Stable and Efficient Cubature-based Filtering in Dynamical Systems

1. Front Matter

   Pages i-xvii

   PDF

2. Introduction

   • Dominik Ballreich

   Pages 1-4

3. Filtering in Dynamical Systems

   • Dominik Ballreich

   Pages 5-45

4. Deterministic Numerical Integration

   • Dominik Ballreich

   Pages 47-91

5. Optimization and Stabilization of Cubature Rules

   • Dominik Ballreich

   Pages 93-108

6. Simulation Studies

   • Dominik Ballreich

   Pages 109-134

7. Results

   • Dominik Ballreich

   Pages 135-138

8. Back Matter

   Pages 139-160

   PDF

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

• University of Hagen, Hagen, Germany

  Dominik Ballreich

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.

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