Fundamentals of Kalman Filtering: A Practical Approach, Second Edition
Containing numerous real-life problems and examples presented in detail, this text demonstrates the many ways in which Kalman filters can be designed.
TABLE OF CONTENTS Fundamentals of Kalman Filtering: A Practical Approach, Second Edition
Chapter 1: Numerical Basics
Introduction
In this chapter we will try to discuss all of the numerical techniques used throughout the text. We will begin with a discussion of vectors and matrices and illustrate various operations that we will need to know when we apply the Kalman-filtering equations. Next, we will show how two different numerical integration techniques can be used to solve both linear and nonlinear differential equations. The numerical integration techniques are necessary when we must integrate differential equations representing the real world in simulations made for evaluating the performance of Kalman filters. In addition, numerical integration techniques are sometimes required to propagate states from nonlinear differential equations. Next, we will review the basic concepts used in representing random phenomena. These techniques will be important in modeling measurement and process noise, which may be used to represent the real world and will also be used to add some uncertainty to the measurement inputs entering the Kalman filter. These concepts will also be useful in understanding how to apply Monte Carlo techniques for evaluating Kalman-filter performance. State-space notation will be introduced as a shorthand notation for representing differential equations. Models of the real world must be placed in state-space notation before Kalman filtering can be applied. Finally, methods for computing the fundamental matrix will be presented. The fundamental matrix is required before a Kalman filter can be put into digital form.
Simple Vector Operations [1]
An array of elements arranged in a column is known as a column vector. The number of elements...
Copyright American Institute of Aeronautics and Astronautics, Inc. 2005 under license agreement with Books24x7
