On recurrent filtering with mutually correlated noises of the plant and the meter

The paper is concerned with a linearly quadratic Gaussian problem of optimal linear filtering with mutual correlation of noises of the plant and the meter. An algorithm is developed for estimating the plant state from the results of current measurements. The properties of the algorithm are described as is its relation to the algorithm of filtering with uncorrected noises. The ill-posed nature of the earlier derivations of a similar algorithm is noted.