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Statistical Methods for Fuzzy Data by Reinhard Viertl

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26.2 Remarks concerning Kalman filtering

Many processes can be modeled by a multivariate state-space model [see Catlin (1989) and Grewal and Andrews (2001)]. This linear dynamic system consists of a system equation

(26.11) Numbered Display Equation

and an observation equation

(26.12) Numbered Display Equation

The vector xtn describes the state of the system at time t, and the system equation models the dynamics of the system. The dynamics is influenced by the disturbance term tl. In this model the state of the system cannot be observed directly but only a linear function ytm can be observed. This linear dependence changes with time and is described by Equation (26.12) which is also influenced by a disturbance ηtm.

(t)t ≥ 0 and (

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