# Accession Number:

## AD0289607

# Title:

## ESTIMATION OF THE SECOND-ORDER STATISTICS OF RANDOMLY TIME-VARYING LINEAR SYSTEMS

# Descriptive Note:

# Corporate Author:

## MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB

# Personal Author(s):

# Report Date:

## 1962-11-02

# Pagination or Media Count:

## 1.0

# Abstract:

This analysis considers the estimation of the second-order statistical characteristics of a randomly time-varying linear system by application of a known input signal and observation of the resulting output which may be obscured by additive white noise. The system is characterized by its impulse response correlation function ftau lambda and is approxim ted by a sampled-data model. It is shown that the estimation of the sampled values of ftau lambda is equivalent to the estimation of the parameters of the covariance matrix of a vector random variable. A least squares method is introduced which provides explicit estimates for these values in terms of the sampled input and output sequences. It is shown that these least squares estimates are unbiased and consistent under general conditions. For Gaussian noise and coherent nondetectability conditions low input signal-tonoise ratio the least squares estimates are a close approximation to the maximum likelihood estimates. The covariance matrix of the estimates is evaluated for this case and is found to be the same as that given by the Cramer-Rao lower bound. Both the low-pass and band-pass situations are discussed. Specific results for a periodic rectangular pulse input and pseudo-random input are given. Author