Stratonovich nonlinear optimal and quasi-optimal filters

A new classification of nonlinear optimal filters is proposed based on the Stratonovich equations. The classification is more adequate to the history of the development of nonlinear optimal filtering than the existing classification. Vector-matrix forms of the Stratonovich nonlinear filters of the first and second orders are derived. Particular cases of such filters (e.g., Kalman-Bucy filter) are considered.