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Set-values filtering and smoothing

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2 Author(s)
Morrell, D.R. ; Dept. of Electr. & Comput. Eng., Arizona State Univ., Tempe, AZ, USA ; Stirling, W.C.

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

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Systems, Man and Cybernetics, IEEE Transactions on  (Volume:21 ,  Issue: 1 )