Overview

This chapter presents two important modeling elements of an integrated navigation system:

1. ellipsoid geometry.

2. ellipsoid gravity.

Like the different navigation frames presented in Chapter 3, there are many models for the Earth's geometry and gravity. These models are based on parameters that have been assigned different values for different uses. For integrated navigation systems, the Earth's shape is modeled by simple oblate spheroid, and the gravity models reflect a similar simplification.

The local level frames discussed in Chapter 3 are to be maintained as locally level as a vehicle moves over the Earth's surface. This movement results in an angular rotation defined by the Earth's geometrical shape, i.e., its radius of curvature. The numerical integration of this motion yields the vehicle position. An accurate model of the Earth's shape is necessary so that an accurate position results from that integration. The radius of curvature expressions developed are used in Chapter 5's developments of navigation system dynamic equations.

The Earth's gravity influences accelerations sensed by the inertial system's instruments. Models for gravity are maintained within the navigation system to determine what part of the sensed acceleration is due to vehicle dynamics and what is due to the Earth's gravitational attraction. The most widely used current Earth model is the World Geodetic System (WGS-84). ^[4]

Approximations to the shape and gravity models are developed that are later used in the linearization of navigation state equations presented in Chapter 5.

Problems are included that expand upon the material presented.