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Оптимизация траектории движения объекта в конфликтной анизотропной среде по вероятностному критерию скрытности И. М. Рудько

By: Рудько, Игорь МихайловичMaterial type: ArticleArticleContent type: Текст Media type: электронный Other title: Optimization of the trajectory of the object in a conflict anisotropic medium according to the probabilistic criterion of stealth [Parallel title]Subject(s): траектория движения объекта | вероятность необнаружения объекта на траектории | анизотропная среда | динамическое программированиеGenre/Form: статьи в журналах Online resources: Click here to access online In: Вестник Томского государственного университета. Управление, вычислительная техника и информатика № 55. С. 71-79Abstract: Рассмотрена задача выбора траектории движения маневрирующего объекта и закона изменения его скорости при движении объекта в трехмерной анизотропной среде распространения сигнала, когда его пытаются обна-ружить несколько наблюдателей, расположенных в заданном районе. Критерием выбора траектории объекта служит вероятность его необнаружения на всей траектории ни одним из наблюдателей. Предложен трехша-говый последовательный дискретный метод оптимизации этого критерия на основе принципа динамического программирования. The problem of choosing the trajectory of a marine moving object (MMO) and the law of change in its velocity during the movement of an object in a three-dimensional anisotropic medium of signal propagation, when several stationary observers (SSS) are located in a given area, are considered. The criterion for choosing the trajectory of an object is the probability of its non-detection on the entire trajectory by any of the observers. An approach is proposed to solve the problem of optimizing the law of MMO evasion from detection by several SSSs for the case when a single detection probability field is known for the entire area intersected by MMO. The MMO control vector includes the evasion path and the law of variation of the velocity V on the path. Relations are derived in the work that make it possible to calculate in a isotropic and anisotropic observation fields a single field (map) of the probability of detecting an object for several SSSs with different technical characteristics. It is shown that for an aniso-tropic field, the map of the probability of detection can be represented as a 4-dimensional matrix in the coordinates (x, y, horig, V), where x, y are the coordinates of the surface of the region, horig is the depth of MMO, V is the MMO velocity. It is shown that using the Pdet detection probability map (x, y, horig, V), when solving the problem of dynamic programming (DP) of the route, it is possible to replace the 4-dimensional vector (x, y, horig, V), according to which optimization is carried out, on a three-step sequential discrete optimization method based on the principle of DP. In this case, at each of the 3 steps, optimization is performed only for two-dimensional vectors: – Construction of the rM route from the Pdet map (x, y) - to the section of the Pdet matrix (x, y, horig, V) with horig = const, Vk = const. – Construction for the chosen route rM of the route according to horig on the Pdet map (rM, horig) - section of the Pdet matrix (x, y, horig, V) along rM at Vk = const. – Calculation for the chosen trajectory Trh (r rM, horig) of the optimal speed Vk according to the Pdet map (Trh, V) - to the section of the Pdet matrix (x, y, horig, V) according to Trh. Such a consistent structure of the algorithm can significantly reduce the amount of computation when constructing the optimal trajectory.
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Рассмотрена задача выбора траектории движения маневрирующего объекта и закона изменения его скорости при движении объекта в трехмерной анизотропной среде распространения сигнала, когда его пытаются обна-ружить несколько наблюдателей, расположенных в заданном районе. Критерием выбора траектории объекта служит вероятность его необнаружения на всей траектории ни одним из наблюдателей. Предложен трехша-говый последовательный дискретный метод оптимизации этого критерия на основе принципа динамического программирования. The problem of choosing the trajectory of a marine moving object (MMO) and the law of change in its velocity during the movement of an object in a three-dimensional anisotropic medium of signal propagation, when several stationary observers (SSS) are located in a given area, are considered. The criterion for choosing the trajectory of an object is the probability of its non-detection on the entire trajectory by any of the observers. An approach is proposed to solve the problem of optimizing the law of MMO evasion from detection by several SSSs for the case when a single detection probability field is known for the entire area intersected by MMO. The MMO control vector includes the evasion path and the law of variation of the velocity V on the path. Relations are derived in the work that make it possible to calculate in a isotropic and anisotropic observation fields a single field (map) of the probability of detecting an object for several SSSs with different technical characteristics. It is shown that for an aniso-tropic field, the map of the probability of detection can be represented as a 4-dimensional matrix in the coordinates (x, y, horig, V), where x, y are the coordinates of the surface of the region, horig is the depth of MMO, V is the MMO velocity. It is shown that using the Pdet detection probability map (x, y, horig, V), when solving the problem of dynamic programming (DP) of the route, it is possible to replace the 4-dimensional vector (x, y, horig, V), according to which optimization is carried out, on a three-step sequential discrete optimization method based on the principle of DP. In this case, at each of the 3 steps, optimization is performed only for two-dimensional vectors: – Construction of the rM route from the Pdet map (x, y) - to the section of the Pdet matrix (x, y, horig, V) with horig = const, Vk = const. – Construction for the chosen route rM of the route according to horig on the Pdet map (rM, horig) - section of the Pdet matrix (x, y, horig, V) along rM at Vk = const. – Calculation for the chosen trajectory Trh (r rM, horig) of the optimal speed Vk according to the Pdet map (Trh, V) - to the section of the Pdet matrix (x, y, horig, V) according to Trh. Such a consistent structure of the algorithm can significantly reduce the amount of computation when constructing the optimal trajectory.

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