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Optimal State Estimation - Kalman, H Infinity and Nonlinear Approaches de Dan Simon

Optimal State Estimation - Kalman, H Infinity and Nonlinear Approaches

Autor Dan Simon
en Limba Engleză Hardback – 21 iul 2006

Actualizarea esențială pe care o aduce Optimal State Estimation rezidă în rigoarea cu care integrează rezultatele cercetărilor recente într-o structură didactică progresivă, facilitând tranziția de la teoria pură la implementarea industrială. Reținem că, spre deosebire de manualele clasice care pot deveni abstracte, Dan Simon adoptă o abordare „bottom-up”, construind competențele cititorului treaptă cu treaptă. Putem afirma că volumul excelează prin echilibrul dintre demonstrațiile matematice și exemplele practice care pot fi rezolvate, inițial, doar cu creionul pe hârtie pentru a consolida intuiția. Ca și John L. Crassidis în Optimal Estimation of Dynamic Systems, autorul distilează experiență reală în principii acționabile, însă pune un accent deosebit pe versatilitatea algoritmilor. În contextul operei sale, această lucrare reflectă aceeași claritate metodologică regăsită în Evolutionary Optimization Algorithms, demonstrând capacitatea lui Dan Simon de a descompune sistemele complexe în componente logice. Merită menționat că textul acoperă teme de frontieră, cum ar fi filtrarea „unscented”, filtrarea Kalman robustă și abordările mixte Kalman/H-infinit, oferind astfel instrumente pentru gestionarea incertitudinilor în sisteme dinamice complexe. Spre deosebire de Introduction to Random Signals, Estimation Theory, and Kalman Filtering de M. Sami Fadali, care se concentrează pe fundalul statistic, volumul de față prioritizează tehnicile de estimare de ultimă oră și simularea prin cod MATLAB. Această simbioză între teorie și suportul software permite inginerilor să experimenteze direct cu parametrii de simulare, transformând o disciplină dificilă într-un set de instrumente pragmatice pentru electronică și comunicații.

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Specificații

ISBN-13: 9780471708582
ISBN-10: 0471708585
Pagini: 552
Ilustrații: Illustrations
Dimensiuni: 183 x 260 x 34 mm
Greutate: 1.23 kg
Editura: John Wiley & Sons, Inc.
Locul publicării:Hoboken, United States

Public țintă

Particularly those studying Optimal control courses.

De ce să citești această carte

Această carte este indispensabilă studenților de la masterat și inginerilor care doresc să stăpânească tehnicile moderne de estimare a stării. Cititorul câștigă nu doar o bază teoretică solidă, ci și capacitatea de a implementa algoritmi complecși, precum filtrele de particule sau filtrele Kalman robuste, direct în proiecte de inginerie, datorită exemplelor MATLAB incluse și abordării practice orientate spre rezultate.

Despre autor

Dan Simon este un autor și cercetător recunoscut pentru capacitatea sa de a explica algoritmi complecși prin abordări pedagogice inovatoare. Cu o vastă experiență academică, acesta activează în cadrul universităților de prestigiu, fiind specializat în sisteme de control și optimizare. Pe lângă lucrarea de față, a publicat titluri fundamentale precum Evolutionary Optimization Algorithms, unde explorează inteligența artificială inspirată din natură. Expertiza sa multidisciplinară, ce îmbină ingineria electronică cu tehnici avansate de comunicație, se reflectă în rigoarea și claritatea expunerii din toate manualele sale tehnice.

Descriere scurtă

A bottom-up approach that enables readers to master and apply the latest techniques in state estimation This book offers the best mathematical approaches to estimating the state of a general system. The author presents state estimation theory clearly and rigorously, providing the right amount of advanced material, recent research results, and references to enable the reader to apply state estimation techniques confidently across a variety of fields in science and engineering. While there are other textbooks that treat state estimation, this one offers special features and a unique perspective and pedagogical approach that speed learning: * Straightforward, bottom-up approach begins with basic concepts and then builds step by step to more advanced topics for a clear understanding of state estimation * Simple examples and problems that require only paper and pen to solve lead to an intuitive understanding of how theory works in practice * MATLAB(r)-based source code that corresponds to examples in the book, available on the author's Web site, enables readers to recreate results and experiment with other simulation setups and parameters Armed with a solid foundation in the basics, readers are presented with a careful treatment of advanced topics, including unscented filtering, high order nonlinear filtering, particle filtering, constrained state estimation, reduced order filtering, robust Kalman filtering, and mixed Kalman/H? filtering. Problems at the end of each chapter include both written exercises and computer exercises. Written exercises focus on improving the reader's understanding of theory and key concepts, whereas computer exercises help readers apply theory to problems similar to ones they are likely to encounter in industry. A solutions manual is available for instructors. With its expert blend of theory and practice, coupled with its presentation of recent research results, Optimal State Estimation is strongly recommended for undergraduate and graduate-level courses in optimal control and state estimation theory. It also serves as a reference for engineers and science professionals across a wide array of industries.

