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We consider a networked control system where information is transmitted over lossy communication channels on both the uplink (sensor to controller) and downlink (controller to actuator). At each time instant, only one out of M different channels can be chosen for transmission. The statistics of the channels are unknown and must be learnt by observing transmission outcomes. We model this scenario as a multi-armed bandit type problem and investigate the use of Thompson sampling for carrying out this learning while simultaneously controlling the system. We derive necessary and sufficient conditions for stability of the controlled system. In addition, the notion of (accumulated) control regret is introduced and shown to scale logarithmically with time. Numerical comparisons show that Thompson sampling outperforms other channel selection methods such as periodic sampling and decaying ɛ -greedy. [ABSTRACT FROM AUTHOR]

Summary: 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 article, 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. [ABSTRACT FROM AUTHOR]

This paper studies a remote state estimation problem where a sensor, equipped with energy harvesting capabilities, observes a dynamical process and transmits local state estimates over a packet dropping channel to a remote estimator. The objective is to decide, at every discrete time instant, whether the sensor should transmit or not, in order to minimize the expected estimation error covariance at the remote estimator over a finite horizon, subject to constraints on the sensor’s battery energy governed by an energy harvesting process. We establish structural results on the optimal scheduling which show that, for a given battery energy level and a given harvested energy, the optimal policy is a threshold policy on the error covariance. Similarly, for a given error covariance and a given harvested energy, the optimal policy is a threshold policy on the current battery level. An extension to the problem of transmission scheduling and control with an energy harvesting sensor is also considered. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the performance of distributed estimation schemes in a wireless sensor network in the presence of an eavesdropper. The sensors transmit observations to the fusion center (FC), which at the same time are overheard by the eavesdropper. Both the FC and the eavesdropper reconstruct a minimum mean-squared error estimate of the physical quantity observed. We address the problem of transmit power allocation for system performance optimization subject to a total average power constraint on the sensor(s), and a security/secrecy constraint on the eavesdropper. We mainly focus on two scenarios: 1) a single sensor with multiple transmit antennas and 2) multiple sensors with each sensor having a single transmit antenna. For each scenario, given perfect channel state information (CSI) of the FC and full or partial CSI of the eavesdropper, we derive the transmission policies for short-term and long-term cases. For the long-term power allocation case, when the sensor is equipped with multiple antennas, we can achieve zero information leakage in the full CSI case, and dramatically enhance the system performance by deploying the artificial noise technique for the partial CSI case. Asymptotic expressions are derived for the long-term distortion at the FC as the number of sensors or the number of antennas becomes large. In addition, we also consider multiple-sensor multiple-antenna scenario, and simulations show that given the same total number of transmitting antennas the multiple-antenna sensor network is superior to the performance of the multiple-sensor single-antenna network. [ABSTRACT FROM PUBLISHER]

• Develop field estimation algorithms which use binary measurements. • Active sensing to allow agents to adaptively choose location of next measurement. • Consider centralized and decentralized multi-agent setups. In this paper we consider the problem of field estimation using binary sensor measurements. A number of agents are equipped with sensors which can make binary measurements of the field. The agents are mobile and can move around to different locations to collect measurements. In estimating the field, we model the field as a sum of radial basis functions, whose parameters are then estimated using sequential Monte Carlo techniques. We incorporate an active sensing mechanism for the agents to adaptively choose their next measurement location, given the information currently collected. In the multi-agent case, we consider both a centralized setup, and a decentralized setup where agents share their past measurements with each other provided they are within communication range. Simulation studies illustrate the performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the distortion outage performance of distributed estimation schemes in wireless sensor networks, where a distortion outage is defined as the event that the estimation error or distortion exceeds a predetermined threshold. The sensors transmit their observation signals using the analog amplify and forward scheme through coherent multiaccess channels to the fusion center, which reconstructs a minimum mean squared error (MMSE) estimate of the physical quantity observed. We consider three power allocation schemes: 1) equal power allocation (EPA); 2) short-term optimal power allocation (ST-OPA), where we minimize the distortion subject to a power constraint at each time step; and 3) long-term optimal power allocation (LT-OPA), where we minimize the distortion outage probability subject to a long-term average power constraint. We study their diversity orders of distortion outage in terms of increasing numbers of sensors, and show that under Rayleigh fading EPA and ST-OPA achieve the same diversity order of N\log N, where N is the number of sensors. This suggests that in the case of a large number of sensors, the spatial diversity gain in EPA can overcome fading equally well as in ST-OPA. On the other hand, in LT-OPA, we find that for N>1 the outage probability can be driven to zero with a finite amount of total power. [ABSTRACT FROM AUTHOR]

