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

摘要

This paper presents a design methodology for optimal transmission energyallocation at a sensor equipped with energy harvesting technology for remotestate estimation of linear stochastic dynamical systems. In this framework, thesensor measurements as noisy versions of the system states are sent to thereceiver over a packet dropping communication channel. The packet dropoutprobabilities of the channel depend on both the sensor's transmission energiesand time varying wireless fading channel gains. The sensor has access to anenergy harvesting source which is an everlasting but unreliable energy sourcecompared to conventional batteries with fixed energy storages. The receiverperforms optimal state estimation with random packet dropouts to minimize theestimation error covariances based on received measurements. The receiver alsosends packet receipt acknowledgments to the sensor via an erroneous feedbackcommunication channel which is itself packet dropping. The objective is to design optimal transmission energy allocation at theenergy harvesting sensor to minimize either a finite-time horizon sum or a longterm average (infinite-time horizon) of the trace of the expected estimationerror covariance of the receiver's Kalman filter. These problems are formulatedas Markov decision processes with imperfect state information. The optimaltransmission energy allocation policies are obtained by the use of dynamicprogramming techniques. Using the concept of submodularity, the structure ofthe optimal transmission energy policies are studied. Suboptimal solutions arealso discussed which are far less computationally intensive than optimalsolutions. Numerical simulation results are presented illustrating theperformance of the energy allocation algorithms.