Notă biografică

DAN SIMON, PhD, is an Associate Professor at Cleveland State University. Prior to this appointment, Dr. Simon spent fourteen years working for such firms as Boeing, TRW, and several smaller companies.

Cuprins

Acknowledgments. Acronyms.
List of algorithms.
Introduction.
PART I INTRODUCTORY MATERIAL.
1 Linear systems theory.
1.1 Matrix algebra and matrix calculus.
1.1.1 Matrix algebra.
1.1.2 The matrix inversion lemma.
1.1.3 Matrix calculus.
1.1.4 The history of matrices.
1.2 Linear systems.
1.3 Nonlinear systems.
1.4 Discretization.
1.5 Simulation.
1.5.1 Rectangular integration.
1.5.2 Trapezoidal integration.
1.5.3 RungeKutta integration.
1.6 Stability.
1.6.1 Continuous-time systems.
1.6.2 Discretetime systems.
1.7 Controllability and observability.
1.7.1 Controllability.
1.7.2 Observability.
1.7.3 Stabilizability and detectability.
1.8 Summary.
Problems.
2 Probability theory.
2.1 Probability.
2.2 Random variables.
2.3 Transformations of random variables.
2.4 Multiple random variables.
2.4.1 Statistical independence.
2.4.2 Multivariate statistics.
2.5 Stochastic Processes.
2.6 White noise and colored noise.
2.7 Simulating correlated noise.
2.8 Summary.
Problems.
3 Least squares estimation.
3.1 Estimation of a constant.
3.2 Weighted least squares estimation.
3.3 Recursive least squares estimation.
3.3.1 Alternate estimator forms.
3.3.2 Curve fitting.
3.4 Wiener filtering.
3.4.1 Parametric filter optimization.
3.4.2 General filter optimization.
3.4.3 Noncausal filter optimization.
3.4.4 Causal filter optimization.
3.4.5 Comparison.
3.5 Summary.
Problems.
4 Propagation of states and covariances.
4.1 Discretetime systems.
4.2 Sampled-data systems.
4.3 Continuous-time systems.
4.4 Summary.
Problems.
PART II THE KALMAN FILTER.
5 The discrete-time Kalman filter.
5.1 Derivation of the discrete-time Kalman filter.
5.2 Kalman filter properties.
5.3 One-step Kalman filter equations.
5.4 Alternate propagation of covariance.
5.4.1 Multiple state systems.
5.4.2 Scalar systems.
5.5 Divergence issues.
5.6 Summary.
Problems.
6 Alternate Kalman filter formulations.
6.1 Sequential Kalman filtering.
6.2 Information filtering.
6.3 Square root filtering.
6.3.1 Condition number.
6.3.2 The square root time-update equation.
6.3.3 Potter's square root measurement-update equation.
6.3.4 Square root measurement update via triangularization.
6.3.5 Algorithms for orthogonal transformations.
6.4 U-D filtering.
6.4.1 U-D filtering: The measurement-update equation.
6.4.2 U-D filtering: The time-update equation.
6.5 Summary.
Problems.
7 Kalman filter generalizations.
7.1 Correlated process and measurement noise.
7.2 Colored process and measurement noise.
7.2.1 Colored process noise.
7.2.2 Colored measurement noise: State augmentation.
7.2.3 Colored measurement noise: Measurement differencing.
7.3 Steady-state filtering.
7.3.1 a-P filtering.
7.3.2 a-P-y filtering.
7.3.3 A Hamiltonian approach to steady-state filtering.
7.4 Kalman filtering with fading memory.
7.5 Constrained Kalman filtering.
7.5.1 Model reduction.
7.5.2 Perfect measurements.
7.5.3 Projection approaches.
7.5.4 A pdf truncation approach.
7.6 Summary.
Problems.
8 The continuous-time Kalman filter.
8.1 Discrete-time and continuous-time white noise.
8.1.1 Process noise.
8.1.2 Measurement noise.
8.1.3 Discretized simulation of noisy continuous-time systems.
8.2 Derivation of the continuous-time Kalman filter.
