Concerning optimal filtering theory of linear distributed-parameter systems

摘要

The optimal filter of Kalman is derived for a general class of linear distributed-parameter systems with Gaussian disturbances and measurement noise. The concept of characteristic functional, which fully describes a distributed infinite-dimensional random variable, is used. The input disturbance and the measurement noise are assumed to be white in time, but they are allowed to have any correlation in space. A numerical example illustrates the theory.