Recursive Estimation with Implicit Constraints
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.
KeywordsExplicit Function Bundle Adjustment Recursive Estimation Unscented Transformation Implicit Constraint
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- 2.Davison, A.J.: Real-Time Simultaneous Localisation and Mapping with a Single Camera. In: Proceeding of the 9th International Conference on Computer Vision, pp. 674–679 (2003)Google Scholar
- 3.Engels, C., Stewenius, H., Nister, D.: Bundle Adjustment Rules. Photogrammetric Computer Vision (PCV) (September 2006)Google Scholar
- 4.Förstner, W., Wrobel, B.: Mathematical Concepts in Photogrammetry. In: McGlome, J.C., Mikhail, E.M., Bethel, J. (eds.) Manual of Photogrammetry, pp. 15–180, ASPRS (2004)Google Scholar
- 5.Grün, A.: An Optimum Algorithm for On-Line Triangulation. International Society for Photogrammetry and Remote Sensing 24 - III/2, 131–151 (1982)Google Scholar
- 9.Julier, S., Uhlmann, J.: A new extension of the Kalman filter to nonlinear systems. In: Int. Symp. Aerospace/Defense Sensing, Simul. and Controls, Orlando, FL (1997)Google Scholar
- 10.Kalman, R.E.: A New Approach to Linear Filtering and Prediction Problems. Journal of Basic Engineering, 35–45 (1960)Google Scholar
- 12.Montiel, J., Civera, J., Davison, A.: Unified Inverse Depth Parametrization for Monocular SLAM. In: Proceedings of Robotics: Science and Systems, Philadelphia, USA (2006)Google Scholar
- 15.Welch, G., Bishop, G.: An Introduction to the Kalman Filter. Technical Report, University of North Carolina at Chapel Hill (1995)Google Scholar