MODEL OF RANDOM-LIKE PLANAR TRAJECTORIES WITH INTERSECTIONS
DOI:
https://doi.org/10.20535/2411-2976.12024.55-65Keywords:
object observation, random trajectory, random path, heading, polar coordinate system, manoeuvrabilityAbstract
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.
References
J. M. Kelner, W. Burzynski, and W. Stecz, “Modeling UAV swarm flight trajectories using Rapidly-exploring Random Tree algorithm,” Journal of King Saud University — Computer and Information Sciences, vol. 36, iss. 1, 101909, 2024.
https://doi.org/10.1016/j.jksuci.2023.101909
K. Gromada and W. Stecz, “Determining UAV flight trajectory for target recognition using EO/IR and SAR,” Sensors, vol. 20, iss. 19, 5712, 2020.
https://doi.org/10.3390/s20195712
M. A. Jasim, H. Shakhatreh, N. Siasi, A. H. Sawalmeh, A. Aldalbahi, and A. Al-Fuqaha, “A survey on spectrum management for unmanned aerial vehicles (UAVs),” IEEE Access, vol. 10, pp. 11443 — 11499, 2022.
https://doi.org/10.1109/ACCESS.2021.3138048
M. Chodnicki, B. Siemiatkowska, W. Stecz, and S. Stepien, “Energy efficient UAV flight control method in an environment with obstacles and gusts of wind,” Energies, vol. 15, iss. 10, 3730, 2022.
https://doi.org/10.3390/en15103730
A. A. Laghari, A. K. Jumani, R. A. Laghari, and H. Nawaz, “Unmanned aerial vehicles: A review,” Cognitive Robotics, vol. 3, pp. 8 — 22, 2023.
https://doi.org/10.1016/j.cogr.2022.12.004
R. Gui, Z. Zheng, and W.-Q. Wang, “Cognitive FDA radar transmit power allocation for target tracking in spectrally dense scenario,” Signal Processing, vol. 183, 108006, 2021.
https://doi.org/10.1016/j.sigpro.2021.108006
V. V. Romanuke, “Accurate detection of multiple targets by uniform rectangular array radar with threshold soft update and area rescanning,” Information and Telecommunication Sciences, vol. 13, no. 2, pp. 62 — 71, 2022.
https://doi.org/10.20535/2411-2976.22022.62-71
J. L. Zhao and H. Y. Li, “Maneuvering identification method for non-cooperative aircraft based on sparse orbital information,” Systems Engineering and Electronics, vol. 44, iss. 6, pp. 1950 — 1956, 2022.
R. Kneusel, Random Numbers and Computers. Springer International Publishing, 2018.
https://doi.org/10.1007/978-3-319-77697-2
V. V. Romanuke, A. Y. Romanov, and M. O. Malaksiano, “Pseudorandom number generator influence on the genetic algorithm performance to minimize maritime cargo delivery route length,” Pomorstvo. Scientific Journal of Maritime Research, vol. 36, pp. 249 — 262, 2022.
https://doi.org/10.31217/p.36.2.9
B. Yang, G. Zhang, H. Rao, S. Wang, B. Yang, and Z. Sun, “Numerical simulation of the maneuvering performance of ships in broken ice area,” Ocean Engineering, vol. 294, 116783, 2024.
https://doi.org/10.1016/j.oceaneng.2024.116783
Z.-L. Ouyang, S.-Y. Liu, and Z.-J. Zou, “Nonparametric modeling of ship maneuvering motion in waves based on Gaussian process regression,” Ocean Engineering, vol. 264, 112100, 2022.
https://doi.org/10.1016/j.oceaneng.2022.112100
E. Cortina, D. Otero, and C. E. D’Attellis, “Maneuvering target tracking using extended Kalman filter,” IEEE Transactions on Aerospace and Electronic Systems, vol. 27, iss. 1, pp. 155 — 158, 1991.
R. Vera-Amaro, M. E. Rivero-Ángeles, and A. Luviano-Juárez, “Phase-type distributions of animal trajectories with random walks,” Mathematics, vol. 11, 3671, 2023.
https://doi.org/10.3390/math11173671
N. L. Sund, G. M. Porta, and D. Bolster, “Upscaling of dilution and mixing using a trajectory based Spatial Markov random walk model in a periodic flow domain,” Advances in Water Resources, vol. 103, pp. 76 — 85, 2017.
https://doi.org/10.1016/j.advwatres.2017.02.018
J. Goldberger and D. Burshtein, “Scaled random trajectory segment models,” Computer Speech and Language, vol. 12, pp. 51 — 73, 1998.
Z. Xi, Y. Kou, Z. Li, Y. Lv, and Y. Li, “An air combat maneuver pattern extraction based on time series segmentation and clustering analysis,” Defence Technology, 2023.
https://doi.org/10.1016/j.dt.2023.11.010
A. R. Pitombeira-Neto, H. P. Santos, T. L. Coelho da Silva, and J. A. F. de Macedo, “Trajectory modeling via random utility inverse reinforcement learning,” Information Sciences, vol. 660, 120128, 2024.
https://doi.org/10.1016/j.ins.2024.120128
G. Technitis and R. Weibel, “An Algorithm for Random Trajectory Generation Between Two Endpoints, Honoring Time and Speed Constraints,” in Proceedings GIScience 2014, 24 — 26 September 2014, Vienna.
Y. A. Ahmed, “Mathematical model of the manoeuvring motion of a ship,” in Engineering Applications for New Materials and Technologies, Springer, 2018, pp. 551 — 566.
https://doi.org/10.1007/978-3-319-72697-7_45
M. Ester, H.-P. Kriegel, J. Sander, and X. Xu, “A density-based algorithm for discovering clusters in large spatial databases with noise,” in Proceedings of the Second International Conference on Knowledge Discovery and Data Mining (KDD-96), AAAI Press, 1996, pp. 226 — 231.
X. Bai, Z. Xie, X. Xu, and Y. Xiao, “An adaptive threshold fast DBSCAN algorithm with preserved trajectory feature points for vessel trajectory clustering,” Ocean Engineering, vol. 280, 114930, 2023.
