Statistical Orbit Determination - 1st Edition - ISBN: 9780126836301, 9780080541730

Statistical Orbit Determination

1st Edition

Authors: Bob Schutz Byron Tapley George Born
eBook ISBN: 9780080541730
Hardcover ISBN: 9780126836301
Imprint: Academic Press
Published Date: 27th May 2004
Page Count: 547
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Statistical Orbit Determination presents fundmentals of orbit determination--from weighted least squares approaches (Gauss) to today's high-speed computer algorithms that provide accuracy within a few centimeters. Numerous examples and problems are provided to enhance readers' understanding of the material.

Key Features

  • Covers such topics as coordinate and time systems, square root filters, process noise techniques, and the use of fictitious parameters for absorbing un-modeled and incorrectly modeled forces acting on a satellite.
  • Examples and exercises serve to illustrate the principles throughout each chapter.


Graduate students and researchers in aerospace engineering, astrodynamics, geodesy, and oceanography.

Researchers in the aerospace industry and related research laboratories interested in satellite navigation and control.

Table of Contents

1 Orbit Determination Concepts

  • Introduction
  • UniformGravity Field Model
  • Background and Overview
  • Summary
  • References
  • Exercises

2 The Orbit Problem

  • Historical Background
  • Problem of Two Bodies: General Properties
  • Perturbed Motion
  • Coordinate Systems and Time: Introduction
  • Orbit Accuracy
  • References
  • Exercises

3 Observations

  • Introduction
  • Observations
  • Conceptual Measurement Systems
  • Realization of Measurements
  • Measurement Systems
  • Differenced Measurements
  • Satellite Positions
  • Angles
  • References
  • Exercises

4 Fundamentals of Orbit Determination

  • Introduction
  • Linearization of the Orbit Determination Process
  • The Least Squares Solution
  • The Minimum Variance Estimate
  • Maximum Likelihood and Bayesian Estimation
  • Compuational Algorithm for the Batch Processor
  • The Sequential Estimation Algorithm
  • Example Problems
  • State Noise Compensation Algorithm
  • Information Filter
  • Batch and Sequential Estimation
  • Observability
  • Error Sources
  • Orbit Accuracy
  • Smoothing
  • The Probability Ellipsoid
  • Combining Estimates
  • References
  • Exercises

5 Square-Root Solution Methods

  • Introduction
  • Cholesky Decomposition
  • Least Squares Solution via Orthogonal Algorithm
  • Givens Transformations
  • The Householder Transformation
  • Numerical Examples
  • Square Root Filter Algorithms
  • Time Update of the Estimation Error Covariance Matrix
  • Continuous State Error Corvariance Propagation
  • The Square Root Information Filter
  • Process Noise Parameter Filtering/Smoothing Using a SRIF
  • References
  • Exercises

6 Consider Covariance Analysis

  • Introduction
  • Bias in Linear Estimation Problems
  • Formulation of the Consider Covariance Matrix
  • The Sensitivity and Perturbation Matrices
  • Inclusion of Time-Dependent Effects
  • Propagation of the Error Covariance
  • Sequential Consider Covariance Analysis
  • Example: Freely Falling Point Mass
  • Example: Spring-Mass Problem
  • Errors in the Observation Noise and A Priori State Covariances
  • Errors in Process Noise, Observation Noise, and State Covariance
  • Corvariance Analysis and Orthogonal Transformations
  • References
  • Exercises

A Probability and Statistics

  • Introduction
  • Axioms of Probability
  • Conditional Probability
  • Probability Density and Distribution Functions
  • Expected Values
  • Examples and Discussion of Expectation
  • Moment Generating Functions
  • Some Important Continuous Distributions
  • Two Random Variables
  • Marginal Distributions
  • Independence of Random Variables
  • Conditional Probability
  • Expected Values of Bivariate Functions
  • The Variance-Covariance Matrix
  • Properties of the Correlation Coefficient
  • Properties of Covariance and Correlation
  • Bivariate Normal Distribution
  • Marginal Distributions
  • The Multivariate Normal Distribution
  • The Central Limit Theorem
  • Bayes Theorem
  • Stochastic Processes
  • References

B Review of Matrix Concepts

  • Introduction
  • Rank
  • Quadratic Forms
  • Determinants
  • Matrix Trace
  • Eigenvalues and Eigenvectors
  • The Derivatives of Matrices and Vectors
  • Maxima and Minima
  • Useful Matrix Inversion Theorems
  • Reference

C Equations of Motion

  • Lagrange Planetary Equations
  • Gaussian Forms
  • References

D Constants

  • Physical Constants
  • Earth Constants
  • Lunar, Solar and Planetary Masses
  • References

E Analytical Theory for Near-Circular Orbits

  • Description
  • Example
  • References

F Example of State Noise and Dynamic Model Compensation

  • Introduction
  • State Noise Compensation
  • Dynamic Model Compensation
  • References

G Solution of the Linearized Equations of Motion

  • Introduction
  • The State Transition Matrix

H ECI and ECF Transformation

  • Introduction
  • Matrix P
  • Matrix N
  • Matrix, S'
  • Matrix W
  • References

Bibliography Abbreviations Bibliography Author Index Index


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© Academic Press 2004
Academic Press
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About the Author

Bob Schutz

Affiliations and Expertise

University of Texas at Austin, U.S.A.

Byron Tapley

George Born

Affiliations and Expertise

University of Colorado, U.S.A.