

“…If we can obtain the covariance ofỹ i,k in the steady state, we can obtain the communication rate [18]. However, it is difficult to analyze the communication rate sinceỹ i,k depends on the consensus and projection stage in the distributed case, though a communication rate is determined using the stochastic event-triggered scheme (13).…”

Event-based particle filtering with point and set-valued measurements

“…However, while Gaussian-based approximation of the eventbased posterior has been investigated extensively, application of non-Gaussian filtering using particle filters [25]- [28] is still in its infancy. To the best of our knowledge, only very recently, EBE using non-Gaussian particle filter approximation is considered in [11] and [12], where in the latter simply the number of particles belonging to the triggering set is used to update particle weights, while the former uses stochastic triggering [19] which results in having a Gaussian posterior. The paper addresses this gap.…”