Optimal Energy Allocation for Kalman Filtering over Packet Dropping Links with Energy Harvesting Constraints

This paper studies the problem of optimal transmission energy allocation for error covariance minimization in Kalman filtering with random packet losses for sensors with energy harvesting capabilities. The energy harvesters provide an everlasting but unreliable energy source compared to conventional batteries with fixed energy storages. The packet loss probabilities of the Kalman filtering depend on both the sensor transmission energy and time varying wireless fading channel gains. We minimize either a finite horizon sum or the long term average (infinite horizon) of the trace of the expected error covariance of the Kalman filter subject to energy harvesting constraints. The resulting Markov decision process problems with constraints are approached using the dynamic programming principle for both causal and non-causal system information. Using the concept of submodularity, the structure of the optimal transmission energy policy is studied. Numerical simulation results are presented illustrating the performance of the energy allocation algorithms.