Компенсация ошибок оценивания местоположения, вызванных тропосферным распространением радиоволн, в широкозонных мультилатерационных системах

Introduction. Wide area multilateration (WAM) systems are the main competitors of secondary surveillance radar (SSR) systems used in air traffic control (ATC). The general principle of WAM operation is based on the assessment of pseudoranges between a signal source (an aircraft airborne transponder) and the ground receivers with precisely known geographical coordinates deployed over the ATC area. The aircraft position is estimated by measuring pseudoranges. A significant factor affecting the accuracy of aircraft positioning is tropospheric refraction, a phenomenon caused by the inhomogeneity of the earth's atmosphere and manifested in a deviation in the direction of the rays along which the signal of an aircraft transponder propagates. Refraction increases the lengths of ray paths, thus increasing the corresponding pseudoranges. As a result, the estimate of the aircraft position receives an additional bias. Altitude estimates produce unreasonably large errors.Aim. To develop a mathematical model for the signals received by a WAM system, which accounts for tropospheric wave propagation, as well as to derive an algorithm for aircraft positioning with compensated tropospheric errors.Materials and methods. Equations for the pseudorange estimation errors caused by wave propagation in a spherically stratified atmosphere were derived using the method of geometrical optics.Results. This paper proposed a mathematical model for pseudorange estimates in WAM systems, which accounts for the bias associated with the phenomenon of tropospheric refraction. An analysis of the proposed model showed that pseudorange errors depend linearly on the distance between the aircraft transponder and the receiver. This conclusion allowed an algorithm for aircraft positioning with compensated tropospheric errors to be developed. The proposed algorithm yields an unbiased estimate of the aircraft position. The standard deviation of altitude estimates increases by 60%, although remaining within the limits permissible for WAM systems.Conclusions. The developed mathematical model of WAM signals, which considers tropospheric propagation errors in pseudorange estimation, as well as the algorithm for aircraft positioning with compensated tropospheric errors, can be used in the development of spatially distributed navigation systems.Введение. Широкозонные мультилатерационные системы навигации (Wide Area Multilateration, WAM) являются основным конкурентом комплексов вторичной радиолокации систем управления воздушным движением. Принцип работы WAM-систем заключается в измерении псевдодальностей сигнала бортового ответчика воздушного судна системой разнесенных в пространстве приемных станций и последующей оценке местоположения. Одним из существенных факторов, влияющих на точность оценки местоположения воздушного судна (ВС), является тропосферная рефракция. Рефракция приводит к увеличению длины оптического пути сигнала, а следовательно, и измеряемых псевдодальностей. Следствием этого является появление дополнительного смещения у оценок местоположения ВС. При этом недопустимо большие значения смещения получаются при оценке высоты.Цель работы. Получение математической модели сигналов приемных станций WAM-системы, которая учитывает особенности тропосферного распространения радиоволн, и синтез алгоритма оценки местоположения ВС с компенсацией тропосферных ошибок при оценивании псевдодальностей.Материалы и методы. Методом геометрической оптики получены уравнения, позволяющие рассчитать ошибки измерения псевдодальностей, вызванные рефракцией в сферически слоистой тропосфере.Результаты. Предложена математическая модель формирования оценок псевдодальностей, учитывающая тропосферную рефракцию. Анализ модели показал, что ошибки измерения псевдодальностей линейно зависят от расстояния между ответчиком ВС и приемным пунктом. Этот вывод позволил синтезировать алгоритм оценивания местоположения ВС с компенсацией тропосферных ошибок. Синтезированный алгоритм позволяет полностью избавиться от смещения у оценок местоположения ВС при увеличении СКО оценки высоты на 60 % и сохранении этого параметра в допустимых для WAM-систем пределах.Заключение. Полученные в статье математическая модель сигналов WAM-системы, учитывающая ошибки тропосферного распространения радиоволн при оценке псевдодальностей, и алгоритм оценивания местоположения ВС с компенсацией тропосферных ошибок могут быть использованы при разработке многопозиционных навигационных систем

