Accuracy evaluation of the filtering algorithms while tracking a maneuvering air target on angular coordinates

Radiolocation and radio navigation


Ispulov A. A.*, Ivanov S. L.**

MESC Air Force “Air Force Academy named after professor N.E. Zhukovskii and Yu.A. Gagarin”, 54a, Starykh bol'shevikov, Voronezh, 394064, Russia



At present, algorithms for coordinates and parameters evaluation of the air target (AT) movement on fighters are realized based on simplified filtering algorithms, particularly by α,β-filtering and α,β,γ-filtering. The main drawbacks of these algorithms are insufficiently accurate and stable tracking of maneuvering AT while low rate of information update and missing of adaptation to rapidly changing air combat (AC) conditions.

Implementing of more complex models of a relative movement of a fighter and AT with refined parameters is one of the possible ways to overcome these shortcomings.

The purpose of the paper is a comparative assessment of the filtration accuracy when tracking a maneuvering AT in angular coordinates using the α,β-filtering algorithms and the Kalman filter (KF) for the Zinger and Song models with refined parameters at a low rate of data update about the target.

In the interests of obtaining an extrapolated evaluation and the operation of filtering algorithms, determination of the values of the maneuverability coefficient when an AT is performing the combat turn is required. The data on the AT spatial movement was obtained by semi-detailed simulation on the flight test-bench.

Maneuverability coefficient determination was performed via correlation-spectral processing, by a transition from the time domain to the spectral domain – the direct Fourier transform.

To achieve the purpose of the work, modeling of the filtering algorithms at a low information update rate about the target has been performed by statistical tests method. The mean square deviation of filtering errors has been used as an accuracy index. The α,β-filtering algorithm for the model of uniform rectilinear motion, the KF algorithm for the Zinger model, and the KF algorithm for the Song model have been analyzed.

Analysis of the presented results allows us to draw the following conclusions:

  • the filtering algorithms considered in this paper are valid, which makes it possible to significantly improve the accuracy of determination of the angular coordinates of the maneuvering AT, compared to their measured values;

  • algorithm III is characterized by the highest accuracy of filtering the AT angular coordinates, which extrapolator functions is based on the Song model with refined parameters. Thus, in the steady state, the increase in the filtration accuracy index can reach up to 40% compared to the α,β-filtering algorithm, and up to 10% compared to the Kalman filter based on the Zinger model;

  • application in the KF of a simpler Zinger model of AT’s the relative movement with refined parameters allows improve the accuracy of angular coordinates filtering of the target compared to the α,β-filter up to 30%;

  • the disadvantage of the KF based on the Song model is a large inertia. Thus, the transient processes time for filtering the AT angular coordinate in the vertical plane ьфн reach 10 seconds or more, while the transient processes in the filter, when using the Zinger model, are completed twice as fast. Another drawback of the filter based on the Song model is obviously a great deal of effort to implement it;

  • it should be expected that application of KF based on Zinger and Song models with refined parameters while tracking an AT performing maneuvers, other than a «combat turn», will lead to a reduction of the filtering accuracy index growth compared to the α,β-filtering algorithm. To eliminate this drawback, it is advisable to apply additional special procedures for reducing the a priori uncertainty relative to the type of AT maneuver.

Thus, to ensure high tracking accuracy of the maneuvering AT in angular coordinates in the AC conditions at a low information update rate in modern aviation sighting systems, it is advisable to apply filters that employ models of relative target movement of higher orders. The filtration accuracy index increase for the KF with the Song model is 40%, as compared to the α,β-filter, and 30% for the KF with the Zinger model. However, if AT maneuver changes, it will be necessary to implement the procedures for adapting the filter parameters to the maneuver type. In addition, the filtering algorithm selection should be performed either by the criterion of the estimation error minimum or by the criterion of the transients minimum time.


maneuvering air target, Zinger model, Song model, maneuverability coefficient, combat turn, mean square deviation


  1. Kanashchenkov A.I., Merkulov V.I., Samarin O.F. Oblik perspektivnykh bortovykh radiolokatsionnykh sistem. Vozmozhnosti i ogranicheniya (The layout of airborne radar systems. Opportunities and constraints), Moscow, IPRZhR, 2002, 176 p.

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

  3. Ispulov A.A., Ivanov S.L., Zledennyi N.P. Trudy MAI, 2016, no. 85, available at:

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

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

  6. Kostin P.S., Vereshchagin Yu.O., Voloshin V.A. Trudy MAI, 2015, no. 81, available at:

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

  8. Kanashchenkov A.I., Merkulov V.I. et al. Aviatsionnye sistemy radioupravleniya. Printsipy postroeniya sistem radioupravleniya. Osnovy sinteza i analiza (Aviation Radio Control Systems. Designing Principles of Radio Control Systems. Fundamentals of Design and Analysis), Moscow, Radiotekhnika, 2003, vol. 1, 191 p.

  9. Kanashchenkov A.I., Merkulov V.I. et al. Aviatsionnye sistemy radioupravleniya. Radioelektronnye sistemy samonavedeniya (Aviation Radio Control Systems. Radio electronic Systems of Homing Guidance), Moscow, Radiotekhnika, 2003, vol. 2, 192 p.

  10. Ryazantsev L.B., Likhachev V.P., Shatovkin R.R. Trudy MAI, 2015, no. 84, available at:

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