Optimal state estimation over gaussian channels with noiseless feedback

This paper addresses an optimal state estimation problem in the presence of limited communication and noiseless feedback. In this setup, the state dynamics is estimated via an additive white Gaussian channel with input power constraint. We present a new communication and estimation strategy based on Kalman-Bucy filtering theory and water filling optimization algorithm. The optimality is established with respect to the minimal mean-square estimation error. As an example, we propose an analogue amplitude modulation scheme for state-estimation of a linear planar dynamics.