
Accession Number : AD0289607
Title : ESTIMATION OF THE SECONDORDER STATISTICS OF RANDOMLY TIMEVARYING LINEAR SYSTEMS
Corporate Author : MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB
Personal Author(s) : LEVIN,MORRIS J.
Report Date : 02 NOV 1962
Pagination or Media Count : 1
Abstract : This analysis considers the estimation of the secondorder statistical characteristics of a randomly timevarying 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 f(tau lambda) and is approxim ted by a sampleddata model. It is shown that the estimation of the sampled values of f(tau 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 signaltonoise 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 CramerRao lower bound. Both the lowpass and bandpass situations are discussed. Specific results for a periodic rectangular pulse input and pseudorandom input are given. (Author)
Descriptors : *COMMUNICATION THEORY, *LINEAR SYSTEMS, *STATISTICAL ANALYSIS, *STATISTICAL FUNCTIONS, *TIME SIGNALS, DATA, LEAST SQUARES METHOD, MATRICES(MATHEMATICS), PROBABILITY, REAL VARIABLES, SAMPLING, SEQUENCES(MATHEMATICS), SIGNALTONOISE RATIC, VECTOR ANALYSIS
Distribution Statement : APPROVED FOR PUBLIC RELEASE