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Register a new userAn event-triggered transmission scheduling strategy for remote state estimation in the presence of an eavesdropper
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We consider a remote state estimation problem in the presence of an eavesdropper over packet dropping links. A smart sensor transmits its local estimates to a legitimate remote estimator, in the course of which an eavesdropper can randomly overhear the transmission. This problem has been well studied for unstable dynamical systems, but seldom for stable systems. In this paper, we target at stable and marginally stable systems and aim to design an event-triggered scheduling strategy by minimizing the expected error covariance at the remote estimator and keeping that at the eavesdropper above a user-specified lower bound. To this end, we model the evolution of the error covariance as an infinite recurrent Markov chain and develop a recurrence relation to describe the stationary distribution of the state at the eavesdropper. Monotonicity and convergence properties of the expected error covariance are further investigated and employed to solve the optimization problem. Numerical examples are provided to validate the theoretical results.
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This paper studies remote state estimation in the presence of an eavesdropper. A sensor transmits local state estimates over a packet dropping link to a remote estimator, while an eavesdropper can successfully overhear each sensor transmission with a certain probability. The objective is to determine when the sensor should transmit, in order to minimize the estimation error covariance at the remote estimator, while trying to keep the eavesdropper error covariance above a certain level. This is done by solving an optimization problem that minimizes a linear combination of the expected estimation error covariance and the negative of the expected eavesdropper error covariance. Structural results on the optimal transmission policy are derived, and shown to exhibit thresholding behaviour in the estimation error covariances. In the infinite horizon situation, it is shown that with unstable systems one can keep the expected estimation error covariance bounded while the expected eavesdropper error covariance becomes unbounded. An alternative measure of security, constraining the amount of information revealed to the eavesdropper, is also considered, and similar structural results on the optimal transmission policy are derived. In the infinite horizon situation with unstable systems, it is now shown that for any transmission policy which keeps the expected estimation error covariance bounded, the expected amount of information revealed to the eavesdropper is always lower bounded away from zero. An extension of our results to the transmission of measurements is also presented.
General nonlinear continuous-time systems are considered for which the state is to be estimated via a packet-based communication network. We assume that the system has multiple sensor nodes, affected by measurement noise, which can transmit output data at discrete (non-equidistant) and asynchronous points in time. For this general system setup, we develop a state estimation framework, where the transmission instances of the individual sensor nodes can be generated in both time-triggered and event-triggered fashions. In the latter case, we guarantee the absence of Zeno behavior by construction. It is shown that, under the provided design conditions, an input-to-state stability property is obtained for the estimation error and that the state is thus reconstructed asymptotically in the absence of noise. A numerical case study shows the strengths of the developed framework.
Novel low-power wireless technologies and IoT applications open the door to the Industrial Internet of Things (IIoT). In this new paradigm, Wireless Sensor Networks (WSNs) must fulfil, despite energy and transmission power limitations, the challenging communication requirements of advanced manufacturing processes and technologies. In industrial networks, this is possible thanks to the availability of network infrastructure and the presence of a network coordinator that efficiently allocates the available radio resources. In this work, we consider a WSN that simultaneously transmits measurements of Networked Control Systems (NCSs) dynamics to remote state estimators over a shared packet-erasure channel. We develop a minimum transmission power control (TPC) policy for the coordination of the wireless medium by formulating an infinite horizon Markov decision process (MDP) optimization problem. We compute the policy using an approximate value iteration algorithm and provide an extensive evaluation of its parameters in different interference scenarios and NCSs dynamics. The evaluation results present a comprehensive characterization of the algorithms performance, proving that it can flexibly adapt to arbitrary use cases.
We consider the problem of communication allocation for remote state estimation in a cognitive radio sensor network~(CRSN). A sensor collects measurements of a physical plant, and transmits the data to a remote estimator as a secondary user (SU) in the shared network. The existence of the primal users (PUs) brings exogenous uncertainties into the transmission scheduling process, and how to design an event-based scheduling scheme considering these uncertainties has not been addressed in the literature. In this work, we start from the formulation of a discrete-time remote estimation process in the CRSN, and then analyze the hidden information contained in the absence of data transmission. In order to achieve a better tradeoff between estimation performance and communication consumption, we propose both open-loop and closed-loop schedules using the hidden information under a Bayesian setting. The open-loop schedule does not rely on any feedback signal but only works for stable plants. For unstable plants, a closed-loop schedule is designed based on feedback signals. The parameter design problems in both schedules are efficiently solved by convex programming. Numerical simulations are included to illustrate the theoretical results.
We study distributed estimation of a high-dimensional static parameter vector through a group of sensors whose communication network is modeled by a fixed directed graph. Different from existing time-triggered communication schemes, an event-triggered asynchronous scheme is investigated in order to reduce communication while preserving estimation convergence. A distributed estimation algorithm with a single step size is first proposed based on an event-triggered communication scheme with a time-dependent decaying threshold. With the event-triggered scheme, each sensor sends its estimate to neighbor sensors only when the difference between the current estimate and the last sent-out estimate is larger than the triggering threshold. We prove that the proposed algorithm has mean-square and almost-sure convergence respectively, under an integrated condition of sensor network topology and sensor measurement matrices. The condition is satisfied if the topology is a balanced digraph containing a spanning tree and the system is collectively observable. Moreover, we provide estimates for the convergence rates, which are related to the step size as well as the triggering threshold. Furthermore, as an essential metric of sensor communication intensity in the event-triggered distributed algorithms, the communication rate is proved to decay to zero with a certain speed almost surely as time goes to infinity. We show that given the step size, adjusting the decay speed of the triggering threshold can lead to a tradeoff between the convergence rate of the estimation error and the decay speed of the communication rate. Specifically, increasing the decay speed of the threshold would make the communication rate decay faster, but reduce the convergence rate of the estimation error. Numerical simulations are provided to illustrate the developed results.
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