On the estimation of correlated noise statistics in a class of 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 parameters describing the model are known except for the state which has to be estimated. In this paper we consider the case when the measurement and observations noise sequences are correlated. A method to estimate the correlation of this noise sequences is introduced. Illustrative examples are presented where we show the benefits of estimating the correlation between the noises at an affordable computational cost.