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

A trajectory of a destination-directed moving object (e.g. an aircraft from an origin airport to a destination airport) has three main components: an origin, a destination, and motion in between. We call such a trajectory that end up at the destination $\mathit{\text{destination-directed}}\mathit{\text{trajectory}}\mathit{\text{(DDT)}}$. A class of conditionally Markov (CM) sequences (called CM${}_{\text{L}}$) has the following main components: a joint density of two endpoints and a Markov-like evolution law. A CM${}_{\text{L}}$ dynamic model can describe the evolution of a DDT but not of a guided object chasing a moving guide. The trajectory of a guided object is called a $\mathit{\text{guided}}\mathit{\text{trajectory}}\mathit{\text{(GT)}}$. Inspired by a CM${}_{\text{L}}$ 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.