bsuirДоклады БГУИРDoklady BGUIR1729-76482708-0382БГУИР10.35596/1729-7648-2026-24-5-51-59bsuir-4447Research ArticleСтатьиОценивание угловой скорости разворота воздушного объекта на основе ансцентного преобразования расширенного вектора состоянияEstimation of the Angular Turn Rate of an Airborne Object Based on the Unscented Transformation of an Augmented State VectorХмарскийП. А.KhmarskiP.

Минск

Khmarski Petr, Cand. Sci. (Tech.), Associate Professor, Leading Researcher  Tel.: +375 17 300-73-98

220072, Minsk, Akademicheskaya St., 16

 

pierre2009@mail.ruАртемьевВ. М.ArtemievV.

Минск

Artemiev V., Corr. Member of the National Academy of Sciences of Belarus , Dr. Sci. (Tech.), Professor, Principal Researcher

Minsk

НаумовА. О.NaumovA.

Минск

Naumov A., Cand. Sci. (Phys. and Math.), Head of Laboratory

Minsk

БондаренкоА. Е.BondarenkoA.

Минск

Bondarenko A., Lecturer

Minsk

МухаммедовБ. М.MuxammedovB.

Карши

Muxammedov B., Head of the Research Laboratory

Qarshi

Институт прикладной физики Национальной академии наук БеларусиБеларусьInstitute of Applied Physics of the National Academy of Sciences of BelarusBelarusВоенная академия Республики БеларусьБеларусьMilitary Academy of the Republic of BelarusBelarusИнститут военной авиации Университета военной безопасности и обороны Республики УзбекистанУзбекистанInstitute of Military Aviation of the University of Military Security and Defense of the Republic of UzbekistanUzbekistan2026071120262455159Copyright © Хмарский П.А., Артемьев В.М., Наумов А.О., Бондаренко А.Е., Мухаммедов Б.М., 20262026Хмарский П.А., Артемьев В.М., Наумов А.О., Бондаренко А.Е., Мухаммедов Б.М.Khmarski P., Artemiev V., Naumov A., Bondarenko A., Muxammedov B.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://doklady.bsuir.by/jour/article/view/4447

Рассмотрен дискретный фильтр совместного оценивания координат, скорости и угловой скорости W цели, совершающей установившийся разворот, по косвенным (полярным/сферическим) измерениям радиолокационных станций. При включении W в расширенный вектор состояния матрица пересчета приращений становится нелинейной функцией самой W, поэтому линеаризация (используемая в ранее рассмотренных модификациях расширенного фильтра Кальмана при косвенных измерениях) требует пересчета матрицы Якоби на каждом шаге и вносит дополнительную методическую ошибку. Предложено ансцентное преобразование расширенного вектора состояния, исключающее линеаризацию модели движения и измерения. Проведено статистическое моделирование методом Монте-Карло (Nоп = 545) алгоритма и его линеаризованного аналога для восьми типовых радиолокационных станций кругового обзора (2D и 3D) и пяти значений угловой скорости разворота цели. Показано, что предложенный алгоритм обеспечивает среднеквадратическое отклонение оценки Ω в среднем в 4,3 раза (медиана 4,0, разброс 1,4–14,0 по всей матрице условий наблюдения) меньше, чем расширенный фильтр Кальмана при косвенных измерениях с линеаризацией, при заметно более скромном (в среднем 1,2 раза) выигрыше по среднеквадратическому отклонению местоположения.

A discrete filter is examined for the joint estimation of the coordinates, velocity, and angular rate W of a target performing a steady turn, based on indirect (polar/spherical) radar measurements. When W is included in the augmented state vector, the increment conversion matrix becomes a nonlinear function of W itself; consequently, linearization – as employed in previously studied versions of the extended Kalman filter for indirect measurements – requires recalculating the Jacobian matrix at each step and introduces an additional methodological error. An unscented transformation of the augmented state vector is proposed to eliminate the need for linearizing the motion and measurement models. Monte Carlo statistical simulations (Nrun = 545) were conducted to compare the proposed algorithm with its linearized counterpart across eight standard surveillance radar types (2D and 3D) and five target turn rates. The results demonstrate that the proposed algorithm yields a root-mean-square error for the W estimate that is, on average, 4.3 times lower (median 4.0; range 1.4–14.0 across all observation conditions) than that of the linearized extended Kalman filter, while offering a more modest improvement (averaging 1.2 times) in the root-mean-square error of the position estimate.

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The authors declare that there are no conflicts of interest present.