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

TL;DR

This paper introduces a new mathematical model for guiding objects following a moving destination, extending existing conditionally Markov models to account for moving guides, with applications in trajectory prediction and filtering.

Contribution

The paper proposes a novel CM$_ ext{L}$-based model for guided trajectories with moving guides, expanding the applicability of CM sequences in dynamic guidance scenarios.

Findings

Model effectively describes guided trajectories with moving guides.

Simulation results validate the proposed approach.

Filtering and prediction methods improve trajectory tracking.

Abstract

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 \textit{destination-directed trajectory (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 \textit{guided trajectory (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.