MODEL OF RANDOM-LIKE PLANAR TRAJECTORIES WITH INTERSECTIONS

Abstract

Background. Recently the task of detecting and identifying trajectories of objects whose genuine purposes are uncertain or strike threatening has become extremely important. The known approaches produce insufficiently smooth trajectories. Objective. The purpose of the paper is to build a model of generating random-like planar trajectories, which would have sufficiently smooth curves. A trajectory may have self-intersections and may intersect other trajectories. Methods. Preliminarily two starting points on a plane are generated. The distance and angle between these points are calculated, which then are successively updated to calculate new trajectory points using the polar coordinate system. A trajectory of points is generated using values of normally distributed random variables with zero mean and unit variance and four values of -uniformly distributed random variables. Results. The random-like trajectory generator has the same time complexity as its predecessors, including the direction randomization generator and its modifications. Exemplary trajectories appear very realistic. Self-intersections are important to manoeuvre and confuse the opponent side. The trajectory has four parameters to adjust its heading, scattering of points, and intensity of turns and twists. These parameters serve as magnitudes to amplify the respective properties. The highest influence has the angle-scattering parameter. Four simple conditions can be embedded to fit the trajectory within a rectangular domain. Conclusions. The suggested model should serve either for generating trajectory datasets to train manoeuvring-object detectors on them or for masking reconnaissance. The model allows balancing the trajectory smoothness and randomness.