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Linear State Space Models and Kalman Filtering

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Restricted Kalman Filtering

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Abstract

A linear wide-sense state space model for an observable p-variate stochastic process Y t , defined on an appropriate probability space \((\Omega,\mathcal{F},\mathcal{P})\), is described by the following set of equations:

$$\begin{array}{rlrlrl}{Y }_{t}& = {Z}_{t}{\alpha }_{t} + {d}_{t} + {\epsilon }_{t},& & \cr {\alpha }_{t+1}& = {T}_{t}{\alpha }_{t} + {c}_{t} + {R}_{t}{\eta }_{t}.& \cr \end{array}$$
(2.1)

The first equation is usually called the measurement equation, and the second is known as the state equation.

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Authors and Affiliations

  1. Department of Statistics Institute of Mathematics and Statistics, Fluminense Federal University, Rio de Janeiro, Brazil

    Adrian Pizzinga

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Pizzinga, A. (2012). Linear State Space Models and Kalman Filtering. In: Restricted Kalman Filtering. SpringerBriefs in Statistics, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4738-2_2

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