TABLE OF CONTENTS Navigation system states position, velocity, and attitude are defined with reference to coordinate frames. These navigation frames are defined differently for the various integrated navigation systems' implementations, and there are a number of different frames in current use.
This chapter presents a survey of the following:
coordinate systems.
coordinate frame transformations.
This survey is intended to help the reader develop an appreciation for the different coordinate frames and develop an ability to manipulate vector variables between coordinate frames.
Coordinate systems that are currently used in integrated navigation systems are presented first. These include several navigation and body reference frames. For the coordinate systems defined, transformation matrices are developed to transform navigation variables (vectors) from one reference frame to another. The navigation reference frames presented include Earth-centered, local level geodetic (geographic), and wander azimuth. Depending on the axis system definitions (orientations of the X Y Z components), different forms of the corresponding transformation matrices result. The relationships between latitude and longitude, and their rates, and wander angle rates are established for different wander azimuth frame definitions.
The concept of position and attitude errors associated with their corresponding direction cosine matrices is presented. Relationships between Euler angles, presented in Chapter 14, and transformation matrix errors are developed. Relationships among latitude, longitude, and wander angle errors, and wander azimuth local level navigation frame angular position errors, are established. Relationships between these errors are used later for transforming error variables from local geodetic (latitude and longitude) and wander azimuth reference frames.
Problems are included that expand...
