Optimal filtering in systems with degenerate noises in observations (Q1882162)

The paper is devoted to the filtering problem for linear stochastic differential systems with degenerate noises in the observations. The implicit value for the filtering estimate can be obtained as a limit in the mean-square sense of a sequence of certain regularized estimates of the Kalman filter. The aim of the author is to construct optimal filtering estimates for the class of observation systems with piecewise constant coefficients. He proposes a special differential transformation for the initial observations. The initial and transformed observations are equivalent in the sense that the respective \(\sigma\)-algebras coincide and the transformation order is not greater than the order of the initial system. The optimal filtering estimate is expressed as the solution of some stochastic differential equation with measure.