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In networked systems, state estimation is hampered by communication limits. Past approaches, which consider scheduling sensors through deterministic event-triggers, reduce communication and maintain estimation quality. However, these approaches destroy the Gaussian property of the state, making it computationally intractable to obtain an exact minimum mean squared error estimate. We propose a stochastic event-triggered sensor schedule for state estimation which preserves the Gaussianity of the system, extending previous results from the single-sensor to the multi-sensor case. © 2015 IEEE.

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 event-triggered sensor schedule, in a problem setting of target tracking, shows the superiority of the proposed sensor schedule.

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In this paper we consider the problem of infinite-horizon sensor scheduling for estimation in linear Gaussian systems. Due to possible channel capacity, energy budget or topological constraints, it is assumed that at each time step only a subset of the available sensors can be selected to send their observations to the fusion center, where the state of the system is estimated by means of a Kalman filter. Several important properties of the infinite-horizon schedules will be presented in this paper. In particular, we prove that the infinite-horizon average estimation error and the boundedness of a schedule are independent of the initial covariance matrix. We further provide a constructive proof that any feasible schedule with finite average estimation error can be arbitrarily approximated by a bounded periodic schedule. We later generalized our result to lossy networks. These theoretical results provide valuable insights and guidelines for the design of computationally efficient sensor scheduling policies. © 2014 Elsevier B.V. All rights reserved., SCOPUS: ar.j, info:eu-repo/semantics/published

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In this paper, we consider the problem of infinite-horizon sensor scheduling for estimation of a discrete-time linear Gaussian system, where the sensor information may be dropped during communication over a memoryless erasure channel, modeled as an independent Bernoulli process. We assume that due to energy or bandwidth constraints, the sensor can only maintain an average communication rate of r. The optimal communication schedule is thus chosen by the sensor to minimize the average estimation error of the receiver. We prove necessary and sufficient conditions for the feasibility of the optimization problem for two classes of protocols, one where deterministic acknowledgments are transmitted from the central location back to the sensor (ACK) and and the other where the acknowledgement structure is absent (No-ACK). We prove that for the No-ACK case, the optimal schedule can be approximated by a periodic schedule with arbitrarily close performance. For the ACK case, we provide the explicit optimal sensor schedule. A numerical example is provided to illustrate the effectiveness of the proposed strategy.

State estimation using wireless sensor networks (WSNs) is an important technique in many commercial and military applications, in which a group of (nonidentical) sensors take noisy observations of system state and send back to a fusion center through wireless broadcasting for state estimation. In order to minimize the terminal estimation error covariance at the fusion center, a partial broadcasting policy should tell which sensors to broadcast at each stage. The limited battery allows each sensor to broadcast only a few times. The limited wireless communication bandwidth allows only a few sensors to broadcast at the same time. Due to these couplings, the optimal partial broadcasting policy is not clear in general. Despite the abundant applications of partial broadcasting policies, theoretical analysis is rare. In this technical note, we provide a first study on the properties of optimal partial broadcasting policies. When there is no packet drop, a good-sensor-late-broadcast (GSLB) rule is shown to perform optimally for both the scalar system and the vector system. When packet drops with positive probability, situations in which the GSLB rule may or may not perform optimally are analyzed. Under different dropping rates, the GSLB rule is compared with several other policies through simulations.

This technical note concerns control applications over lossy data networks. Sensor data is transmitted to an estimation-control unit over a network and control commands are issued to subsystems over the same network. Sensor and control packets may be randomly lost according to a Bernoulli process. In this context, the discrete-time linear quadratic gaussian (LQG) optimal control problem is considered. In Schenato ,a complete analysis was carried out for the case that sensor measurements and control inputs are delivered into a single packet to the estimator and to the actuators respectively. Here, a nontrivial generalization for MIMO systems is presented under the assumption that each sensor and each actuator exchange data with the control unit in an independent way by using their own data packet (no aggregation). In such a framework, it is shown that the separation principle still holds in the case where packet arrivals are acknowledged by the receiver. Moreover, the optimal LQG control is a linear function of the state that explicitly depends on the loss probabilities of the actuator channels. Such a dependence is not present in the single channel case considered in mean-square. In the infinite horizon case, stability conditions on the packet arrival probabilities are provided in terms of linear matrix inequalities (LMIs)., SCOPUS: ar.j, info:eu-repo/semantics/published

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Distributed consensus and other linear systems with system stochastic matrices $W_k$ emerge in various settings, like opinion formation in social networks, rendezvous of robots, and distributed inference in sensor networks. The matrices $W_k$ are often random, due to, e.g., random packet dropouts in wireless sensor networks. Key in analyzing the performance of such systems is studying convergence of matrix products $W_kW_{k-1}... W_1$. In this paper, we find the exact exponential rate $I$ for the convergence in probability of the product of such matrices when time $k$ grows large, under the assumption that the $W_k$'s are symmetric and independent identically distributed in time. Further, for commonly used random models like with gossip and link failure, we show that the rate $I$ is found by solving a min-cut problem and, hence, easily computable. Finally, we apply our results to optimally allocate the sensors' transmission power in consensus+innovations distributed detection.

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We establish the large deviations asymptotic performance (error exponent) of consensus+innovations distributed detection over random networks with generic (non-Gaussian) sensor observations. At each time instant, sensors 1) combine theirs with the decision variables of their neighbors (consensus) and 2) assimilate their new observations (innovations). This paper shows for general non-Gaussian distributions that consensus+innovations distributed detection exhibits a phase transition behavior with respect to the network degree of connectivity. Above a threshold, distributed is as good as centralized, with the same optimal asymptotic detection performance, but, below the threshold, distributed detection is suboptimal with respect to centralized detection. We determine this threshold and quantify the performance loss below threshold. Finally, we show the dependence of the threshold and performance on the distribution of the observations: distributed detectors over the same random network, but with different observations' distributions, for example, Gaussian, Laplace, or quantized, may have different asymptotic performance, even when the corresponding centralized detectors have the same asymptotic performance., Comment: 30 pages, journal, submitted Nov 17, 2011; revised Apr 3, 2012

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