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Bemerkungen zu den Riccati-Gleichungen beim Entwurf von Kalman-Filtern. (Comments on the Riccati equations for Kalman filter design). (German) Zbl 0693.93079

Summary: In control as well as in communications theory Kalman filters are used to obtain linear unbiased minimum-variance state estimates from noisy measurements. Based on the so-called “covariance propagation equations” for linear stochastic systems, the existing derivations for the filter equations can be unified, yielding the classical full-order and the reduced-order Kalman filters as well as the optimal Luenberger observer. The developments start from the specific linear error covariance equations, resulting in the nonlinear Riccati equations and a good possibility for comparing the different forms. Thus a better view of the connections between the different approaches to the filter design is given.

MSC:

93E11 Filtering in stochastic control theory
93C05 Linear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
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