FINITE DIMENSIONAL SENSOR ORBITS AND OPTIMAL NONLINEAR FILTERING.
UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES DEPT OF AEROSPACE ENGINEERING
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The filtering problem of a system with linear dynamics and non-Guassian 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