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Filtering for Stochastic Processes with Applications to Guidance: Second Edition
 
Richard S. Bucy
Peter D. Joseph
Filtering for Stochastic Processes with Applications to Guidance
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
eBook ISBN:  978-1-4704-6771-5
Product Code:  CHEL/326.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Add to cart
Filtering for Stochastic Processes with Applications to Guidance
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Filtering for Stochastic Processes with Applications to Guidance: Second Edition
Richard S. Bucy
Peter D. Joseph
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
eBook ISBN:  978-1-4704-6771-5
Product Code:  CHEL/326.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Add to cart
  • Book Details
     
     
    AMS Chelsea Publishing
    Volume: 326; 1987; 217 pp
    MSC: Primary 93

    This second edition preserves the original text of 1968, with clarification and added references.

    From the Preface to the Second Edition: “Since the First Edition of this book, numerous important results have appeared—in particular stochastic integrals with respect to martingales, random fields, Riccati equation theory and realization of nonlinear filters, to name a few. In Appendix D, an attempt is made to provide some of the references that the authors have found useful and to comment on the relation of the cited references to the field ... [W]e hope that this new edition will have the effect of hastening the day when the nonlinear filter will enjoy the same popularity in applications as the linear filter does now.”
  • Table of Contents
     
     
    • Front Cover
    • Preface to the Second Edition
    • Preface to the First Edition
    • Acknowledgments
    • Contents
    • Notation
    • PART I: THEORY
    • CHAPTER I: Ordinary Differential Equations and Stability
    • Differential Equations
    • Stability Theory
    • CHAPTER II: Random Processes and Stochastic Models
    • Introduction
    • Random Variables and Processes
    • Random Differential Equations
    • Linear Models
    • Dynamical Models
    • CHAPTER III: Observability and Controllability
    • Introduction
    • Observability and Controllability
    • Canonical Forms
    • Stochastic Modelling
    • CHAPTER IV: Filtering Theory
    • Introduction
    • The Minimum Variance Unbiased Estimator
    • Function Space Integrals for the Conditional Distribution
    • Alternative Approaches for the Linear Estimation Problem
    • Linear and Non-Linear Filtering in Discrete Time
    • "Wide-Sense" Solution of the Linear Filtering Problem
    • CHAPTER V: Global Theory of Filtering
    • Introduction
    • Properties of the Riccati Equation
    • Exponential Stability
    • Examples and Problems
    • Effects of Errors in Optimal Gains
    • A Table of Results for the Asymptotic Theory
    • CHAPTER VI: Stochastic Stability
    • Information and Filtering
    • CHAPTER VII: Optimal Filtering for Correlated Noise Processes
    • lntroduction
    • Filtering for Colored Noise
    • CHAPTER VIII: Approximate Optimal Non-Linear Filtering
    • The Separation Principle
    • Numerical Solution of the Riccati Equation
    • Equilibrium Solutions of the Riccati Equation
    • Numerical Methods
    • CHAPTER IX: Optimum Filtering for Discrete Time Random Processes
    • CHAPTER X: Stochastic Control
    • Markov Processes and Semi-Groups
    • Control of Markov Processes with Complete State Information
    • CHAPTER XI: Open Questions and Historical Comments
    • Open Questions
    • Historical Comments
    • PART Il: APPLICATIONS
    • CHAPTER XII: Application to Navigation
    • The Application of a Mathematical Theory
    • Modeling
    • Computational Solution
    • CHAPTER XIII: Applications of Filter Theory and Modeling Techniques
    • Equation Formulation and Notation
    • Advantages of the Sequential Estimator
    • Curve Fitting
    • Comparison of Curve Fitting and Sequential Filtering
    • Linearization
    • Noise and Error Terms
    • The Random Disturbance
    • CHAPTER XIV: Free Flight and Powered Flight Navigation
    • State Transition Matrix
    • Measurement Geometry
    • Radio Inertial Systems
    • Radio Systems
    • CHAPTER XV: Error Analysis and Sub-Optimal Modeling
    • Sub-Optimal Error Analysis
    • Imprecise Knowledge of Variance
    • Imprecise Knowledge of Spectrum
    • Deliberate Simplification
    • A General Sub-Optimal Formulation
    • Sub-Optimal Problem
    • A Sub-Optimal Filter
    • Evaluation Problem
    • Design of Filters
    • CHAPTER XVI: Errors in the Filtering Process
    • Errors in the G Matrix
    • Relationship between 𝛿G and 𝛿λi
    • Examples of Application
    • Roundoff Errors
    • APPENDIX A: Least Squares Curve Fitting
    • APPENDIX B: Probability Review
    • Probability in a General Setting
    • Convergence of Random Variables
    • Integration and Expectation
    • Conditional Probability and Expectation
    • Distributions and Densities
    • References
    • APPENDIX C: The Riccati Equation and Its Bounds
    • APPENDIX C: The Riccati Equation and Its Bounds*
    • APPENDIX D: Further References
    • Index
    • Back Cover
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
AMS Chelsea Publishing
Volume: 326; 1987; 217 pp
MSC: Primary 93

This second edition preserves the original text of 1968, with clarification and added references.

