State Estimation With an Energy Harvesting Sensor Over a Noisy Channel: A Gaussian Mixture Method

This paper investigates a remote state estimation problem with an energy harvesting sensor over an additive noise channel. An energy-based sensor scheduler results in the random intermittent measurements at the remote estimator. Due to the corruption of channel noises, the transmission indicator variables are unknown to the remote estimator. First, the conditional probability distributions of the sensor energy and the closed-form expression of the expected communication rate are given. Then, the exact minimum mean squared error (MMSE) state estimator is derived to be a Gaussian mixture filter with exponentially increasing components. Finally, an approximate MMSE estimator is proposed to reduce the computational complexity, in which the mixing coefficients of the Gaussian mixture filter is calculated numerically by the particle filtering method. Simulation results show the effectiveness of the exact MMSE estimator in Gaussian mixture form and the computational advantage of the approximate MMSE estimator.