Grid-based Nonlinear Estimation and Its Applications  book cover
1st Edition

Grid-based Nonlinear Estimation and Its Applications

ISBN 9781138723092
Published April 29, 2019 by CRC Press
252 Pages 74 B/W Illustrations

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Book 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



Random variables and random process

Gaussian distribution

Bayesian estimation


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


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



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



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



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



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



Application: Tracking and Navigation

Single Target Tracking

Multiple Target Tracking

Spacecraft Relative Attitude Estimation





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Bin Jia is a Project Manager at Intelligent Fusion Technology, Inc. in Germantown, Maryland, a research and development company focusing on information fusion technologies from fundamental research to industry transition and product development and support. Dr. Jia received a Ph.D. in Aerospace Engineering from Mississippi State University in 2012, a M.S from Graduate University of the Chinese Academy of Sciences, and a B.S from Jilin University, China, in 2007 and 2004, respectively. From 2012 to 2013, he worked as a postdoctoral research scientist at Columbia University. Dr. Jia’s research experience includes Bayesian estimation, multi-sensor multi-target tracking, information fusion, guidance and navigation, and space situational awareness.

Ming Xin is an Associate Professor in the Department of Mechanical and Aerospace Engineering at University of Missouri-Columbia. He received his B.S. and M.S. degrees from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 1993 and 1996, respectively, both in Automatic Control. He received his Ph.D. in Aerospace Engineering from Missouri University of Science and Technology in 2002. His research interests include guidance, navigation, and control of aerospace vehicles, flight mechanics, estimation theory and applications, cooperative control of multi-agent systems, and sensor networks. Dr. Xin was the recipient of the National Science Foundation CAREER Award in 2009. He is an Associate Fellow of AIAA and a Senior Member of IEEE and AAS.


"This book is a comprehensive account on one such practical estimation technique, based on approximation of the conditional distribution by mixtures of Gaussian densities and replacing the emerging integrals by grid-based numerical schemes. In summary, this book is a carefully written guide to a particular approach to the approximation of optimal estimation algorithms and its implementation in concrete real-life applications."
— Pavel Chigansky, Mathematical Reviews Clippings, July 2020