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A New Perspective and Extension of the Gaussian Filter





The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. The GF represents the belief of the current state by a Gaussian distribution, whose mean is an affine function of the measurement. We show that this representation can be too restrictive to accurately capture the dependences in systems with nonlinear observation models, and we investigate how the GF can be generalized to alleviate this problem. To this end, we view the GF as the solution to a constrained optimization problem. From this new perspective, the GF is seen as a special case of a much broader class of filters, obtained by relaxing the constraint on the form of the approximate posterior. On this basis, we outline some conditions which potential generalizations have to satisfy in order to maintain the computational efficiency of the GF. We propose one concrete generalization which corresponds to the standard GF using a pseudo measurement instead of the actual measurement. Extending an existing GF implementation in this manner is trivial. Nevertheless, we show that this small change can have a major impact on the estimation accuracy.

Author(s): Manuel Wüthrich and Sebastian Trimpe and Garcia Cifuentes, Cristina and Daniel Kappler and Stefan Schaal
Journal: The International Journal of Robotics Research
Volume: 35
Number (issue): 14
Pages: 1731-1749
Year: 2016
Month: December

Department(s): Autonomous Motion, Intelligent Control Systems
Research Project(s): Gaussian Filtering as Variational Inference
Bibtex Type: Article (article)
Paper Type: Journal

DOI: 10.1177/0278364916684019
State: Published
Attachments: PDF


  title = {A New Perspective and Extension of the Gaussian Filter},
  author = {W{\"u}thrich, Manuel and Trimpe, Sebastian and Garcia Cifuentes, Cristina and Kappler, Daniel and Schaal, Stefan},
  journal = {The International Journal of Robotics Research},
  volume = {35},
  number = {14},
  pages = {1731-1749},
  month = dec,
  year = {2016},
  month_numeric = {12}