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Grid-based nonlinear estimation and its applications / Bin Jia (Intelligent Fusion Technology, Inc., Germantown, Maryland, USA), Ming Xin (Department of Mechanical and Aerospace Engineering [University of Missouri]).

By: Jia, Bin, 1982- [author.]Contributor(s): Xin, Ming, 1972- [author.]Material type: TextTextPublisher: Boca Raton, FL : CRC Press, Taylor & Francis Group, 2019Description: 1 online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9781315193212; 1315193213; 9781351757393; 1351757393; 9781351757409; 1351757407; 9781351757416; 1351757415Subject(s): Estimation theory | Nonlinear theories | MATHEMATICS / Applied | SCIENCE / Life Sciences / General | TECHNOLOGY / ElectricityDDC classification: 519.5/44 LOC classification: QA276.8 | .J53 2019ebOnline resources: Taylor & Francis | OCLC metadata license agreement
Contents:
Cover; Title Page; Copyright Page; Table of Contents; Preface; 1: Introduction; 1.1 Random Variables and Random Process; 1.2 Gaussian Distribution; 1.3 Bayesian Estimation; References; 2: Linear Estimation of Dynamic Systems; 2.1 Linear Discrete-Time Kalman Filter; 2.2 Information Kalman Filter; 2.3 The Relation Between the Bayesian Estimation and Kalman Filter; 2.4 Linear Continuous-Time Kalman Filter; References; 3: Conventional Nonlinear Filters; 3.1 Extended Kalman Filter; 3.2 Iterated Extended Kalman Filter; 3.3 Point-Mass Filter; 3.4 Particle Filter; 3.5 Combined Particle Filter
3.5.1 Marginalized Particle Filter3.5.2 Gaussian Filter Aided Particle Filter; 3.6 Ensemble Kalman Filter; 3.7 Zakai Filter and Fokker Planck Equation; 3.8 Summary; References; 4: Grid-based Gaussian Nonlinear Estimation; 4.1 General Gaussian Approximation Nonlinear Filter; 4.2 General Gaussian Approximation Nonlinear Smoother; 4.3 Unscented Transformation; 4.4 Gauss-Hermite Quadrature; 4.5 Sparse-Grid Quadrature; 4.6 Anisotropic Sparse-Grid Quadrature and Accuracy Analysis; 4.6.1 Anisotropic Sparse-Grid Quadrature; 4.6.2 Analysis of Accuracy of the Anisotropic Sparse-Grid Quadrature
4.7 Spherical-Radial Cubature4.8 The Relations Among Unscented Transformation, Sparse-Grid Quadrature, and Cubature Rule; 4.8.1 From the Spherical-Radial Cubature Rule to the Unscented Transformation; 4.8.2 The Connection between the Quadrature Rule and the Spherical Rule; 4.8.3 The Relations Between the Sparse-Grid Quadrature Rule and the Spherical-Radial Cubature Rule; 4.9 Positive Weighted Quadrature; 4.10 Adaptive Quadrature; 4.10.1 Global Measure of Nonlinearity for Stochastic Systems; 4.10.2 Local Measure of Nonlinearity for Stochastic Systems; 4.11 Summary; References
5: Nonlinear Estimation: Extensions5.1 Grid-based Continuous-Discrete Gaussian Approximation Filter; 5.2 Augmented Grid-based Gaussian Approximation Filter; 5.3 Square-root Grid-based Gaussian Approximation Filter; 5.4 Constrained Grid-based Gaussian Approximation Filter; 5.4.1 Interval-constrained Unscented Transformation; 5.4.2 Estimation Projection and Constrained Update; 5.5 Robust Grid-based Gaussian Approximation Filter; 5.5.1 Huber-based Filter; 5.5.2 H
5.9 Interacting Multiple Model Filter5.10 Summary; References; 6: Multiple Sensor Estimation; 6.1 Main Fusion Structures; 6.2 Grid-based Information Kalman Filters and Centralized Gaussian Nonlinear Estimation; 6.3 Consensus-based Strategy; 6.3.1 Consensus Algorithm; 6.3.2 Consensus-based Filter; 6.4 Covariance Intersection Strategy; 6.4.1 Covariance Intersection; 6.4.2 Iterative Covariance Intersection; 6.4.3 Distributed Batch Covariance Intersection; 6.4.4 Analysis; 6.5 Diffusion-based Strategy; 6.6 Distributed Particle Filter; 6.7 Multiple Sensor Estimation and Sensor Allocation
Summary: 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.
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"A science publishers book."

