VELOCITY ESTIMATION OF A MOVING FUNCTION USING STOCHASTIC APPROXIMATION,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1969
- Accession Number
- AD0695414
Entities
People
- Russell J. Gershman
Organizations
- Columbia University