On the estimation of state matrix and noise statistics in state-space models

State-space models have been extensively used in various applications. When the linearity of the system and the Gaussianity of the noise are assumed, this type of models lead to the implementation of Kalman filter in order to estimate the state. The optimality of the Kalman filter is based on the fact that all the quantities describing the model are known except for the state which has to be estimated. In this paper we investigate the estimation of several important quantities involved in Kalman filter recursions. The proposed techniques are investigated in both toy and communications-type of scenarios.