# Accession Number:

## AD0650641

# Title:

## LOWER ORDER LINEAR FILTERING AND PREDICTION OF NONSTATIONARY RANDOM SEQUENCES.

# Descriptive Note:

## Final rept.,

# Corporate Author:

## FRANK J SEILER RESEARCH LAB UNITED STATES AIR FORCE ACADEMY COLO

# Personal Author(s):

# Report Date:

## 1967-02-10

# Pagination or Media Count:

## 37.0

# Abstract:

The method of Kalman and Bucy for the optimal linear filtering and prediction of nonstationary sample functions has been modified by Bryson and Johansen. They do not require all measurements to contain white noise. The observations without white noise and some of their derivatives are used to reduce the order of the optimal filter. An analogous philosophy is applied here in the discrete time case. The purpose is to specify a lower order optimal filter, in the presence of measurements free of white noise. In a self-contained derivation, the optimal filter is shown to consist of a dynamical part in the form of a difference equation, and a direct algebraic feed-forward path parallel to it. The order of the dynamical part is n-p, where n is the combined number of state variables of the observed signal and noise processes, and p is the number of measurements without white noise. The parameters of the optimal filter are specified by a set of recurrence equations, similar to those of the discrete-time Kalman filter.

# Descriptors:

# Subject Categories:

- Theoretical Mathematics