TABLE OF CONTENTS This chapter provides the mathematical foundations for explaining the principles of navigation systems and their integration. Section 2.1 introduces the concept of a coordinate frame and how it may be used to represent an object, reference, or set of resolving axes. The main coordinate frames used in navigation are described. Section 2.2 explains the different methods of representing attitude and shows how to convert between them. It also defines the Cartesian position, velocity, acceleration, and angular rate in a multiple coordinate frame environment where the reference frame or resolving axes may be rotating. Section 2.3 shows how the Earth's surface is modeled and defines latitude, longitude, and height. It also introduces specific force and explains the difference between gravity and gravitation. Finally, Section 2.4 presents the equations for transforming between different coordinate frame representations.
In simple mechanics problems, motion is modeled with respect to the Earth while pretending that the Earth is an inertial frame, ignoring its rotation. For navigation this does not work; the Earth's rotation has a significant impact on navigation computation as shown later. Navigation is also a multiple coordinate frame problem. Inertial sensors measure their motion with respect to an inertial frame. GPS measures the position and velocity of a receiver's antenna with respect to a constellation of satellites. However, the user wants to know their position with respect to the Earth. [1]
Thus, for accurate navigation, the...
