Accession Number:

ADA070439

Title:

Detection and MMSE Estimation of Nonlinear Memoryless Functionals of Random Processes Using the Volterra Functional Expansion,

Descriptive Note:

Corporate Author:

GENERAL ELECTRIC CO SYRACUSE N Y HEAVY MILITARY EQUIPMENT DEPT

Personal Author(s):

Report Date:

1979-05-01

Pagination or Media Count:

202.0

Abstract:

This report considers the general problem of detection and MMSE estimation of nonlinear memoryless functionals of random processes. In all cases considered, the observation process is assumed to be contaminated by additive Gaussian white noise. A Volterra functional expansion is derived for the likelihood ratio used in the detection of a nonlinear memoryless functional of a random process. This expansion is reduced to well known results for the special case of detection of a Gaussian process. For the case of detection of a nonlinear memoryless functional of a stationary Gaussian random process, it is shown that the likelihood ratio has an asymptotic form for which performance can be obtained provided the nonlinearities and processes satisfy Suns theorem. A Volterra functional expansion for MMSE estimation of a nonlinear memoryless functional of a random process using nonlinear observations is also derived. It is shown that, using linear observations, the Volterra expansion reduces to well known results for the case of MMSE estimation of a zero mean Gaussian process. A stochastic differential equation for the logarithm of the likelihood ratio is also derived to demonstrate agreement with known results. Author

Subject Categories:

  • Statistics and Probability
  • Active and Passive Radar Detection and Equipment

Distribution Statement:

APPROVED FOR PUBLIC RELEASE