Optimal filtering over linear observations with unknown parameters |
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| Authors: | Michael Basin Dario Calderon-Alvarez |
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| Institution: | Department of Physical and Mathematical Sciences, Autonomous University of Nuevo Leon Apdo postal 144-F, C.P. 66450, San Nicolas de los Garza Nuevo Leon, Mexico |
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| Abstract: | This paper presents the optimal filtering and parameter identification problem for linear stochastic systems over linear observations with unknown parameters, where the 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 resulting filtering system is bilinear in state and linear in observations. 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, positive and negative, parameter values. |
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| Keywords: | Kalman filtering Parameter identification Uncertain linear stochastic system |
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