
Accession Number : AD0695414
Title : VELOCITY ESTIMATION OF A MOVING FUNCTION USING STOCHASTIC APPROXIMATION,
Corporate Author : COLUMBIA UNIV DOBBS FERRY N Y HUDSON LABS
Personal Author(s) : Gershman,Russell J.
Report Date : APR 1969
Pagination or Media Count : 29
Abstract : There is a class of estimation problems that is not solvable by ordinary means. Consider a function which has a constant velocity with respect to some coordinate system. Assume further that observations of this function are made sequentially and include an additive noise component. If the velocity is known and certain assumptions are placed on the noise, the function can be estimated to any desired accuracy by statistically averaging superimposed versions of the observed functions. If the velocity is unknown, no such simple solution exists. Using the theory of stochastic approximation, this report describes a method which, under certain conditions, can estimate the velocity. Assuming the correlation function of the noise is known and making certain regularity assumptions on the nature of the function, it is shown that the true value of the velocity can be estimated with probability 1 as the number of iterations m approaches infinity, where m is directly proportional to the number of observations. Furthermore, the estimation error in the velocity is shown to be asymptotically normal with a variance that approaches 0 as m approaches infinity. (Author)
Descriptors : (*INFORMATION THEORY, VELOCITY), (*STOCHASTIC PROCESSES, APPROXIMATION(MATHEMATICS)), (*SONAR SIGNALS, *RANGE FINDING), RADAR SIGNALS, REGRESSION ANALYSIS, DECISION THEORY, THEOREMS
Subject Categories : Cybernetics
Acoustic Detection and Detectors
Distribution Statement : APPROVED FOR PUBLIC RELEASE