Abstract
In most instances in inertial navigation, we are going to be concerned with multiple reference frames. For example, the accelerometers may form their measurements with respect to a set of axes that are fixed in the vehicle; but navigation is usually performed with respect to a set of axes that is fixed in the Earth. This is certainly true for applications that are on or near the surface of the Earth.First of all, we have to understand what these various reference frames are and how they are defined and used within inertial navigation. Once we have defined the various reference frames, then we will need to discuss how to convert between them. As we have discussed previously, Newton's laws are valid in an inertial reference frame and an inertial frame is one that is moving at fixed velocity with respect to the stars. The background stars in our galaxy serve as a reference frame and any frame that is moving at constant velocity (including zero) with respect to the background stars also is an inertial frame. The true inertial frame is the only frame in which Newton's laws are valid.
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