estimation theory, filtering and prediction theory, matrix algebra, probability, set theory, state estimation
A theory of discrete-time optimal filtering and smoothing based on convex sets of probability distributions is presented. Rather than propagating a single conditional distribution as does conventional Bayesian estimation, a convex set of conditional distributions is evolved. For linear Gaussian systems, the convex set can be generated by a set of Gaussian distributions with equal covariance with means in a convex region of state space. The conventional point-valued Kalman filter is generated to a set-valued Kalman filter consisting of equations of evolution of a convex set of conditional means and a conditional covariance. The resulting estimator is an exact solution to the problem of running an infinity of Kalman filters and fixed-interval smoothers, each with different initial conditions. An application is presented to illustrate and interpret the estimator results.
Original Publication Citation
Morrell, D. R., and W. C. Stirling. "Set-Values Filtering and Smoothing." Systems, Man and Cybernetics, IEEE Transactions on 21.1 (1991): 184-93
BYU ScholarsArchive Citation
Stirling, Wynn C. and Morrell, Darryl, "Set-valued Filtering And Smoothing" (1991). Faculty Publications. 725.
Ira A. Fulton College of Engineering and Technology
Electrical and Computer Engineering
© 1991 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Copyright Use Information