Power Allocation for Outage Minimization in State Estimation Over Fading Channels

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.