Coordinate and motion parameter extrapolation of evading air target using Song model

Dynamics, ballistics, movement control of flying vehicles


Ispulov A. A.*, Zledenny N. P.**, Ivanov S. L.***

Air force academy named after professor N.E. Zhukovskii and Y.A. Gagarin, Voronezh, Russia



In air surveillance mode, fighter’s airborne sighting systems make use of air target motion coordinate and parameter assessment algorithms based on α,β-filtering with low data update rate which is insufficiently effective in close maneuver air combat environment and doesn’t provide aimed engagement of air target.

One of the possible ways to overcome the noted shortcoming is air target motion coordinate and parameter extrapolation accuracy enhancement using more complex models of spatial target motion, Song model in particular.

Objective of this paper is to define Song model characteristics to improve air target motion coordinate and parameter extrapolation accuracy in close maneuver air combat with low target data update rate.

To specify Song model characteristics, it is required to define maneuverability factor values at maneuvering of fighter relatively air target in close maneuver air combat with execution of «Combat turn» and «Oblique loop» space maneuvers, «Rolling» and «Ordinary loop» vertical maneuvers and «Banking» yaw maneuver.

To accomplish the objective, there was performed semi-realistic simulation of close maneuver air combat resulting in definition of ensemble of realizations for random process of closure jerk (third range derivative) for each type of air target maneuver. This enabled to calculate experimental correlation functions of lighter-to air target closure jerk averaged by the number of realizations.

Maneuverability factor was estimated using spectra-correlation processing via transition from time domain to spectral domain — direct Fourier transform.

To validate practicability for employment of the results obtained, there was performed comparative analysis of range extrapolation accuracy to air target. Absolute magnitude of extrapolated estimate error was taken as accuracy figure.

Improvement in accuracy of range extrapolation to air target for Song model, as compared with second-order air target motion model, can achieve 18%, 15% — with rectilinear uniform motion model and 11% — with Singer model.

So, based on spectral-correlation processing of the semi-natural experiment results, there were defined parameter values of Song model describing spatial relative motion of fighter and air target in close maneuver air combat. The comparative analysis proved availability of improvement in accuracy of air target coordinate extrapolation with making use of the refined Song model. Employment of this model together with prior uncertainty handling algorithms relatively type of air target maneuver, Mane parametric identification algorithm in a fighter’s airborne sighting systems will provide improvement in accuracy of coordinate and motion parameter estimation in the air surveillance mode and, as a consequence, improvement in accuracy of weapon delivery.


air target, Song model, maneuverability factor, spectral-correlation processing


  1. Kanashchenkov A.I. Oblik perspektivnykh bortovykh radiolokatsionnykh sistem. Vozmozhnosti i ogranicheniya (Appearance of perspective board radar-tracking systems. Opportunities and restrictions), Moscow, IPRZhR, 2002, 176 p.

  2. Shatovkin R.R. Modelirovanie funktsionirovaniya sistem upravleniya vooruzheniem istrebitelya v rezhime radiolokatsionnogo molchaniya (Modeling of functioning of control systems of arms of the fighter in the mode of radar silence), Voronezh, Izd-vo VAIU, 2010, 328 p.

  3. Song, T.L. Suboptimal filter design with pseudomeasurements for target tracking. T.L. Song, J.Y. Ahn, C. Park//IEEE Transactions on Aerospace and Electronic Systems. 1988. no.3. pp. 294-304.

  4. Kostin P. S., Vereshchagin Yu. O., Voloshin V. A. Zhurnal «Trudy MAI», 2015, no. 81, available at: (accessed 15.05. 2015).

  5. Tikhonov V.I. Statisticheskaya radiotekhnika (Statistical radio engineering), Moscow, Radio i svyaz’, 1982, 624 p.

  6. Zinger R.A. Zarubezhnaya radioelektronika, 1971, no. 8, pp. 40-57.

  7. Kanashchenkov A.I., Merkulov V.I. Aviatsionnye sistemy radioupravleniya. Aviatsionnye sistemy radioupravleniya. Radioelektronnye sistemy samonavedeniya (Aviation systems of radio control. Radioelectronic self guidance systems.) Moscow, Radiotekhnika, 2003, 389 p.

Download — informational site MAI

Copyright © 2000-2024 by MAI