The Autocovariance Prediction of the Earth Rotation Parameters

  • Wiesław Kosek
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 112)

Abstract

Let X t = X 1,X 2,...,X N be an equidistant stationary stochastic process of N observations. Our main interest is in estimating the prediction \({{\hat{X}}_{{N + 1}}} \) in a time of N + 1. In the autocovariance prediction method the first prediction point satisfies the following condition:
$$ P = \sum\limits_{k = 0}^{N - 1} {(\hat c'_k - \hat c_k )^2 = \min } $$
(1)
where
$$ \hat c_k = h_k /\left( {N - k} \right)\sum\limits_{t = 1}^{N - k} {X_t } X_{t + k} ,{\text{ }}for{\text{ }}k = 0,1,...,N - 1 $$
(2)
is the autocovariance estimation of N number of data, \( \hat c'_k \) is the autocovariance estimation of N + 1 number of data including the first prediction point \({{{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{X}}}_{{N + 1}}} \) and h k is a lag window.

Keywords

Entropy Covariance 

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Wiesław Kosek
    • 1
  1. 1.Space Research Centre of P.A.S.WarsawPoland

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