Forgetting factor Kalman filter with dependent noise processes

The paper addresses the problem of filtering
the state of a normal dynamical process with a dependency between the process and the measurement noise variables in the presence of an inaccurate model description. As regards the time occurrence of the noise dependency, we discuss the dependency structure where both the variables are correlated at the same time. An adaptive formulation of the Kalman filter (KF) is designed in order to mitigate the impact of the process model uncertainty on the degradation of the filter performance. The filter we propose exploits the collaborative decision to introduce a variable forgetting factor into the time update to reduce artificially the effect of obsolete knowledge on the filtering solution. Within the decision-making rules, a loss functional quantifying the time update is constructed to optimally combine the prediction alternatives possessing the form of the normal probability density function (pdf). The result is an adjustment of the Kalman gain matrix in response to empirically confirmed performance.