On linear filtering under dependent white noises
Agamirza E. Bashirov, L. R. Mishné · Stochastics and stochastics reports · 1991
Two linear filtering problems with dependent Gaussian white noises on the signal and observation processes are considered. The dependence of the noises is modelled as a point delay of one of the noises with respect to the other. In the first problem the observation noise anticipates the signal noise and in the second problem it delays. In both problems the values of the delays are functions of time. It is proved that the optimal filters in both problems are of Kalman type. Formulas realizing these filters are obtained