How to handle colored noise in large least-squares problems in the presence of data gaps?

  • R. Klees
  • P. Ditmar
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 127)


An approach to handle stationary colored noise in least-squares problems in the presence of data gaps is presented. The presence of colored noise implies that a non-diagonal covariance matrix has to be inverted. The problem is reduced to the solution of systems of linear equations with the covariance matrix as equation matrix. Each system is solved using a pre-conditioned conjugate gradient method. An ARMA representation of the colored noise is used both to design an efficient pre-conditioner and to compute the product of the covariance matrix with a vector. This results in an algorithm that has a numerical complexity of O(N) operations, where N is the number of observations. This makes the algorithm particularly suited for large least-squares problems. It is shown that the approach works perfectly in the sense that no edge effects show up and no observations have to be thrown away.


Colored noise ARMA filters data gaps satellite gravity gradiometry (SGG) 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • R. Klees
    • 1
  • P. Ditmar
    • 1
  1. 1.Department of Geodesy, Physical, Geometric and Space GeodesyDelft University of TechnologyDelftThe Netherlands

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