作者简介:
Dan Simon博士是克利夫兰州立大学的副教授。在此之前,他曾在Boeing, TRW等公司工作过14年。
内容简介:
本书采用自下而上的方法,使读者能够掌握并应用最新的状态估计技术。作者清晰严谨地呈现了状态估计的理论,提供了适量的有价值的材料、最新的研究成果以及能使读者信心十足地应用状态估计技术于科学和工程中的引文材料。
本书具有以下独特的特点:
以简单的、自下而上的方法从基本概念讲起,然后一步步生成并使读者清楚地了解状态估计的更高级主题;
用简单的例子和问题使读者只需笔和纸就可了解理论在实践中是如何应用的;
与书中例子对应的基于MATLAB(r)的源代码可在作者的网站上找到,读者可以对其重新创建结果,并可重新设置参数模拟
试验。
有了坚实的基础以后,读者可进一步考虑其它的问题,包括U-滤波、高阶非线性滤波、粒子滤波、约束状态估计、降阶滤波、鲁棒卡尔曼滤波,
以及混合卡尔曼/H∞滤波等。
每一章末尾的问题包括书面的练习和计算机演习。书面练习可以帮助读者理解书中的理论和关键的概念,而计算机演习可以帮助读者将理论应用于那些他们可能在行业中遇到的类似问题。
本书既有理论和实践的结合,又有最新研究成果的介绍,既可作为本科和研究生的课程教材,也可作为工程科学及其它领域的专业人士的参考书。
英文目录:
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 Runge-Kutta integration
1.6 Stability
1.6.1 Continuous-time systems
1.6.2 Discrete-time 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 Discrete-time 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-β filtering
7.3.2 a-β-γ 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 x0 and wk
11.3.2 Stationarity with respect to 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 Kalman/H∞ 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