Time Series Analysis and Nonlinear Filtering.
GRUMMAN AEROSPACE CORP BETHPAGE N Y RESEARCH DEPT
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The identification of the parameters of a linear differential equation model for a system operating in a random noisy environment is one of the practical problems that must be overcome before extensive use of optimal control theory is possible. This problem arises in such diverse areas as aircraft control where stability derivatives are required and in the reduction of data for ships operating in a random sea. Motivated by these problems, in this memorandum the author describes a rpomising approach to the identification of the parameters that uses nonlinear filtering theory. Two approximations to nonlinear filters have been tried, one of which gives very good estimates of the unknown parameters. Further, a new third moment filter is described that, while it is not yet tested, offers great promise. Some statistical tests are also described that show when the estimates have converged, and results of numerical experiments are presented. Author
- Statistics and Probability