Abstract: Nonlinear filters in the framework of recursive Baycsian estimation were classified. These filters were divided into three categories based on their designed ideas. These categories include nonlinear filters based on functions’approximation or transform and nonlinear filters based on moments' approximation and nonlinear filters based on conditional posterior probability density function's approximation. At the same time, common properties and special properties among the linear regression Kalman filter and divided difference 2 Kalman filter and unscented Kalman filter and Gauss-Hermite filter were discussed in detail. Deficiencies of filters' synthesis which is used to design new nonlinear filters were indicated. Sufficiency of designed ideas in nonlinear filters was analyzed, and deficiencies in some designed ideas were detected. Potential breakthrough directions in nonlinear filters were specified.

Key words: Recursive bayesian estimation, Nonlinear filter, Classification, Sufficiency