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E-raamat: Grid-based Nonlinear Estimation and Its Applications

, (University of Missouri)
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 25-Apr-2019
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781351757409
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Grid-based Nonlinear Estimation and Its ApplicationsSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 25-Apr-2019
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781351757409
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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.

Arvustused

"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

Preface iii
1 Introduction
1(12)
1.1 Random Variables and Random Process
2(6)
1.2 Gaussian Distribution
8(2)
1.3 Bayesian Estimation
10(2)
References
12(1)
2 Linear Estimation of Dynamic Systems
13(22)
2.1 Linear Discrete-Time Kalman Filter
13(3)
2.2 Information Kalman Filter
16(5)
2.3 The Relation Between the Bayesian Estimation and Kalman Filter
21(12)
2.4 Linear Continuous-Time Kalman Filter
33(1)
References
34(1)
3 Conventional Nonlinear Filters
35(17)
3.1 Extended Kalman Filter
36(1)
3.2 Iterated Extended Kalman Filter
37(1)
3.3 Point-Mass Filter
38(2)
3.4 Particle Filter
40(4)
3.5 Combined Particle Filter
44(3)
3.5.1 Marginalized Particle Filter
45(1)
3.5.2 Gaussian Filter Aided Particle Filter
46(1)
3.6 Ensemble Kalman Filter
47(1)
3.7 Zakai Filter and Fokker Planck Equation
48(2)
3.8 Summary
50(1)
References
50(2)
4 Grid-based Gaussian Nonlinear Estimation
52(55)
4.1 General Gaussian Approximation Nonlinear Filter
53(3)
4.2 General Gaussian Approximation Nonlinear Smoother
56(1)
4.3 Unscented Transformation
57(1)
4.4 Gauss-Hermite Quadrature
58(1)
4.5 Sparse-Grid Quadrature
59(10)
4.6 Anisotropic Sparse-Grid Quadrature and Accuracy Analysis
69(10)
4.6.1 Anisotropic Sparse-Grid Quadrature
69(3)
4.6.2 Analysis of Accuracy of the Anisotropic Sparse-Grid Quadrature
72(7)
4.7 Spherical-Radial Cubature
79(5)
4.8 The Relations Among Unscented Transformation, Sparse-Grid Quadrature, and Cubature Rule
84(14)
4.8.1 From the Spherical-Radial Cubature Rule to the Unscented Transformation
84(2)
4.8.2 The Connection between the Quadrature Rule and the Spherical Rule
86(6)
4.8.3 The Relations Between the Sparse-Grid Quadrature Rule and the Spherical-Radial Cubature Rule
92(6)
4.9 Positive Weighted Quadrature
98(4)
4.10 Adaptive Quadrature
102(2)
4.10.1 Global Measure of Nonlinearity for Stochastic Systems
102(1)
4.10.2 Local Measure of Nonlinearity for Stochastic Systems
103(1)
4.11 Summary
104(1)
References
105(2)
5 Nonlinear Estimation: Extensions
107(26)
5.1 Grid-based Continuous-Discrete Gaussian Approximation Filter
108(2)
5.2 Augmented Grid-based Gaussian Approximation Filter
110(2)
5.3 Square-root Grid-based Gaussian Approximation Filter
112(2)
5.4 Constrained Grid-based Gaussian Approximation Filter
114(2)
5.4.1 Interval-constrained Unscented Transformation
114(1)
5.4.2 Estimation Projection and Constrained Update
115(1)
5.5 Robust Grid-based Gaussian Approximation Filter
116(6)
5.5.1 Huber-based Filter
116(1)
5.5.2 H∞ Filter
117(5)
5.6 Gaussian Mixture Filter
122(3)
5.7 Simplified Grid-based Gaussian Mixture Filter
125(1)
5.8 Adaptive Gaussian Mixture Filter
126(2)
5.9 Interacting Multiple Model Filter
128(2)
5.10 Summary
130(1)
References
130(3)
6 Multiple Sensor Estimation
133(34)
6.1 Main Fusion Structures
134(1)
6.2 Grid-based Information Kalman Filters and Centralized Gaussian Nonlinear Estimation
135(4)
6.3 Consensus-based Strategy
139(8)
6.3.1 Consensus Algorithm
139(4)
6.3.2 Consensus-based Filter
143(4)
6.4 Covariance Intersection Strategy
147(10)
6.4.1 Covariance Intersection
147(3)
6.4.2 Iterative Covariance Intersection
150(1)
6.4.3 Distributed Batch Covariance Intersection
151(2)
6.4.4 Analysis
153(4)
6.5 Diffusion-based Strategy
157(2)
6.6 Distributed Particle Filter
159(2)
6.7 Multiple Sensor Estimation and Sensor Allocation
161(2)
6.8 Summary
163(1)
References
164(3)
7 Application: Uncertainty Propagation
167(50)
7.1 Gaussian Quadrature-based Uncertainty Propagation
169(5)
7.2 Multi-element Grid-based Uncertainty Propagation
174(4)
7.3 Uncertainty Propagator
178(2)
7.4 Gaussian Mixture based Uncertainty Propagation
180(7)
7.5 Stochastic Expansion based Uncertainty Propagation
187(23)
7.5.1 Generalized Polynomial Chaos
187(4)
7.5.2 Arbitrary Generalized Polynomial Chaos
191(13)
7.5.3 Multi-element Generalized Polynomial Chaos
204(6)
7.6 Graphics Process Unit aided Uncertainty Propagation
210(1)
7.7 MapReduce aided Uncertainty Propagation
211(3)
7.8 Summary
214(1)
References
214(3)
8 Application: Tracking and Navigation
217(32)
8.1 Single Target Tracking
217(10)
8.2 Multiple Target Tracking
227(4)
8.2.1 Nearest Neighbor Filter
227(1)
8.2.2 Probabilistic Data Association Filter
228(3)
8.3 Spacecraft Relative Navigation
231(13)
8.4 Summary
244(1)
References
245(4)
Index 249
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. Jias 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.
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