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New results in linear filtering and prediction theory
 TRANS. ASME, SER. D, J. BASIC ENG
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
Abstract

Cited by 585 (0 self)
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A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary statistics. The variance equation is closely related to the Hamiltonian (canonical) differential equations of the calculus of variations. Analytic solutions are available in some cases. The significance of the variance equation is illustrated by examples which duplicate, simplify, or extend earlier results in this field. The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results. In several examples, the estimation problem and its dual are discussed sidebyside. Properties of the variance equation are of great interest in the theory of adaptive systems. Some aspects of this are considered briefly.
On Minimax Robustness: A General Approach and Applications
, 1984
"... The minimax approach to the design of systems that are robust with respect to modeling uncertainties is studied using a game theoretic formulation in which the peiformance functional and the sets of modeling uncertainties and admissible design policies are arbitrary. The existence and characterizati ..."
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Cited by 45 (1 self)
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The minimax approach to the design of systems that are robust with respect to modeling uncertainties is studied using a game theoretic formulation in which the peiformance functional and the sets of modeling uncertainties and admissible design policies are arbitrary. The existence and characterization of minimax robust solutions that form saddle points are discussed through various methods that take into account several common features of the games encountered in applications. In particular, it is shown that if the performance functional and the uncertainty set are convex then a certain type of regularity condition on the functional is sufficient to ensure that the optimal strategy for a least favorable element of the uncertainly set is minimax robust. The efficacy of the methods proposed for a general game is tested in the problems of matched filtering, Wiener filtering, quadratic detection, and output energy filtering, in which uncertainties in their respective signal and noise models are assumed to exist. These problems are analyzed in a common Hilbert