Designing nonlinear filters based on Daum's theory

The purpose of this paper is to present a method for designing nonlinear filters based on work by Frederick £. Daum. The evolution of a probability density function on an interval between measurements can be described by the Fokker-Plank equation that, under certain conditions, can be written as the product of a scalar function and an exponential function. The parameters defining the latter satisfy coupled ordinary differential equations and can be updated. However, it is very difficult to obtain the mean and covariance at this stage in the development of the theory. A major theoretical result communicated in this paper is the derivation of sufficient conditions, stated in terms of the nonlinear function defining the dynamic system, under which a probability density function exists satisfying Da urn's conditions. This leads to algorithms for propagating the mean and covariance that generalize the Kalman-Bucy equations. A nonlinear filter for the exoatmospheric intercept of an intercontinental ballistic missile is given as an example.