Constrained target motion modeling - Part I: Straight line track

Straight line motion is one of the most fundamental target motions. Its modeling has been well studied for unconstrained targets, e.g., air targets. However, the existing straight line motion models can not be directly used for the constrained case on straight line tracks, which has wide application, e.g., in ground target tracking. In this paper, modeling of the constrained target motion on a straight line track is considered. First, the constraints imposed by the straight track are explicitly set up. Then both direct elimination and projection along-track are applied to obtain two forms of constrained motion models in the 2D Cartesian plane and 3D Cartesian space. The connections between these two forms are studied. It is found that the traditional linear Gaussian assumption is still valid for the nearly constant velocity models, the nearly constant acceleration models and the Singer model. Inspired by this, a general condition under which the traditional linear Gaussian assumption is valid for modeling of constrained motion on a straight track is also discussed.