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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]

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]

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]