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A trajectory of a destination-directed moving object (e.g. an aircraft froman origin airport to a destination airport) has three main components: anorigin, a destination, and motion in between. We call such a trajectory thatend up at the destination \textit{destination-directed trajectory (DDT)}. Aclass of conditionally Markov (CM) sequences (called CM$_\text{L}$) has thefollowing main components: a joint density of two endpoints and a Markov-likeevolution law. A CM$_\text{L}$ dynamic model can describe the evolution of aDDT but not of a guided object chasing a moving guide. The trajectory of aguided object is called a \textit{guided trajectory (GT)}. Inspired by aCM$_\text{L}$ model, this paper proposes a model for a GT with a moving guide.The proposed model reduces to a CM$_\text{L}$ model if the guide is not moving.We also study filtering and trajectory prediction based on the proposed model.Simulation results are presented.

Mathematical Modeling of Guidance Trajectory with a Moving Destination Using Conditionally Markov Modeling