Details

Autor(en) / Beteiligte

• Bar-Shalom, Yaakov
• Li, Xiao-Rong
• Kirubarajan, Thiagalingam

Titel

Estimation with applications to tracking and navigation

Beschreibungen/Notizen

• "A Wiley-Interscience publication."
• Includes bibliographical references and index.
• CONTENTS; PREFACE; ACRONYMS; MATHEMATICAL NOTATIONS; 1 INTRODUCTION; 1.1 BACKGROUND; 1.1.1 Estimation and Related Areas; 1.1.2 Applications of Estimation; 1.1.3 Preview of Estimation/Filtering; 1.1.4 An Example of State Estimation: Vehicle Collision Avoidance; 1.2 SCOPE OF THE TEXT; 1.2.1 Objectives; 1.2.2 Overview and Chapter Prerequisites; 1.3 BRIEF REVIEW OF LINEAR ALGEBRA AND LINEAR SYSTEMS; 1.3.1 Definitions and Notations; 1.3.2 Some Linear Algebra Operations; 1.3.3 Inversion and the Determinant of a Matrix; 1.3.4 Orthogonal Projection of Vectors; 1.3.5 The Gradient, Jacobian and Hessian
• 1.3.6 Eigenvalues, Eigenvectors, and Quadratic Forms1.3.7 Continuous-Time Linear Dynamic Systems - Controllability and Observability; 1.3.8 Discrete-Time Linear Dynamic Systems - Controllability and Observability; 1.4 BRIEF REVIEW OF PROBABILITY THEORY; 1.4.1 Events and the Axioms of Probability; 1.4.2 Random Variables and Probability Density Function; 1.4.3 Probability Mass Function; 1.4.4 Mixed Random Variable and Mixed Probability-PDF; 1.4.5 Expectations and Moments of a Scalar Random Variable; 1.4.6 Joint PDF of Two Random Variables
• 1.4.7 Independent Events and Independent Random Variables1.4.8 Vector-Valued Random Variables and Their Moments; 1.4.9 Conditional Probability and PDF; 1.4.10 The Total Probability Theorem; 1.4.11 Bayes' Formula; 1.4.12 Conditional Expectations and Their Smoothing Property; 1.4.13 Gaussian Random Variables; 1.4.14 Joint and Conditional Gaussian Random Variables; 1.4.15 Expected Value of Quadratic and Quartic Forms; 1.4.16 Mixture Probability Density Functions; 1.4.17 Chi-Square Distributed Random Variables; 1.4.18 Weighted Sum of Chi-Square Random Variables; 1.4.19 Random Processes
• 1.4.20 Random Walk and the Wiener Process1.4.21 Markov Processes; 1.4.22 Random Sequences, Markov Sequences and Markov Chains; 1.4.23 The Law of Large Numbers and the Central Limit Theorem; 1.5 BRIEF REVIEW OF STATISTICS; 1.5.1 Hypothesis Testing; 1.5.2 Confidence Regions and Significance; 1.5.3 Monte Carlo Runs and Comparison of Algorithms; 1.5.4 Tables of the Chi-Square and Gaussian Distributions; 1.6 NOTES AND PROBLEMS; 1.6.1 Bibliographical Notes; 1.6.2 Problems; 2 BASIC CONCEPTS IN ESTIMATION; 2.1 INTRODUCTION; 2.1.1 Outline; 2.1.2 Basic Concepts - Summary of Objectives
• 2.2 THE PROBLEM OF PARAMETER ESTIMATION2.2.1 Definitions; 2.2.2 Models for Estimation of a Parameter; 2.3 MAXIMUM LIKELIHOOD AND MAXIMUM A POSTERIORI ESTIMATORS; 2.3.1 Definitions of ML and MAP Estimators; 2.3.2 MLE vs. MAP Estimator with Gaussian Prior; 2.3.3 MAP Estimator with One-Sided Exponential Prior; 2.3.4 MAP Estimator with Diffuse Prior; 2.3.5 The Sufficient Statistic and the Likelihood Equation; 2.4 LEAST SQUARES AND MINIMUM MEAN SQUARE ERROR ESTIMATION; 2.4.1 Definitions of LS and MMSE Estimators; 2.4.2 Some LS Estimators; 2.4.3 MMSE vs. MAP Estimator in Gaussian Noise
• 2.5 UNBIASED ESTIMATORS
• Expert coverage of the design and implementation of state estimation algorithms for tracking and navigation Estimation with Applications to Tracking and Navigation treats the estimation of various quantities from inherently inaccurate remote observations. It explains state estimator design using a balanced combination of linear systems, probability, and statistics. The authors provide a review of the necessary background mathematical techniques and offer an overview of the basic concepts in estimation. They then provide detailed treatments of all the major issues in estimatio
• English