This paper studies the outage minimization problem for state estimation of linear dynamical systems using multiple sensors. The sensors amplify and forward their measurements to a remote fusion center over wireless fading channels. For stable systems, the resulting infinite horizon problem is a constrained Markov decision process (MDP). A suboptimal power allocation that is less computationally intensive is proposed, and numerical results demonstrate very close performance to the power

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... n obtained from the solution of the MDP. Motivated by practical considerations, assuming that sensors can transmit only a finite number of power levels, optimization of the values of these levels is also considered. In the case of unstable systems, finite horizon and discounted cost formulations of the outage minization problem are presented and solved. An extension to the problem of minimization of expected error covariance is also studied. DRAFT 2 delay constrained outage capacity problem in [3] , and the notion of service outage in [4] . In the signal processing literature, the notions of estimation outage and detection outage for the distributed estimation and detection of i.i.d. sources was introduced recently in [5] and [6] respectively. The estimation outage minimization problem, in the estimation of an i.i.d. Gaussian source, has been solved in [7] . In much of these previous works, the systems that have been studied have been memoryless, so that how the resources are allocated at one time instant does not necessarily affect the evolution of the system at future times. The focus of this paper is on extending the notions of estimation outage, and solving the outage minimization problem, for dynamical systems. In particular we consider state estimation of linear dynamical system using multiple sensors, where the sensors transmit their measurements to a fusion center over wireless channels using the analog amplify and forward technique of [8], which is a scheme that has been shown to be optimal in certain distributed estimation scenarios [9] . An outage will be defined as the event that the estimation error covariance exceeds a given threshold, and we are interested in how to optimally allocate the transmit powers of the sensors in order to minimize the probability of outage, subject to an average sum power constraint. We will use Markov decision process (MDP) and dynamic programming techniques to numerically solve these problems. Dynamic programming techniques have also been used in solving related problems such as the delay constrained outage capacity problem in [3], and estimation error minimization problems for hidden Markov model state estimation in [10], [11] . Another area related to this paper is the analysis of the performance of Kalman filtering with packet losses, under different notions of performance such as the expected error covariance [12], [13] and a probabilistic notion of performance [14] , [15] . For continuous fading channels, the behaviour of the expected error covariance has also been studied in [16] , [17] . However, the focus of these works is more on determining conditions under which the filter remains stable, and power control is not explicitly considered. Summary of Contributions This paper is concerned with solving the estimation outage minimization problem, in the state estimation of linear dynamical systems. In particular, we make the following contributions: • In the case of stable systems, we formulate the outage minimization problem over an infinite horizon. This will turn out to be a constrained average cost Markov decision process (MDP) [18] , which we can transform using a Lagrangian technique into an unconstrained MDP, that can then be solved numerically with standard techniques such as the relative value iteration algorithm. • In the case of unstable systems, an infinite horizon average cost problem formulation is not appropriate since increasingly large amounts of power will need to be transmitted. Instead we study both DRAFT