8.3 Alternate solutions to the Riccati equation.
8.3.1 The transition matrix approach.
8.3.2 The Chandrasekhar algorithm.
8.3.3 The square root filter.
8.4 Generalizations of the continuous-time filter.
8.4.1 Correlated process and measurement noise.
8.4.2 Colored measurement noise
8.5 The steady-state continuous-time Kalman filter
8.5.1 The algebraic Riccati equation.
8.5.2 The Wiener filter is a Kalman filter.
8.5.3 Duality.
8.6 Summary.
Problems.
9 Optimal smoothing.
9.1 An alternate form for the Kalman filter.
9.2 Fixed-point smoothing.
9.2.1 Estimation improvement due to smoothing.
9.2.2 Smoothing constant states.
9.3 Fixed-lag smoothing.
9.4 Fixed-interval smoothing.
9.4.1 Forward-backward smoothing.
9.4.2 RTS smoothing.
9.5 Summary.
Problems.
10 Additional topics in Kalman filtering.
10.1 Verifying Kalman filter performance.
10.2 Multiple-model estimation.
10.3 Reduced-order Kalman filtering.
10.3.1 Anderson's approach to reduced-order filtering.
10.3.2 The reduced-order Schmidt-Kalman filter.
10.4 Robust Kalman filtering.
10.5 Delayed measurements and synchronization errors.
10.5.1 A statistical derivation of the Kalman filter.
10.5.2 Kalman filtering with delayed measurements.
10.6 Summary.
Problems.
PART III THE H, FILTER.
11 The H, filter.
11.1 Introduction.
11.1.1 An alternate form for the Kalman filter.
11.1.2 Kalman filter limitations.
11.2 Constrained optimization.
11.2.1 Static constrained optimization.
11.2.2 Inequality constraints.
11.2.3 Dynamic constrained optimization.
11.3 A game theory approach to H, filtering.
11.3.1 Stationarity with respect to xo and wk.
11.3.2 Stationarity with respect to 2 and y.
11.3.3 A comparison of the Kalman and H, filters.
11.3.4 Steady-state H, filtering.
11.3.5 The transfer function bound of the H, filter.
11.4 The continuous-time H, filter.
11.5 Transfer function approaches.
11.6 Summary.
Problems.
12 Additional topics in H, filtering.
12.1 Mixed KalmanIH, filtering.
12.2 Robust Kalman/H, filtering.
12.3 Constrained H, filtering.
12.4 Summary.
Problems.
PART IV NONLINEAR FILTERS.
13 Nonlinear Kalman filtering.
13.1 The linearized Kalman filter.
13.2 The extended Kalman filter.
13.2.1 The continuous-time extended Kalman filter.
13.2.2 The hybrid extended Kalman filter.
13.2.3 The discrete-time extended Kalman filter.
13.3 Higher-order approaches.
13.3.1 The iterated extended Kalman filter.
13.3.2 The second-order extended Kalman filter.
13.3.3 Other approaches.
13.4 Parameter estimation.
13.5 Summary.
Problems.
14 The unscented Kalman filter.
14.1 Means and covariances of nonlinear transformations.
14.1.1 The mean of a nonlinear transformation.
14.1.2 The covariance of a nonlinear transformation.
14.2 Unscented transformations.
14.2.1 Mean approximation.
14.2.2 Covariance approximation.
14.3 Unscented Kalman filtering.
14.4 Other unscented transformations.
14.4.1 General unscented transformations.
14.4.2 The simplex unscented transformation.
14.4.3 The spherical unscented transformation.
14.5 Summary.
Problems.
15 The particle filter.
15.1 Bayesian state estimation.
15.2 Particle filtering.
15.3 Implementation issues.
15.3.1 Sample impoverishment.
15.3.2 Particle filtering combined with other filters.
15.4 Summary.
Problems.
Appendix A: Historical perspectives.
Appendix B: Other books on Kalman filtering.
Appendix C: State estimation and the meaning of life.
References.
Index.