From the Preface to the Second Edition: “Since the First Edition of this book, numerous important results have appeared—in particular stochastic integrals with respect to martingales, random fields, Riccati equation theory and realization of nonlinear filters, to name a few. In Appendix D, an attempt is made to provide some of the references that the authors have found useful and to comment on the relation of the cited references to the field ... [W]e hope that this new edition will have the effect of hastening the day when the nonlinear filter will enjoy the same popularity in applications as the linear filter does now.”
  • Front Cover
  • Preface to the Second Edition
  • Preface to the First Edition
  • Acknowledgments
  • Contents
  • Notation
  • PART I: THEORY
  • CHAPTER I: Ordinary Differential Equations and Stability
  • Differential Equations
  • Stability Theory
  • CHAPTER II: Random Processes and Stochastic Models
  • Introduction
  • Random Variables and Processes
  • Random Differential Equations
  • Linear Models
  • Dynamical Models
  • CHAPTER III: Observability and Controllability
  • Introduction
  • Observability and Controllability
  • Canonical Forms
  • Stochastic Modelling
  • CHAPTER IV: Filtering Theory
  • Introduction
  • The Minimum Variance Unbiased Estimator
  • Function Space Integrals for the Conditional Distribution
  • Alternative Approaches for the Linear Estimation Problem
  • Linear and Non-Linear Filtering in Discrete Time
  • "Wide-Sense" Solution of the Linear Filtering Problem
  • CHAPTER V: Global Theory of Filtering
  • Introduction
  • Properties of the Riccati Equation
  • Exponential Stability
  • Examples and Problems
  • Effects of Errors in Optimal Gains
  • A Table of Results for the Asymptotic Theory
  • CHAPTER VI: Stochastic Stability
  • Information and Filtering
  • CHAPTER VII: Optimal Filtering for Correlated Noise Processes
  • lntroduction
  • Filtering for Colored Noise
  • CHAPTER VIII: Approximate Optimal Non-Linear Filtering
  • The Separation Principle
  • Numerical Solution of the Riccati Equation
  • Equilibrium Solutions of the Riccati Equation
  • Numerical Methods
  • CHAPTER IX: Optimum Filtering for Discrete Time Random Processes
  • CHAPTER X: Stochastic Control
  • Markov Processes and Semi-Groups
  • Control of Markov Processes with Complete State Information
  • CHAPTER XI: Open Questions and Historical Comments
  • Open Questions
  • Historical Comments
  • PART Il: APPLICATIONS
  • CHAPTER XII: Application to Navigation
  • The Application of a Mathematical Theory
  • Modeling
  • Computational Solution
  • CHAPTER XIII: Applications of Filter Theory and Modeling Techniques
  • Equation Formulation and Notation
  • Advantages of the Sequential Estimator
  • Curve Fitting
  • Comparison of Curve Fitting and Sequential Filtering
  • Linearization
  • Noise and Error Terms
  • The Random Disturbance
  • CHAPTER XIV: Free Flight and Powered Flight Navigation
  • State Transition Matrix
  • Measurement Geometry
  • Radio Inertial Systems
  • Radio Systems
  • CHAPTER XV: Error Analysis and Sub-Optimal Modeling
  • Sub-Optimal Error Analysis
  • Imprecise Knowledge of Variance
  • Imprecise Knowledge of Spectrum
  • Deliberate Simplification
  • A General Sub-Optimal Formulation
  • Sub-Optimal Problem
  • A Sub-Optimal Filter
  • Evaluation Problem
  • Design of Filters
  • CHAPTER XVI: Errors in the Filtering Process
  • Errors in the G Matrix
  • Relationship between 𝛿G and 𝛿λi
  • Examples of Application
  • Roundoff Errors
  • APPENDIX A: Least Squares Curve Fitting
  • APPENDIX B: Probability Review
  • Probability in a General Setting
  • Convergence of Random Variables
  • Integration and Expectation
  • Conditional Probability and Expectation
  • Distributions and Densities
  • References
  • APPENDIX C: The Riccati Equation and Its Bounds
  • APPENDIX C: The Riccati Equation and Its Bounds*
  • APPENDIX D: Further References
  • Index
  • Back Cover
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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