This paper is concerned with decentralized estimation of a Gaussian source using multiple sensors. We consider a diversity scheme where only the sensor with the best channel sends their measurements over a fading channel to a fusion center, using the analog amplify and forwarding technique. The fusion centre reconstructs a minimum mean squared error (MMSE) estimate of the source based on the received measurements. A distributed version of the diversity scheme where sensors decide whether to transmit based only on their local channel information is also considered. We derive asymptotic expressions for the expected distortion (of the MMSE estimate at the fusion centre) of these schemes as the number of sensors becomes large. For comparison, asymptotic expressions for the expected distortion for a coherent multiaccess scheme and an orthogonal access scheme are derived. It is seen that as opposed to the coherent multiaccess scheme and the orthogonal scheme (where the expected distortion decays as 1/M, M being the number of sensors), the expected distortion decays only as 1/\ln(M) for the diversity schemes. This reduction of the decay rate can be seen as a tradeoff between the simplicity of the diversity schemes and the strict synchronization and large bandwidth requirements for the coherent multiaccess and the orthogonal schemes, respectively. We study for the diversity schemes, the optimal power allocation for minimizing the expected distortion subject to average power constraints. The effect of optimizing the probability of transmission on the expected distortion in the distributed scenario is also studied. It is proved that for Rayleigh fading optimal sensor transmit power allocation achieves the same asymptotic scaling law as the constant power allocation scheme, whereas it is observed that optimizing the sensor transmission probability (with or without optimal power allocation) in the distributed case makes very little difference to the asymptotic scaling laws. [ABSTRACT FROM AUTHOR]

This paper studies the outage probability minimization problem for state estimation of linear dynamical systems using multiple sensors, where an estimation outage is defined as an event when the state estimation error exceeds a pre-determined threshold. The sensors amplify-and-forward their measurements (using uncoded analog transmission) to a remote fusion center over wireless fading channels. For stable systems, the resulting infinite horizon problem can be formulated as a constrained average cost Markov decision process (MDP) control problem. A suboptimal power allocation that is less computationally intensive is proposed and numerical results demonstrate very close performance to the power allocation obtained from the solution of the MDP based average cost optimality equation. Motivated by practical considerations, assuming that sensors can transmit with only a finite number of power levels, optimization of the values of these levels is also considered using a stochastic approximation technique. In the case of unstable systems, a finite horizon formulation of the estimation outage minization problem is presented and solved. An extension to the problem of minimization of the expected error covariance is also studied. [ABSTRACT FROM PUBLISHER]

Abstract: This paper considers a sensor network where single or multiple sensors amplify and forward their measurements of a common linear dynamical system (analog uncoded transmission) to a remote fusion center via noisy fading wireless channels. We show that the expected error covariance (with respect to the fading process) of the time-varying Kalman filter is bounded and converges to a steady state value, based on some earlier results on asymptotic stability of Kalman filters with random parameters. More importantly, we provide explicit expressions for sequences which can be used as upper bounds on the expected error covariance, for specific instances of fading distributions and scalar measurements (per sensor). Numerical results illustrate the effectiveness of these bounds. [Copyright &y& Elsevier]

This correspondence studies the performance of Kalman fixed lag smoothers with random packet losses and its comparison with the Kalman filter with packet loss. In terms of estimator stability via boundedness of the expectation of the error covariance, we show that smoothing does not provide any benefit over filtering. On the other hand, it is demonstrated that using a probabilistic notion of performance, smoothing can provide significant gains when compared to Kalman filtering. An analysis of Kalman filtering using two simple retransmission schemes and its comparison with Kalman smoothing is also made. [ABSTRACT FROM AUTHOR]

A numerical method for computing the error exponent for Neyman-Pearson detection of two-state Markov chains in noise is presented, for both time-invariant and fading channels. We give numerical studies showing the behavior of the error exponent as the transition parameters of the Markov chain and the signal-to-noise ratio (SNR) are varied. Comparisons between the high-SNR asymptotics in Gaussian noise for the time-invariant and fading situations will also be made. [ABSTRACT FROM AUTHOR]

