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# Accession Number:

## AD0608944

# Title:

## INVARIANT IMBEDDING AND NONLINEAR FILTERING THEORY,

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CALIF

# Report Date:

## 1964-12-01

# Pagination or Media Count:

##
19.0

# Abstract:

## Suppose that a system is undergoing a process which we believe can be described by the differential equation dxdt gx, 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 xt - yt 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

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#