  In some problems there is information about the destination of a moving
object. An example is an airliner flying from an origin to a destination. Such
problems have three main components: an origin, a destination, and motion in
between. To emphasize that the motion trajectories end up at the destination,
we call them \textit{destination-directed trajectories}. The Markov sequence is
not flexible enough to model such trajectories. Given an initial density and an
evolution law, the future of a Markov sequence is determined probabilistically.
One class of conditionally Markov (CM) sequences, called the $CM_L$ sequence
(including the Markov sequence as a special case), has the following main
components: a joint endpoint density (i.e., an initial density and a final
density conditioned on the initial) and a Markov-like evolution law. This paper
proposes using the $CM_L$ sequence for modeling destination-directed
trajectories. It is demonstrated how the $CM_L$ sequence enjoys several
desirable properties for destination-directed trajectory modeling. Some
simulations of trajectory modeling and prediction are presented for
illustration.
