Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches (Hardcover)
暫譯: 最佳狀態估計：卡爾曼、H 無窮大及非線性方法 (精裝版)

Dan Simon

Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches (Hardcover)
  • 出版商: Wiley
  • 出版日期: 2006-06-01
  • 售價: $5,730
  • 貴賓價: 9.5 折 $5,444
  • 語言: 英文
  • 頁數: 552
  • 裝訂: Hardcover
  • ISBN: 0471708585
  • ISBN-13: 9780471708582

    • 已絕版

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Description

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.

A solutions manual is available upon request from the Wiley editorial board

Table of Contents

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.

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.

商品描述(中文翻譯)

**描述**
一種自下而上的方法，使讀者能夠掌握並應用最新的狀態估計技術。
本書提供了估計一般系統狀態的最佳數學方法。作者清晰而嚴謹地介紹了狀態估計理論，提供了適量的進階材料、近期研究成果和參考文獻，使讀者能夠自信地在科學和工程的各個領域應用狀態估計技術。
雖然有其他教科書也涉及狀態估計，但本書提供了特殊的特點和獨特的視角及教學方法，加速學習：
* 直接的自下而上的方法，從基本概念開始，然後逐步構建到更高級的主題，以清晰理解狀態估計。
* 只需紙和筆即可解決的簡單範例和問題，導致對理論在實踐中如何運作的直觀理解。
* 基於MATLAB(r)的源代碼對應於書中的範例，並可在作者的網站上獲得，使讀者能夠重現結果並實驗其他模擬設置和參數。

在掌握基礎知識的基礎上，讀者將接觸到對進階主題的仔細處理，包括無味濾波、高階非線性濾波、粒子濾波、約束狀態估計、降階濾波、穩健的卡爾曼濾波和混合卡爾曼/濾波。
每章結尾的問題包括書面練習和計算機練習。書面練習專注於提高讀者對理論和關鍵概念的理解，而計算機練習則幫助讀者將理論應用於類似於他們在行業中可能遇到的問題。解答手冊可供教師使用。
憑藉其理論與實踐的專業結合，以及對近期研究成果的呈現，《最佳狀態估計》強烈推薦用於本科和研究生層次的最佳控制和狀態估計理論課程。它也作為各行各業工程師和科學專業人士的參考資料。
解答手冊可根據要求向Wiley編輯部索取。

**目錄**
致謝。
縮寫詞。
算法列表。
導言。
第一部分 介紹材料。
1 線性系統理論。
1.1 矩陣代數和矩陣微積分。
1.1.1 矩陣代數。
1.1.2 矩陣反演引理。
1.1.3 矩陣微積分。
1.1.4 矩陣的歷史。
1.2 線性系統。
1.3 非線性系統。
1.4 離散化。
1.5 模擬。
1.5.1 矩形積分。
1.5.2 梯形積分。
1.5.3 龍格-庫塔積分。
1.6 穩定性。
1.6.1 連續時間系統。
1.6.2 離散時間系統。
1.7 可控性和可觀性。
1.7.1 可控性。
1.7.2 可觀性。
1.7.3 穩定性和可檢測性。
1.8 總結。
問題。
概率論。
2.1 概率。
2.2 隨機變量。
2.3 隨機變量的變換。
2.4 多個隨機變量。
2.4.1 統計獨立性。
2.4.2 多變量統計。
2.5 隨機過程。
2.6 白噪聲和有色噪聲。
2.7 模擬相關噪聲。
2.8 總結。
問題。
3 最小二乘估計。
3.1 常數的估計。
3.2 加權最小二乘估計。
3.3 遞歸最小二乘估計。
3.3.1 替代估計器形式。
3.3.2 曲線擬合。
3.4 威納濾波。
3.4.1 參數濾波器優化。
3.4.2 一般濾波器優化。
3.4.3 非因果濾波器優化。
3.4.4 因果濾波器優化。
3.4.5 比較。
3.5 總結。
問題。
4 狀態和協方差的傳播。
4.1 離散時間系統。
4.2 取樣數據系統。
4.3 連續時間系統。
4.4 總結。
問題。
第二部分 卡爾曼濾波。
5 離散時間卡爾曼濾波。
5.1 離散時間卡爾曼濾波的推導。
5.2 卡爾曼濾波的特性。
5.3 一步卡爾曼濾波方程。
5.4 協方差的替代傳播。
5.4.1 多狀態系統。
5.4.2 標量系統。
5.5 發散問題。
5.6 總結。
問題。
6 替代卡爾曼濾波公式。
6.1 順序卡爾曼濾波。
6.2 信息濾波。
6.3 平方根濾波。
6.3.1 條件數。
6.3.2 平方根時間更新方程。
6.3.3 波特的平方根測量更新方程。
6.3.4 通過三角化的平方根測量更新。
6.3.5 正交變換的算法。
6.4 U-D濾波。
6.4.1 U-D濾波：測量更新方程。
6.4.2 U-D濾波：時間更新方程。
6.5 總結。
問題。
7 卡爾曼濾波的概括。
7.1 相關的過程和測量噪聲。
7.2 有色過程和測量噪聲。
7.2.1 有色過程噪聲。
7.2.2 有色測量噪聲：狀態擴增。
7.2.3 有色測量噪聲：測量差分。
7.3 穩態濾波。
7.3.1 a-P濾波。
7.3.2 a-P-y濾波。
7.3.3 一種哈密頓方法的穩態濾波。
7.4 帶衰減記憶的卡爾曼濾波。
7.5 約束卡爾曼濾波。
7.5.1 模型降維。
7.5.2 完美測量。
7.5.3 投影方法。
7.5.4 一種pdf截斷方法。
7.6 總結。
問題。
8 連續時間卡爾曼濾波。
8.1 離散時間和連續時間白噪聲。
8.1.1 過程噪聲。
8.1.2 測量噪聲。
8.1.3 含噪連續時間系統的離散化模擬。
8.2 連續時間卡爾曼濾波的推導。
8.3 Riccati方程的替代解。
8.3.1 轉移矩陣方法。
8.3.2 Chandrasekhar算法。
8.3.3 平方根濾波器。
8.4 連續時間濾波的概括。
8.4.1 相關的過程和測量噪聲。
8.4.2 有色測量噪聲。
8.5 穩態連續時間卡爾曼濾波。
8.5.1 代數Riccati方程。
8.5.2 威納濾波器是卡爾曼濾波器。
8.5.3 對偶性。
8.6 總結。
問題。
9 最佳平滑。
9.1 卡爾曼濾波的替代形式。
9.2 固定點平滑。
9.2.1 由於平滑而改善的估計。
9.2.2 平滑常數狀態。
9.3 固定延遲平滑。
9.4 固定區間平滑。
9.4.1 前向-後向平滑。
9.4.2 RTS平滑。
9.5 總結。
問題。

作者簡介

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.

作者簡介(中文翻譯)

丹·西蒙（DAN SIMON），博士，是克里夫蘭州立大學的副教授。在此之前，西蒙博士曾在波音（Boeing）、TRW 及幾家較小的公司工作了十四年。

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