
Accession Number : AD0691855
Title : FINITE DIMENSIONAL SENSOR ORBITS AND OPTIMAL NONLINEAR FILTERING.
Descriptive Note : Doctoral thesis,
Corporate Author : UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES DEPT OF AEROSPACE ENGINEERING
Personal Author(s) : Lo,James TingHo
Report Date : AUG 1969
Pagination or Media Count : 61
Abstract : The filtering problem of a system with linear dynamics and nonGuassian a priori distribution is throughly investigated. The conditional probability density, conditional mean and conditional error covariance for this class of nonlinear problem are obtained in terms of an ordinary integral which is analogous to the solution of a heat flow problem of an infinitely long, homogeneous rod with a certain initial heat distribution. An approximation made in the construction of a mathematical model is introduced. It renders the optimal estimation to a combination of linear estimations and thus gives satisfactory filtering in practice. The asymtotic behavior of the filter is examined. The limiting distributions of the conditional mean and the conditional error covariance exist as the time interval of observation becomes infinite. In the autonomous case, the estimate for the Wiener problem satisfies a linear stochastic differential equation. A large class of nonlinear problems with more nonlinear features than the one discussed above can be reduced to it through the idea of finite dimensional sensor orbit. The general idea and a number of examples are discussed briefly. (Author)
Descriptors : (*INFORMATION THEORY, NONLINEAR SYSTEMS), ELECTRIC FILTERS, CONDUCTION(HEAT TRANSFER), ANALYSIS OF VARIANCE, DIFFERENTIAL EQUATIONS, HILBERT SPACE, PROBABILITY DENSITY FUNCTIONS, STOCHASTIC PROCESSES, THEOREMS, THESES
Subject Categories : Cybernetics
Distribution Statement : APPROVED FOR PUBLIC RELEASE