Recursive Estimation with Implicit Constraints

  • Richard Steffen
  • Christian Beder
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4713)


Recursive estimation or Kalman filtering usually relies on explicit model functions, that directly and explicitly describe the effect of the parameters on the observations. However, many problems in computer vision, including all those resulting in homogeneous equation systems, are easier described using implicit constraints between the observations and the parameters. By implicit we mean, that the constraints are given by equations, that are not easily solvable for the observation vector.

We present a framework, that allows to incorporate such implicit constraints as measurement equations into a Kalman filter. The algorithm may be used as a black-box, simplifying the process of specifying suitable measurement equations for many problems. As a byproduct, the possibility of specifying model equations non-explicitly, some non-linearities may be avoided and better results can be achieved for certain problems.


Explicit Function Bundle Adjustment Recursive Estimation Unscented Transformation Implicit Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Richard Steffen
    • 1
  • Christian Beder
    • 2
  1. 1.Department of Photogrammetry, Bonn UniversityGermany
  2. 2.Computer Science Department, Kiel UniversityGermany

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