Global Positioning Systems, Inertial Navigation, and Integration, Second Edition

APPENDIX B

VECTORS AND MATRICES

The “S” in “GPS” and in “INS” stands for “system,” and “systems science” for modeling, analysis, design, and integration of such systems is based largely on linear algebra and matrix theory. Matrices model the ways that components of systems interact dynamically and how overall system performance depends on characteristics of components and subsystems and on the ways they are used within the system.

This appendix presents an overview of matrix theory used for GPS/INS integration and the matrix notation used in this book. The level of presentation is intended for readers who are already somewhat familiar with vectors and matrices. A more thorough treatment can be found in most college-level textbooks on linear algebra and matrix theory.

B.1 SCALARS

Vectors and matrices are arrays composed of scalars, which we will assume to be real numbers. Unless constrained by other conventions, we represent scalars by italic lowercase letters.

In computer implementations, these real numbers will be approximated by floating-point numbers, which are but a finite subset of the rational numbers. The default MATLAB representation for real numbers on 32-bit personal computers is in 64-bit ANSI standard floating point, with a 52-bit mantissa.

B.2 VECTORS

B.2.1 Vector Notation

Vectors are arrays of scalars, either column vectors,

or row vectors,

Unless specified otherwise, ...