Modeling of target motion constrained on straight line

Straight line motion is a fundamental target motion. Its modeling has been well studied for unconstrained targets (e.g., air targets). However, existing straight line motion models cannot be directly used for tracks constrained on a straight line, which has wide application, e.g., in ground target tracking. In this paper, modeling of the target motion constrained on a straight line is considered. First, linear equality constraints imposed by the straight line are set up explicitly. Then both direct elimination and along-track motion projection are applied to obtain two forms of constrained motion models. Connections between the two forms are studied. For the first form, conditions that guarantee the traditional linear Gaussian assumption are obtained. For the second form, conditions under which the motion along each axis is similar to the along-track motion are obtained. Supporting numerical examples are also provided.