Bayesian Estimation and Tracking: A Practical Guide

19.2 The Process (Dynamic) Model for Rigid Body Motion

Our motion model will describe the translational and rotational motion of a rigid body as a function of time. Consider an instantaneous state vector that 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 with respect to the reference frame given as an axis-angle vector [, , ]^T. Under certain conditions the vector a can become numerically unstable (specifically when where n is a positive integer), so instead we use a unit quaternion q = [q_s, q_x, q_y, q_z]^T that when combined with a represents the orientation. We discuss the need for q in more detail in Section 19.2.2 and in Appendix 19.A.2. In addition, in the dynamic (process) models ...