A Spherical Constant Velocity Model for Target Tracking in Three Dimensions
In this case study we address a very important estimation problem that is intrinsic to many engineering endeavors, the problem of tracking an object in three dimensional space. Many three-dimensional tracking algorithms use an inertial frame Cartesian constant velocity linear dynamic model for target motion and a nonlinear observation model that relates the Cartesian state vector x to a set of spherical observations z. If the dynamic and observation noises are considered to be Gaussian, Kalman filter implementation results in a set of linear Kalman filter state prediction equations and nonlinear observation prediction equations that can utilize any one of the suboptimal filtering techniques presented in Part II of this book.
The issue of tracking a maneuvering (accelerating) target has been addressed in a variety of ways. For tracking in Cartesian coordinates, the simplest approach is to remove the constant velocity constraint from the target dynamic model by including acceleration components in the state vector and replacing the constant velocity constraint with a constant acceleration constraint [1-3]. Problems with this method are encountered when it is applied to targets that only maneuver for short periods and are nonmaneuvering for the majority of their trajectory. To address these cases, several authors have proposed the use of a filter that switches from a constant velocity model to ...