# Accession Number:

## AD0649259

# Title:

## ON OPTIMAL LINEAR SMOOTHING THEORY

# Descriptive Note:

# Corporate Author:

## NORTHWESTERN UNIV EVANSTON IL INFORMATION-PROCESSING AND CONTROL SYSTEMS LAB

# Personal Author(s):

# Report Date:

## 1967-03-01

# Pagination or Media Count:

## 29.0

# Abstract:

The algorithm for generating the smoothed estimate xtt T of the state xt of a continuous linear system, where t is continuous time, T is a positive real constant, and t T is the time of the most recent measurement, is developed. A linear matrix differential equation whose solution gives the covariance matrix of the smoothing error xtt Txtt T is then derived. Computational aspects involved in mechanizing the algorithm are discussed in terms of the algorithms dependence on the solution of the prediction, filtering, and fixed-point smoothing problems. The results are then discussed in terms of the classical Wiener smoothing problem.

# Descriptors:

# Subject Categories:

- Theoretical Mathematics