Stable and Efficient Cubature-based Filtering in Dynamical Systems [Hardcover]

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.

Contents vi

List of Figures viii

List of Tables ix

List of symbols and abbreviations x

1 Introduction 1

1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Filtering in dynamical systems 5

2.1 The general discrete state-space model . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 The Bayes lter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 The Kalman lter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.1 The Kalman lter algorithm in the case of the Gaussian linear discrete statespace

model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3.2 The nonlinear Kalman lter and the Gaussian assumption . . . . . . . . . . 12

2.4 Parameter estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4.1 Maximum Likelihood estimation . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4.2 Bayesian parameter estimation . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.5 l]