最优状态估计 卡尔曼，H∞及非线性滤波英文原版，国外经典教材，非常值得学习和收藏，讲解详细具体容易理解，适合初学者，也可作为工程技术人员参考书。Copyright o 2006 by John Wiley sons, Inc. 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For information about wiley products, visit our web site atwww.wiley.comLibrary of Congress Cataloging-in-Publication is available.ISBN-139780471-708582ISBN-100-471-70858-5Printed in the United States of america10987654321CONTENTSAcknowledgmentsXIIlAcronymsXVList of algorithmsXVIlIntroductionPART INTRODUCTORY MATERIAL1 Linear systems theory1.1 Matrix algebra and matrix calculus41. 1. 1 Matrix algebra61.1.2 The matrix inversion lemma1.1.3 Matrix calculus141.1.4 The history of matrices171.2 Linear systems181.3 Nonlinear systems221.4 Discretization261.5 Simulation271.5. 1 Rectangular integration1.5.2 Trapezoidal integration1.5.3 Runge-Kutta integration311.6 Stabilit33CONTENTS1.6.1 Continuous-time systems331.6.2 Discrete-time systems1.7 Controllability and observability1.7.1 Controllability8801.7.2 Observability1.7.3 Stabilizability and detectability8 Summary45Problems452 Probability theory492.1 Probability502.2 Random variables532.3 Transformations of random variables592.4 Multiple random variables612.4.1 Statistical independence622.4.2 Multivariate statistics652.5 Stochastic Processes2.6 White noise and colored noise2.7 Simulating correlated noise2. 8 Summary74Problems3 Least squares estimation793.1 Estimation of a constant3.2 Weighted least squares estimation823. 3 Recursive least squares estimation4.3.1 Alternate estimator forms3.3.2 Curve fitting3.4 Wiener filtering943.4.1 Parametric filter optimization63.4.2 General filter optimization973.4.3 Noncausal filter optimization983. 4.4 Causal filter optimization003.4.5 Comparison1013.5 Summary102Proble1024 Propagation of states and covariances10774.1 Discrete-time systems4.2 Sampled-data systems1114.3 Continuous-time systems114CONTENTS4.4 Summary117Problems117PART THE KALMAN FILTER5 The discrete-time Kalman filter1235.1 Derivation of the discrete-time Kalman filter1245.2 Kalman filter properties1295. 3 One-step Kalman filter equations1315.4 Alternate propagation of covariance1355.4.1 Multiple state systems1355.4.2 Scalar systems1375.5 Divergence issues1395.6 Summary144Problems1456 Alternate Kalman filter formulations1496. 1 Sequential Kalman filtering1506.2 Information filtering1566. 3 Square root filtering1586.3.1 Condition number1596.3.2 The square root time-update equation1626.3.3 Potters square root measurement-update equation1656.3.4 Square root measurement update via triangularization1696.3.5 Algorithms for orthogonal transformations6.4 U-D filtering1746.4.1 U-D iltering: The measurement-update equation1746.4.2 U-D filtering: The time-update equation1766.5 Summary178Problems1797 Kalman filter generalizations1837. 1 Correlated process and measurement noise1847. 2 Colored process and measurement noise1887.2.1 Colored process noise1887.2.2 Colored measurement noise: State augmentation1897.2. 3 Colored measurement noise: Measurement differencing1907. 3 Steady-state filtering1937.3.1 a-B filtering1997.3.2 a-By filtering2027.3.3 A Hamiltonian approach to steady-state filtering2037.4 Kalman filtering with fading memory208CONTENTS7.5 Constrained Kalman filtering2127.5.1 Model reduction2127.5.2 Perfect measurements2137.5. 3 Projection approaches2147.5.4 A pdf truncation approach2187.6 Summary223Problems2258 The continuous-time Kalman filter2298.1 Discrete-time and continuous-time white noise2308. 1. 1 Process noise2308.1.2 Measurement noise2328. 