Power allocation for error covariance minimization in Kalman filtering over packet dropping links

This paper studies the problem of optimal power allocation for Kalman filtering with random packet losses. We consider the problem of minimizing the trace of the expected error covariance subject to an average transmit power constraint. Adopting a model for the packet loss probabilities that depends on both the sensor transmit power and time-varying fading channel gain, the problem is formulated as a constrained Markov decision process (MDP) that is solved numerically with dynamic programming techniques. Simpler suboptimal power allocation policies, namely a constant power allocation scheme and a truncated channel inversion scheme, are also considered and numerical comparisons made with the optimal policy.