Front Cover
Stochastic models, estimation, and control
Copyright Page
Contents
Preface
Contents of Volume 2
Notation
Chapter 1. Introduction
1.1 Why Stochastic Models, Estimation, and Control?
1.2 Overview of the Text
1.3 The Kalman Filter: An Introduction to Concepts
1.4 Basic Assumptions
1.5 A Simple Example
1.6 A Preview
General References
Appendix and Problems
References
Chapter 2. Deterministic system models
2.1 Introduction
2.2 Continuous-Time Dynamic Models
2.3 Solutions to State Differential Equations
2.4 Discrete-Time Measurements
2.5 Controllability and Observability
2.6 Summary
References
Problems
Chapter 3. Probability theory and static models
3.1 Introduction
3.2 Probability and Random Variables
3.3 Probability Distributions and Densities
3.4 Conditional Probability and Densities
3.5 Functions of Random Variables
3.6 Expectation and Moments of Random Variables
3.7 Conditional Expectations
3.8 Characteristic Functions
3.9 Gaussian Random Vectors
3.10 Linear Operations on Gaussian Random Variables
3.11 Estimation with Static Linear Gaussian System Models
3.12 Summary
References
Problems
Chapter 4. Stochastic processes and linear dynamic system models
4.1 Introduction
4.2 Stochastic Processes
4.3 Stationary Stochastic Processes and Power Spectral Density
4.4 System Modeling: Objectives and Directions
4.5 Foundations: White Gaussian Noise and Brownian Motion
4.6 Stochastic Integrals
4.7 Stochastic Differentials
4.8 Linear Stochastic Differential Equations
4.9 Linear Stochastic Difference Equations
4.10 The Overall System Model
4.11 Shaping Filters and State Augmentation
4.12 Power Spectrum Concepts and Shaping Filters
4.13 Generating Practical System Models
4.14 Summary
References
Problems
Chapter 5. Optimal filtering with linear system models
5.1 Introduction
5.2 Problem Formulation
5.3 The Discrete-Time (Sampled Data) Optimal Estimator: The Kalman Filter
5.4 Statistics of Processes within the Filter Structure
5.5 Other Criteria of Optimality
5.6 Covariance Measurement Update Computations
5.7 Inverse Covariance Form
5.8 Stability
5.9 Correlation of Dynamic Driving Noise and Measurement Noise
5.10 Time-Correlated Measurement Noise: Perfect Measurements
5.11 Continuous-Time Filter
5.12 Wiener Filtering and Frequency Domain Techniques
5.13 Summary
References
Problems
Chapter 6. Design and performance analysis of Kalman filters
6.1 Introduction
6.2 The Requisite of Engineering Judgment
6.3 Application of Kalman Filtering to Inertial Navigation Systems
6.4 INS Aided by Position Data: A Simple Example
6.5 Doppler-Aided INS
6.6 INS Calibration and Alignment Using Direct Kalman Filter
6.7 Generating Alternative Designs
6.8 Performance (Sensitivity) Analysis
6.9 Systematic Design Procedure
6.10 INS Aided by Navigation Satellites
6.11 Practical Aspects of Implementation
6.12 Summary
References
Problems
Chapter 7. Square root filtering
7.1 Introduction
7.2 Matrix Square Roots
7.3 Covariance Square Root Filter for Qd = 0
7.4 Vector-Valued Measurements
7.6 Inverse Covariance Square Root Filter
7.7 UโD Covariance Factorization Filter
7.8 Filter Performance and Requirements
7.9 Summary
References
Problems
Index