Sequential Bayesian Inference for Dynamical Systems Using the Finite Volume Method

  • Colin FoxEmail author
  • Richard A. Norton
  • Malcolm E. K. Morrison
  • Timothy C. A. Molteno
Part of the MATRIX Book Series book series (MXBS, volume 2)


Optimal Bayesian sequential inference, or filtering, for the state of a deterministic dynamical system requires simulation of the Frobenius-Perron operator, that can be formulated as the solution of an initial value problem in the continuity equation on filtering distributions. For low-dimensional, smooth systems the finite-volume method is an effective solver that conserves probability and gives estimates that converge to the optimal continuous-time values. A Courant–Friedrichs–Lewy condition assures that intermediate discretized solutions remain positive density functions. We demonstrate this finite-volume filter (FVF) in a simulated example of filtering for the state of a pendulum, including a case where rank-deficient observations lead to multi-modal probability distributions.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Colin Fox
    • 1
    Email author
  • Richard A. Norton
    • 1
  • Malcolm E. K. Morrison
    • 1
  • Timothy C. A. Molteno
    • 1
  1. 1.University of OtagoDunedinNew Zealand

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