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About Resolvability of the Problem of Lightning Coordinates Finding by the Time of Lightning Discharge Arrival

Journal of Geoscience and Environment Protection 2021年第3期9卷 209-221页

作者： Yuriy Reingoldovich shpadi Alexandr Sergeevich Inchin Anatoliy yurievich Lozbin Galymzhan Ayazbayev maxim yurievich shpadi Ludmila Ismailovna Mailibayeva Institute of Space Techniques and Technologies Kazakhstan Almaty Institute of Mathematics and Mathematical Modeling Kazakhstan Almaty

On the unit sphere, the geometric problem of calculating the position of a point relative to three given points is considered. We know the length of three spherical segments that go out from the given points in the direction of the unknown point. The requirement must be fulfilled: the distance from each point to an unknown point must be equal to the sum of the length of the segment outgoing from this point, and some increment, the same for all three segments. In the article, the conditions for the solvability of a geometric problem are established by the methods of spherical trigonometry and vector algebra. It is proved that when they are fulfilled, the problem is always solvable. The number of solutions is two, except in rare cases where there is only one solution. A solution method is presented. One of the practical applications is the problem of determining the time and location of a cloud-to-ground lightning discharge, which is directly reduced to this problem.

关键词： Meteorology Lightning Discharge Positioning Spherical Trigonometry Vector Algebra Algorithms

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Triangles Technique for Time and Location Finding of the Lightning Discharge in Spherical Model of the Earth

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Journal of Geoscience and Environment Protection 2016年第4期4卷 125-135页

作者： Anatoliy Lozbin Yuriy shpadi Alexander Inchin Scientific Space Systems Laboratory Institute of Space Techniques and Technologies Almaty Kazakhstan

The spherical model of time and location calculation of the lightning discharge is given. The calculations are made by means of radio signals detection by sensors of the distributed network. The full solution of a problem of lightning discharge cloud-ground type location for three sensors is given. Based on this task the lightning location method for a network of sensors was developed. By means of computational experiments, the analysis of accuracy of the model depending on radio signals detection accuracy at observing stations was done.

关键词： Lightning Time of Arrival Technique (TOA) Atmospheric Spherical Trigonometry

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