Quantum Jordanian twist

The quantum deformation of the Jordanian twist F_qJ for the standard quantum Borel algebra U_q(B) is constructed. It gives the family U_qJ(B) of quantum algebras depending on parameters x and h. In a generic point these algebras represent the hybrid (standard-nonstandard) quantization. The quantum Jordanian twist can be applied to the standard quantization of any Kac-Moody algebra. The corresponding classical r-matrix is a linear combination of the Drinfeld- Jimbo and the Jordanian ones. The obtained two-parametric families of Hopf algebras are smooth and for the limit values of the parameters the standard and nonstandard quantizations are recovered. The twisting element F_qJ also has the correlated limits, in particular when q tends to unity it acquires the canonical form of the Jordanian twist. To illustrate the properties of the quantum Jordanian twist we construct the hybrid quantizations for U(sl(2)) and for the corresponding affine algebra U(hat(sl(2))). The universal quantum R-matrix and its defining representation are presented.Comment: 12 pages, Late

Compensation of Positioning Errors Caused by Tropospheric Wave Propagation in Wide-Area Multilateration Systems

Introduction. Wide area multilateration (WAM) systems are the main competitors of secondary surveillance radar (SSR) systems used in air traffic control (ATC). The general principle of WAM operation is based on the assessment of pseudoranges between a signal source (an aircraft airborne transponder) and the ground receivers with precisely known geographical coordinates deployed over the ATC area. The aircraft position is estimated by measuring pseudoranges. A significant factor affecting the accuracy of aircraft positioning is tropospheric refraction, a phenomenon caused by the inhomogeneity of the earth's atmosphere and manifested in a deviation in the direction of the rays along which the signal of an aircraft transponder propagates. Refraction increases the lengths of ray paths, thus increasing the corresponding pseudoranges. As a result, the estimate of the aircraft position receives an additional bias. Altitude estimates produce unreasonably large errors.Aim. To develop a mathematical model for the signals received by a WAM system, which accounts for tropospheric wave propagation, as well as to derive an algorithm for aircraft positioning with compensated tropospheric errors.Materials and methods. Equations for the pseudorange estimation errors caused by wave propagation in a spherically stratified atmosphere were derived using the method of geometrical optics.Results. This paper proposed a mathematical model for pseudorange estimates in WAM systems, which accounts for the bias associated with the phenomenon of tropospheric refraction. An analysis of the proposed model showed that pseudorange errors depend linearly on the distance between the aircraft transponder and the receiver. This conclusion allowed an algorithm for aircraft positioning with compensated tropospheric errors to be developed. The proposed algorithm yields an unbiased estimate of the aircraft position. The standard deviation of altitude estimates increases by 60%, although remaining within the limits permissible for WAM systems.Conclusions. The developed mathematical model of WAM signals, which considers tropospheric propagation errors in pseudorange estimation, as well as the algorithm for aircraft positioning with compensated tropospheric errors, can be used in the development of spatially distributed navigation systems

Momentary radical removal of lymphangioma in children. The results of prospective cohort study in parallel groups

Lymphangioma is a benign neoplasm caused by a congenital malformation of the lymphatic vessels.Purpose. To study the possibility of momentary radical removal of lymphangioma in children based on a prospective cohort study in parallel groups.Characteristics of children and research methods. The article presents the results of treatment of 152 patients with lymphangioma, reported from the Department of Vascular Surgery of the Children’s Republican Clinical Hospital of Tatarstan. All patients were divided into 3 groups according to the applied method of treatment. The patients in Group 1 (n=95) underwent radical removal of lymphangioma, patients in Group 2 and Group 3 underwent partial removal followed by sclerotherapy of the residual cavity of the lymphangioma.Results. The authors observed relapse in 17 (11.2%) cases, 11 of these cases were observed after previous operation of complete excision (Group 1). According to the study of the distribution of relapses, there was no difference between the groups.Conclusion. Momentary radical excision of lymphangioma is implementable in 63.3% of cases. If it is impossible to remove lymphangioma completely they use partial excision and sclerotherapy of the residual cavity. The probability of relapse does not increase in case of impossibility to remove lymphangioma completely. Minimal invasive procedure is a priority of modern surgery, as it reduces surgical trauma, facilitates postoperative period and improves cosmetic result