An introduction to optimal estimation of dynamical systems

ISBN-13: 9789400999220 / Angielski / Miękka / 2012 / 354 str.

J.L. Junkins

Opis

This text 1s designed to introduce the fundamentals of esti mation to engineers, scientists, and applied mathematicians. The level of the presentation should be accessible to senior under graduates and should prove especially well-suited as a self study guide for practicing professionals. My primary motivation for writing this book 1s to make a significant contribution toward minimizing the painful process most newcomers must go through in digesting and applying the theory. Thus the treatment 1s intro ductory and essence-oriented rather than comprehensive. While some original material 1s included, the justification for this text lies not in the contribution of dramatic new theoretical re sults, but rather in the degree of success I believe that I have achieved in providing a source from which this material may be learned more efficiently than through study of an existing text or the rather diffuse literature. This work is the outgrowth of the author's mid-1960's en counter with the subject while motivated by practical problems aSSociated with space vehicle orbit determination and estimation of powered rocket trajectories. The text has evolved as lecture notes for short courses and seminars given to professionals at Pr>efaae various private laboratories and government agencies, and during the past six years, in conjunction with engineering courses taught at the University of Virginia. To motivate the reader's thinking, the structure of a typical estimation problem often assumes the following form: Given a dynamical system, a mathematical model is hypothesized based upon the experience of the investigator."

Spis treści

1. Least Square Approximation.- 1.1 A Curve Fitting Example.- 1.2 Linear Batch Estimation.- 1.3 Constrained Least Square Estimation.- 1.4 Linear Sequential Estimation.- 1.5 Nonlinear Estimation: Least Square Differential Correction.- 1.6 Remarks.- 1.7 Exercises.- 1.8 References.- 2. Minimal Variance Estimation.- 2.1 Preliminary Remarks.- 2.2 Minimal Variance Estimation (without apriori State Estimates).- 2.3 Minimal Variance Estimation (with apriori State information).- 2.4 Covariance Propagation in Linear Estimation Algorithms.- 2.5 Nonuniqueness of the Weight Matrix.- 2.6 Remarks.- 2.7 Exercises.- 2.8 References.- 3. Parameter Estimation: Applications.- 3.1 Preliminary Comments.- 3.2 Planar Triangulation.- 3.3 Stellar Resection Photogrammetry/Spacecraft Orientation Estimation.- 3.4 Triangulation of Orbital Photography.- 3.5 Mathematical Modeling of the Earth’s Topography.- 3.6 Mathematical Models of the Gravitational Potential.- 3.7 Remarks.- 3.8 References.- 4. Survey of Ordinary Differential Equations.- 4.1 Preliminary Remarks.- 4.2 The State Space Approach.- 4.3 Linear Dynamical Systems.- 4.3.1 Homogeneous Linear Dynamical Systems.- 4.3.2 Linear State Variable Transformations.- 4.3.3 Forced Linear Systems.- 4.4 Nonlinear Dynamical Systems.- 4.4.1 Overview.- 4.4.2 Analytical Continuation Methods.- 4.4.3 Runge-Kutta Methods.- 4.4.4 Closure Error Analysis.- 4.5 Parametric Differentiation.- 4.6 Remarks.- 4.7 Exercises.- 4.8 References.- 5. Estimation of Dynamical Systems.- 5.1 Preliminary Remarks.- 5.2 Initial State Estimation.- 5.3 Initial State and Model Parameter Estimation.- 5.4 Sequential State Estimation for Linear Dynamic Systems.- 5.4.1 Unforced Linear Systems.- 5.4.2 Process Noise Forced Dynamic Systems.- 5.5 Optimal Continuous State Estimation.- 5.6 Sequential Estimation of Nonlinear Dynamical Systems.- 5.7 Remarks.- 5.8 Exercises.- 5.9 References.- 6. Estimation of Dynamical Systems: Applications.- 6.1 Projectile Trajectory Estimation.- 6.2 Loss of Precision in Covariance Propagation Algorithms.- 6.3 Dynamically Constrained Satellite Photogrammetry.- 6.4 Remarks.- 6.5 References.- Appendix A Minimization of Functions of n-Vaviahles.- Appendix B Basic Probability Concepts.- Appendix C Linear Algebraic Equations.