Invariant Imbedding and Nonlinear Filtering Theory

Abstract

Abstract : Suppose that a system is undergoing a process which we believe can be described by the differential equation dx/dt= g(x, t). On the time interval (0, T) we observe the function x, in a noisy manner, and denote this experimental function by the symbol y. We wish to determine the state of the system at time t = T which is such that J is minimized, where J = the integral with respect to dt, from 0 to T, of (x(t) - y(t)) to the second power. Many problems of orbit determination and adaptive control are of this type. A solution is suggested in both the scalar and vector cases, which makes use of certain ideas from the theory of invariant imbedding, and some numerical examples are provided. (Author)