Description
Grid-based Nonlinear Estimation and its Applications presents new Bayesian nonlinear estimation techniques developed in the last two decades. Grid-based estimation techniques are based on efficient and precise numerical integration rules to improve performance of the traditional Kalman filtering based estimation for nonlinear and uncertainty dynamic systems. The unscented Kalman filter, Gauss-Hermite quadrature filter, cubature Kalman filter, sparse-grid quadrature filter, and many other numerical grid-based filtering techniques have been introduced and compared in this book.
Theoretical analysis and numerical simulations are provided to show the relationships and distinct features of different estimation techniques. To assist the exposition of the filtering concept, preliminary mathematical review is provided. In addition, rather than merely considering the single sensor estimation, multiple sensor estimation, including the centralized and decentralized estimation, is included. Different decentralized estimation strategies, including consensus, diffusion, and covariance intersection, are investigated. Diverse engineering applications, such as uncertainty propagation, target tracking, guidance, navigation, and control, are presented to illustrate the performance of different grid-based estimation techniques.
Table of Contents
Contents
Introduction
Random variables and random process
Gaussian distribution
Bayesian estimation
Reference
Linear Estimation of Dynamic Systems
Linear Discrete-Time Kalman Filter
Information Kalman Filter
The relation between the Bayesian Estimation and Kalman Filter
Linear Continuous-Time Kalman Filter
Reference
Conventional Nonlinear Filters
Extended Kalman Filter
Iterated Extended Kalman Filter
Point-mass Filter
Particle Filter
Combined Particle Filter
Ensemble Kalman Filter
Zakai Filter and Fokkle Planck Equation
Summary
Reference
Grid-Based Gaussian Nonlinear Estimation
General Gaussian Approximation Nonlinear Filter
General Gaussian Approximation Nonlinear Smoother
Unscented Transformation
Gauss-Hermite Quadrature
Sparse-Grid Quadrature
Anisotropic Sparse-grid Quadrature and Accuracy Analysis
Spherical-Radial Cubature
The relation among Unscented Transformation, Sparse-Grid Quadrature, and Cubature Rule
Positive Weighted Quadrature
Adaptive Quadrature
Summary
Reference
Nonlinear Estimation: Extensions
Grid-based Continuous-Discrete Gaussian Approximation Kalman Filter
Augmented Grid-based Gaussian Approximation Filter
Square-root Grid-based Gaussian Approximation Filter
Constrained Grid-based Gaussian Approximation Filter
Robust Grid-based Gaussian Approximation Filter
Gaussian Mixture Filter
Simplified Grid-based Gaussian Mixture Filter
Adaptive Gaussian Mixture Filter
Interacting Multiple Model Filter
Summary
Reference
Multiple Sensor Estimation
Main Fusion Structures
Grid-based Information Kalman Filters and Centralized Gaussian Nonlinear Estimation
Consensus-based Strategy
Covariance Intersection Strategy
Diffusion-based Strategy
Distributed Particle Filter
Multiple Sensor Estimation and Sensor Allocation
Summary
Reference
Application: Uncertainty Propagation
Gaussian Quadrature –based Uncertainty Propagation
Multi-element Grid-based Uncertainty Propagation
Uncertainty Propagator
Gaussian Mixture based Uncertainty Propagation
Stochastic Expansion based Uncertainty Propagation
Graphic Process Unit aided Uncertainty Propagation
MapReduce aided Uncertainty Propagation
Summary
Reference
Application: Tracking and Navigation
Single Target Tracking
Multiple Target Tracking
Spacecraft Relative Attitude Estimation
Summary
Reference