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.

Cover; Title Page; Copyright Page; Table of Contents; Preface; 1: Introduction; 1.1 Random Variables and Random Process; 1.2 Gaussian Distribution; 1.3 Bayesian Estimation; References; 2: Linear Estimation of Dynamic Systems; 2.1 Linear Discrete-Time Kalman Filter; 2.2 Information Kalman Filter; 2.3 The Relation Between the Bayesian Estimation and Kalman Filter; 2.4 Linear Continuous-Time Kalman Filter; References; 3: Conventional Nonlinear Filters; 3.1 Extended Kalman Filter; 3.2 Iterated Extended Kalman Filter; 3.3 Point-Mass Filter; 3.4 Particle Filter; 3.5 Combined Particle Filter

3.5.1 Marginalized Particle Filter3.5.2 Gaussian Filter Aided Particle Filter; 3.6 Ensemble Kalman Filter; 3.7 Zakai Filter and Fokker Planck Equation; 3.8 Summary; References; 4: Grid-based Gaussian Nonlinear Estimation; 4.1 General Gaussian Approximation Nonlinear Filter; 4.2 General Gaussian Approximation Nonlinear Smoother; 4.3 Unscented Transformation; 4.4 Gauss-Hermite Quadrature; 4.5 Sparse-Grid Quadrature; 4.6 Anisotropic Sparse-Grid Quadrature and Accuracy Analysis; 4.6.1 Anisotropic Sparse-Grid Quadrature; 4.6.2 Analysis of Accuracy of the Anisotropic Sparse-Grid Quadrature

4.7 Spherical-Radial Cubature4.8 The Relations Among Unscented Transformation, Sparse-Grid Quadrature, and Cubature Rule; 4.8.1 From the Spherical-Radial Cubature Rule to the Unscented Transformation; 4.8.2 The Connection between the Quadrature Rule and the Spherical Rule; 4.8.3 The Relations Between the Sparse-Grid Quadrature Rule and the Spherical-Radial Cubature Rule; 4.9 Positive Weighted Quadrature; 4.10 Adaptive Quadrature; 4.10.1 Global Measure of Nonlinearity for Stochastic Systems; 4.10.2 Local Measure of Nonlinearity for Stochastic Systems; 4.11 Summary; References

5: Nonlinear Estimation: Extensions5.1 Grid-based Continuous-Discrete Gaussian Approximation Filter; 5.2 Augmented Grid-based Gaussian Approximation Filter; 5.3 Square-root Grid-based Gaussian Approximation Filter; 5.4 Constrained Grid-based Gaussian Approximation Filter; 5.4.1 Interval-constrained Unscented Transformation; 5.4.2 Estimation Projection and Constrained Update; 5.5 Robust Grid-based Gaussian Approximation Filter; 5.5.1 Huber-based Filter; 5.5.2 H

5.9 Interacting Multiple Model Filter5.10 Summary; References; 6: Multiple Sensor Estimation; 6.1 Main Fusion Structures; 6.2 Grid-based Information Kalman Filters and Centralized Gaussian Nonlinear Estimation; 6.3 Consensus-based Strategy; 6.3.1 Consensus Algorithm; 6.3.2 Consensus-based Filter; 6.4 Covariance Intersection Strategy; 6.4.1 Covariance Intersection; 6.4.2 Iterative Covariance Intersection; 6.4.3 Distributed Batch Covariance Intersection; 6.4.4 Analysis; 6.5 Diffusion-based Strategy; 6.6 Distributed Particle Filter; 6.7 Multiple Sensor Estimation and Sensor Allocation

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