Stable and efficient cubature-based filtering in dynamical systems / Dominik Ballreich.

Foreword; Acknowledgments; Contents; List of Figures; List of Tables; List of Symbols and Abbreviations; 1 Introduction; 1.1 Problem Statement and Objective; 1.2 Outline; 2 Filtering in Dynamical Systems; 2.1 The General Discrete State-Space Model; 2.2 The Bayes Filter; 2.3 The Kalman Filter; 2.3.1 The Kalman Filter Algorithm in the Case of the Gaussian Linear Discrete State-Space Model; 2.3.2 The Nonlinear Kalman Filter and the GaussianAssumption; 2.4 Parameter Estimation; 2.4.1 Maximum Likelihood Estimation; 2.4.2 Bayesian Parameter Estimation; 2.5 Conditional Filtering

2.6 Stabilization of Nonlinear Kalman Filter Algorithms2.7 Treatment of Missing Data; 3 Deterministic Numerical Integration; 3.1 One-Dimensional Deterministic Numerical Integration; 3.1.1 Lagrange Interpolation; 3.1.2 Moment Equations for the One-Dimensional Case; 3.1.3 Gauss Quadrature; 3.1.4 Clenshaw-Curtis Quadrature; 3.2 Multidimensional Deterministic Numerical Integration; 3.2.1 Stability Factor; 3.2.2 A Lower Bound for the Number of Abscissae; 3.2.3 Polynomials in d Dimensions; 3.2.4 Product Cubature Rules; 3.2.5 Moment Equations for the d-Dimensional Case; 3.2.6 Smolyak Cubature

3.2.7 Compound Rules3.2.8 Change of Variables; 4 Optimization and Stabilization of Cubature Rules; 4.1 Cubature Rules Based on a Least Squares Approach; 4.2 Construction of Stabilized Smolyak Cubature Rules; 4.2.1 Stabilized(1) Rules; 4.2.2 Stabilized(2) Rules; 4.2.3 Smolyak Cubature Rules with an Approximate Degree of Exactness; 5 Simulation Studies; 5.1 The Univariate Non-Stationary Growth Model; 5.2 The Six-Dimensional Coordinated Turn Model; 5.3 The Lorenz Model; 5.4 The Ginzburg-Landau Model; 6 Results; A The Conditional Mean; B The Moments of the Conditional Normal Distribution

C The Golub-Welsch AlgorithmD Simplified Multidimensional Moment Equations; Bibliography; Index