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Optimal State Estimation Kalman, H Infinity, and Nonlinear Approaches

ISBN-10: 0471708585
ISBN-13: 9780471708582
Edition: 2006
Authors: Dan Simon
List price: $157.00 Buy it from $133.01
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Description: Dan Simon presents a clear and lucid presentation of the technically difficult area of state estimation. In addition to the basic theory of state estimation, the text presents recent research results in a way that is both mathematically rigorous and  More...

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Book details

List price: $157.00
Copyright year: 2006
Publisher: John Wiley & Sons, Incorporated
Publication date: 6/23/2006
Binding: Hardcover
Pages: 552
Size: 7.25" wide x 10.00" long x 1.00" tall
Weight: 1.672
Language: English

Dan Simon presents a clear and lucid presentation of the technically difficult area of state estimation. In addition to the basic theory of state estimation, the text presents recent research results in a way that is both mathematically rigorous and practical.

Dan Simon is Professor of Law and Psychology at the University of Southern California.

Acknowledgments
Acronyms
List of algorithms
Introduction
Introductory Material
Linear systems theory
Matrix algebra and matrix calculus
Matrix algebra
The matrix inversion lemma
Matrix calculus
The history of matrices
Linear systems
Nonlinear systems
Discretization
Simulation
Rectangular integration
Trapezoidal integration
Runge-Kutta integration
Stability
Continuous-time systems
Discrete-time systems
Controllability and observability
Controllability
Observability
Stabilizability and detectability
Summary
Problems
Probability theory
Probability
Random variables
Transformations of random variables
Multiple random variables
Statistical independence
Multivariate statistics
Stochastic Processes
White noise and colored noise
Simulating correlated noise
Summary
Problems
Least squares estimation
Estimation of a constant
Weighted least squares estimation
Recursive least squares estimation
Alternate estimator forms
Curve fitting
Wiener filtering
Parametric filter optimization
General filter optimization
Noncausal filter optimization
Causal filter optimization
Comparison
Summary
Problems
Propagation of states and covariances
Discrete-time systems
Sampled-data systems
Continuous-time systems
Summary
Problems
The Kalman Filter
The discrete-time Kalman filter
Derivation of the discrete-time Kalman filter
Kalman filter properties
One-step Kalman filter equations
Alternate propagation of covariance
Multiple state systems
Scalar systems
Divergence issues
Summary
Problems
Alternate Kalman filter formulations
Sequential Kalman filtering
Information filtering
Square root filtering
Condition number
The square root time-update equation
Potter's square root measurement-update equation
Square root measurement update via triangularization
Algorithms for orthogonal transformations
U-D filtering
U-D filtering: The measurement-update equation
U-D filtering: The time-update equation
Summary
Problems
Kalman filter generalizations
Correlated process and measurement noise
Colored process and measurement noise
Colored process noise
Colored measurement noise: State augmentation
Colored measurement noise: Measurement differencing
Steady-state filtering
[alpha]-[beta] filtering
[alpha]-[beta]-[gamma] filtering
A Hamiltonian approach to steady-state filtering
Kalman filtering with fading memory
Constrained Kalman filtering
Model reduction
Perfect measurements
Projection approaches
A pdf truncation approach
Summary
Problems
The continuous-time Kalman filter
Discrete-time and continuous-time white noise
Process noise
Measurement noise
Discretized simulation of noisy continuous-time systems
Derivation of the continuous-time Kalman filter
Alternate solutions to the Riccati equation
The transition matrix approach
The Chandrasekhar algorithm
The square root filter
Generalizations of the continuous-time filter
Correlated process and measurement noise
Colored measurement noise
The steady-state continuous-time Kalman filter
The algebraic Riccati equation
The Wiener filter is a Kalman filter
Duality
Summary
Problems
Optimal smoothing
An alternate form for the Kalman filter
Fixed-point smoothing
Estimation improvement due to smoothing
Smoothing constant states
Fixed-lag smoothing
Fixed-interval smoothing
Forward-backward smoothing
RTS smoothing
Summary
Problems
Additional topics in Kalman filtering
Verifying Kalman filter performance
Multiple-model estimation
Reduced-order Kalman filtering
Anderson's approach to reduced-order filtering
The reduced-order Schmidt-Kalman filter
Robust Kalman filtering
Delayed measurements and synchronization errors
A statistical derivation of the Kalman filter
Kalman filtering with delayed measurements
Summary
Problems
The H[subscript infinity] Filter
The H[subscript infinity] filter
Introduction
An alternate form for the Kalman filter
Kalman filter limitations
Constrained optimization
Static constrained optimization
Inequality constraints
Dynamic constrained optimization
A game theory approach to H[subscript infinity] filtering
Stationarity with respect to x[subscript 0] and w[subscript k]
Stationarity with respect to x and y
A comparison of the Kalman and H[subscript infinity] filters
Steady-state H[subscript infinity] filtering
The transfer function bound of the H[subscript infinity] filter
The continuous-time H[subscript infinity] filter
Transfer function approaches
Summary
Problems
Additional topics in H[subscript infinity] filtering
Mixed Kalman/H[subscript infinity] filtering
Robust Kalman/H[subscript infinity] filtering
Constrained H[subscript infinity] filtering
Summary
Problems
Nonlinear Filters
Nonlinear Kalman filtering
The linearized Kalman filter
The extended Kalman filter
The continuous-time extended Kalman filter
The hybrid extended Kalman filter
The discrete-time extended Kalman filter
Higher-order approaches
The iterated extended Kalman filter
The second-order extended Kalman filter
Other approaches
Parameter estimation
Summary
Problems
The unscented Kalman filter
Means and covariances of nonlinear transformations
The mean of a nonlinear transformation
The covariance of a nonlinear transformation
Unscented transformations
Mean approximation
Covariance approximation
Unscented Kalman filtering
Other unscented transformations
General unscented transformations
The simplex unscented transformation
The spherical unscented transformation
Summary
Problems
The particle filter
Bayesian state estimation
Particle filtering
Implementation issues
Sample impoverishment
Particle filtering combined with other filters
Summary
Problems
Historical perspectives
Other books on Kalman filtering
State estimation and the meaning of life
References
Index

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