© 2017

Stable and Efficient Cubature-based Filtering in Dynamical Systems

  • Develops new methods of deterministic numerical integration

  • Derives and describes state of the art filter algorithms

  • Presents methods of deterministic numerical integration


Table of contents

  1. Front Matter
    Pages i-xvii
  2. Dominik Ballreich
    Pages 1-4
  3. Dominik Ballreich
    Pages 5-45
  4. Dominik Ballreich
    Pages 47-91
  5. Dominik Ballreich
    Pages 93-108
  6. Dominik Ballreich
    Pages 109-134
  7. Dominik Ballreich
    Pages 135-138
  8. Back Matter
    Pages 139-160

About this book


The book addresses the problem of calculation of d-dimensional integrals (conditional expectations) in filter problems. It develops new methods of deterministic numerical integration, which can be used to speed up and stabilize filter algorithms. With the help of these methods, better estimates and predictions of latent variables are made possible in the fields of economics, engineering and physics. The resulting procedures are tested within four detailed simulation studies.


Kalman filter Recursive Bayesian estimation State-space models Smolyak cubature Numerical integration Cubature Kalman filter Maximum Likelihood estimation Deterministic numerical integration Univariate non-stationary growth model Six-dimentional coordinated turn model Lorenz model Ginzburg-Landau model Optimization and stabilization of cubature rules Smolyak cubature rules with an approximate degree of exactness Filtering in dynamical systems

Authors and affiliations

  1. 1.University of HagenHagenGermany

About the authors

Dominik Ballreich is a research assistant at the Chair for Applied Statistics and Methods of Empirical Social Research at the University of Hagen. His research interests lie in the fields of recursive Bayesian estimation, numerical integration and heuristic optimization.

Bibliographic information

Industry Sectors
Finance, Business & Banking
Oil, Gas & Geosciences