1.3 Discretized simulation of noisy continuous-time systems2328.2 Derivation of the continuous-time Kalman filter2338. 3 Alternate solutions to the Riccati equation2388.3. 1 The transition matrix approach2388.3.2 The Chandrasekhar algorithm2428.3.3 The square root filter2468.4 Generalizations of the continuous-time filter2478.4.1 Correlated process and measurement noise2488. 4.2 Colored measurement noise2498.5 The steady-state continuous-time Kalman filter2528.5. 1 The algebraic Riccati equation2538.5.2 The Wiener filter is a Kalman filter2578.5.3 Duality2588.6 Summary259Problems2609 Optimal smoothing2639.1 An alternate form for the Kalman filter2659.2 Fixed-point smoothing2679.2.1 Estimation improvement due to smoothing2709.2.2 Smoothing constant states2749.3 Fixed-lag smoothing2749.4 Fixed-interval smoothing2799.4.1 Forward-backward smoothing2809.4.2 RTS smoothing2869.5 Summary294Problems294CONTENTS10 Additional topics in Kalman filtering29710. 1 Verifying Kalman filter performance29810.2 Multiple-model estimation30110.3 Reduced-order Kalman filtering30510. 3. 1 Andersons approach to reduced-order filtering30610.3.2 The reduced-order Schmidt-Kalman filter30910.4 Robust Kalman filtering31210.5 Delayed measurements and synchronization errors31710.5.1 A statistical derivation of the Kalman filter31810.5.2 Kalman filtering with delayed measurements32010.6 Summary325Problems326PART川THEH。 FILTER11 The H filter33311.1 Introduction33411.1.1 An alternate form for the Kalman filter33411.1.2 Kalman flter limitations33611. 2 Constrained optimization33711.2.1 Static constrained optimization33711.2.2 Inequality constraints33911.2. 3 Dynamic constrained optimization34111. 3 A game theory approach to Hoo filtering34311.3.1 Stationarity with respect to o and wk34511.3.2 Stationarity with respect to i and y34711.3.3 A comparison of the Kalman and Hoo filters35411.3.4 Steady-state Hoo filtering35411.3.5 The transfer function bound of the ho filter35711.4 The continuous-time Hoo filter36111.5 Transfer function approaches36511. 6 Summar367Problems36912 Additional topics in Hoo filtering37312.1 Mixed Kalman/Hoo fltering37412.2 Robust Kalman Hoo filtering37712.3 Constrained Hoo filtering38112.4 Summary388Problems389CONTENTSPART V NONLINEAR FILTERS13 Nonlinear Kalman filtering39513. 1 The linearized kalman filter39713.2 The extended Kalman filter40013.2.1 The continuous-time extended Kalman filter40013. 2. 2 The hybrid extended Kalman filter40313.2.3 The discrete-time extended Kalman filter40713.3 Higher-order approaches41013.3.1 The iterated extended Kalman filter41013.3, 2 The second-order extended Kalman flter41313.3.3 Other approaches4203.4 Parameter estimation42213.5 Summar2Problems42614 The unscented Kalman filter43314.1 Means and covariances of nonlinear transformations43414.1.1 The mean of a nonlinear transformation14.1.2 The covariance of a nonlinear transformation43714.2 Unscented transformations44114.2.1 Mean approximation44114.2.2 Covariance approximation44414.3 Unscented Kalman Altering14.4 Other unscented transformations45214.4.1 General unscented transformations45214.4.2 The simplex unscented transformation45414.4.3 The spherical unscented transformation45514.5 Summary457Problems45815 The particle filter4615.1 Bayesian state estimation46215.2 Particle filtering46615.3 Implementation issues46915. 3. 1 Sample impoverishment46915.3.2 Particle filtering combined with other filters47715.4 Summary480roblems481CONTENTS XIAppendix A: Historical perspectives485Appendix B: Other books on Kalman filtering489Appendix C: State estimation and the meaning of life493References501Index521