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Smoothing and Interpolation

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Linear Stochastic Systems

Part of the book series: Series in Contemporary Mathematics ((SCMA,volume 1))

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Abstract

Given a linear stochastic system of dimension n in either discrete or continuous time, the smoothing problem amounts to determining the least-squares estimates

$$\displaystyle{\hat{x}(t) =\mathop{ \mathrm{E}}\nolimits \{x(t)\mid y(s);\;t_{0} \leq s \leq t_{1}\},\quad t_{0} \leq t \leq t_{1}}$$

for some finite interval [t 0, t 1]. When t 0 → −∞ and t 1 → ∞, we end up in the stationary setting of Sect. 14.3, and we shall use this fact to reduce the dimension of the smoothing algorithms.

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Authors and Affiliations

  1. Departments of Automation and Mathematics, Shanghai Jiaotong University, Shanghai, China

    Anders Lindquist

  2. Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden

    Anders Lindquist

  3. Department of Information Engineering, University of Padova, Padova, Italy

    Giorgio Picci

Authors
  1. Anders Lindquist
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  2. Giorgio Picci
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Lindquist, A., Picci, G. (2015). Smoothing and Interpolation. In: Linear Stochastic Systems. Series in Contemporary Mathematics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45750-4_15

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