A recursive linear MMSE filter for dynamic systems with unknown state vector means

  • Amir Khodabandeh
  • Peter J. G. TeunissenEmail author
Original Paper


In this contribution we extend Kalman-filter theory by introducing a new recursive linear minimum mean squared error (MMSE) filter for dynamic systems with unknown state-vector means. The recursive filter enables the joint MMSE prediction and estimation of the random state vectors and their unknown means, respectively. We show how the new filter reduces to the Kalman-filter in case the state-vector means are known and we discuss the fundamentally different roles played by the intitialization of the two filters.


Minimum mean squared error (MMSE) Best linear unbiased estimation (BLUE) Best linear unbiased prediction (BLUP) Kalman filter BLUE-BLUP recursion 

Mathematics Subject Classification

60G25 60G35 93E11 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Spatial Sciences, GNSS Research CentreCurtin University of TechnologyPerthAustralia
  2. 2.Department of Geoscience and Remote SensingDelft University of TechnologyDelftThe Netherlands

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