Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches / Edition 1

Hardcover (Print)
Buy New
Buy New from BN.com
Used and New from Other Sellers
Used and New from Other Sellers
from $82.09
Usually ships in 1-2 business days
(Save 45%)
Other sellers (Hardcover)
  • All (13) from $82.09   
  • New (9) from $87.99   
  • Used (4) from $82.09   


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. 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.

Read More Show Less

Editorial Reviews

From the Publisher
"This book is obviously written with care and reads very easily. A very valuable resource for students, teachers, and practitioners…highly recommended." (CHOICE, February 2007)

"The dozens of helpful step-by-step examples, visual illustrations, and lists of exercises proposed at the end of each chapter significantly facilitate a reader's understanding of the book's content." (Computing Reviews.com, December 4, 2006)

Read More Show Less

Product Details

  • ISBN-13: 9780471708582
  • Publisher: Wiley
  • Publication date: 6/23/2006
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 552
  • Sales rank: 548,221
  • Product dimensions: 7.20 (w) x 10.04 (h) x 1.23 (d)

Meet the Author

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.

Read More Show Less

Table of Contents



List of algorithms.



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.


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.


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.


4 Propagation of states and covariances.

4.1 Discretetime systems.

4.2 Sampled-data systems.

4.3 Continuous-time systems.

4.4 Summary.



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.


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.


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.


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.


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.


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.



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.


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.



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.


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.


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.


Appendix A: Historical perspectives.

Appendix B: Other books on Kalman filtering.

Appendix C: State estimation and the meaning of life.



Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)