Bayesian Estimation and Tracking: A Practical Guide

20.2 The Process (Dynamic) Model for Rigid Body Motion

The dynamic motion model for the motion of a rigid body was described in Section 2 of Chapter 19. We refer the reader to Chapter 19 for a full description of those dynamic models. At the end of Chapter 19 we showed that the best relative performance was achieved using the second order constant acceleration model, where we modified the state vector to include rate and acceleration vectors governing both translational and rotational motion. We will use that model exclusively for the analysis in this chapter. Our motion model describes the translational and rotational motion of a rigid body as a function of time in terms of an instantaneous state vector that, along with the external unit quaternion defines both the translation of the center of mass of a rigid body relative to a fixed reference Cartesian coordinate frame, , and the orientation of the body about the center of mass as given by the combination of the axis-angle vector, [, , ]^T and the external unit quaternion [, , , ]^T.

In general, we can write the state vector temporal ...