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Linear Observations (linear + observation)
Selected AbstractsOptimal filtering for incompletely measured polynomial states over linear observationsINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 5 2008Michael Basin Abstract In this paper, the optimal filtering problem for polynomial system states over linear observations with an arbitrary, not necessarily invertible, observation matrix is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. A transformation of the observation equation is introduced to reduce the original problem to the previously solved one with an invertible observation matrix. The procedure for obtaining a closed system of the filtering equations for any polynomial state over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular case of a third-order state equation. In the example, performance of the designed optimal filter is verified against a conventional extended Kalman,Bucy filter. Copyright © 2007 John Wiley & Sons, Ltd. [source] Optimal filtering for polynomial system states with polynomial multiplicative noiseINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2006Michael Basin Abstract In this paper, the optimal filtering problem for polynomial system states with polynomial multiplicative noise over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for any polynomial state with polynomial multiplicative noise over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular cases of a linear state equation with linear multiplicative noise and a bilinear state equation with bilinear multiplicative noise. In the example, performance of the designed optimal filter is verified for a quadratic state with a quadratic multiplicative noise over linear observations against the optimal filter for a quadratic state with a state-independent noise and a conventional extended Kalman,Bucy filter. Copyright © 2006 John Wiley & Sons, Ltd. [source] Optimal state filtering and parameter identification for linear systemsOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 2 2008Michael Basin Abstract This paper presents the optimal filtering and parameter identification problem for linear stochastic systems with unknown multiplicative and additive parameters over linear observations, where unknown parameters are considered Wiener processes. The original problem is reduced to the filtering problem for an extended state vector that incorporates parameters as additional states. The obtained optimal filter for the extended state vector also serves as the optimal identifier for the unknown parameters. Performance of the designed optimal state filter and parameter identifier is verified for both stable and unstable linear uncertain systems. Copyright © 2007 John Wiley & Sons, Ltd. [source] | ||||||||||