This paper studies the probability of error for maximum a posteriori (MAP) estimation of hidden Markov models, where measurements can be either lost or received according to an- other Markov process. Analytical expressions for the error prob- abilities are derived for the noiseless and noisy cases. Some relationships between the error probability and the parameters of the loss process are demonstated via both analysis and numerical resuIts. In the high signal-to-noise ratio (SNR) regime, approximate expressions which can be more easily computed than the exact analytical form for the noisy case are presented. [ABSTRACT FROM AUTHOR]

In many cyber–physical systems, we encounter the problem of remote state estimation of geographically distributed and remote physical processes. This paper studies the scheduling of sensor transmissions to estimate the states of multiple remote, dynamic processes. Information from the different sensors has to be transmitted to a central gateway over a wireless network for monitoring purposes, where typically fewer wireless channels are available than there are processes to be monitored. For effective estimation at the gateway, the sensors need to be scheduled appropriately, i.e., at each time instant one needs to decide which sensors have network access and which ones do not. To address this scheduling problem, we formulate an associated Markov decision process (MDP). This MDP is then solved using a Deep Q-Network, a recent deep reinforcement learning algorithm that is at once scalable and model-free. We compare our scheduling algorithm to popular scheduling algorithms such as round-robin and reduced-waiting-time, among others. Our algorithm is shown to significantly outperform these algorithms for many example scenarios. [ABSTRACT FROM AUTHOR]

Multi-Gas source localization and mapping is a challenging problem because multiple measurements must be taken to ensure accurate localization. This paper presents a novel flocking control strategy for multi-robot exploration and gas field mapping to address this problem. The algorithm includes an active sensing mechanism for driving a flock of agents towards target measurement locations that optimize the posterior probability density and a collaborative sequential Monte Carlo information fusion approach for estimating gas fields. We tested the performance of our system on Jackal mobile robots in a chemical leak scenario with two gas leakage sources. Through a series of comparison experiments, we demonstrate that our proposed strategy has superior performance to recent single-agent and centralized sequential Monte Carlo-based gas concentration mapping in terms of the estimate accuracy, the convergence time, and the mapping error. • Present a collaborative Sequential Monte Carlo method for estimating gas fields. • Propose a flocking model to keep the robots close enough to avoid disconnections. • Include an active sensing method for moving a robot swarm towards measurement locations. • Construct an evaluation of our algorithm in a setting with multiple leakage plumes. • Conduct a comparative study benchmarking our algorithm against other strategies. [ABSTRACT FROM AUTHOR]

State estimation of linear systems using analog amplify and forwarding with multiple sensors, for both multiple access and orthogonal access schemes is considered. Optimal state estimation can be achieved at the fusion center using a time-varying Kalman filter. We show that in many situations, the estimation error covariance decays at a rate of 1/M when the number of sensors M is large. We consider optimal allocation of transmission powers that 1) minimizes the sum power usage subject to an error covariance constraint, and 2) minimizes the error covariance subject to a sum power constraint. In the case of fading channels with channel-state information, the optimization problems are solved using a greedy approach, while for fading channels without channel state information (CSI) but with channel statistics available, a suboptimal linear estimator is derived. [ABSTRACT FROM AUTHOR]

Abstract: We study stochastic stability of centralized Kalman filtering for linear time-varying systems equipped with wireless sensors. Transmission is over fading channels where variable channel gains are counteracted by power control to alleviate the effects of packet drops. We establish sufficient conditions for the expected value of the Kalman filter covariance matrix to be exponentially bounded in norm. The conditions obtained are then used to formulate stabilizing power control policies which minimize the total sensor power budget. In deriving the optimal power control laws, both statistical channel information and full channel information are considered. The effect of system instability on the power budget is also investigated for both these cases. [Copyright &y& Elsevier]

In remote state estimation, data transmitted by a sensor through a wireless communication channel may be overheard by an eavesdropper. One possible way to avoid information leakage is to encrypt the transmitted data all the time. However, this may impose an extra operation energy burden on the sensor. In this paper, we investigate the optimal encryption scheduling in order to protect data privacy and ensure estimation accuracy under an energy constraint. Specifically, the sensor computes its local state estimate and then quantizes it using a non-subtractively dithered quantizer. Before each transmission, the sensor determines whether encrypting the data or not in order to strike a balance between data privacy and estimation accuracy. As the information about eavesdropper is unknown to the estimator, we introduce the concept of eavesdropper-invariant schedules and derive associated structural results. In addition, we propose a practical algorithm that compares a finite number of points to obtain an ε -optimal encryption schedule. Numerical examples are provided to illustrate performance benefits of the proposed methods. [ABSTRACT FROM AUTHOR]