Optimal State Estimation

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.

Autorentext
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.

Zusammenfassung
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.

Inhalt
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...