Analytical method for determining coordinates of the radiation source in a homogeneous medium

H. V. Velichko

doi:10.15222/TKEA2015.5-6.64

H. V. Velichko Tavria State Agrotechnological University, Melitopol, Ukraine

DOI: https://doi.org/10.15222/TKEA2015.5-6.64

Keywords: task of location, inverse kinematic problem, range-difference method, the point source of radiation, the homogeneous medium, residual function

Abstract

The article considers the problem of determining the position of a radiation source in space, the wave speed and the start of radiation according to the sensors located in the same plane. Sensors (not less than five) detect the passage of the wave front and do not fix the phase of the transmitted wave. In the scientific literature, some authors approach such problem as the inverse kinematic problem, others use the range difference method.
The problem is reduced to finding the minimum of a nonlinear function of five variables. This function is the sum of the squares of the differences of the calculated and the actual time of the wave front passing through the sensor for each of the sensors. In contrast to the well-known works, where the values of parameters are found by iterative methods, in this article we obtain explicit formulas. The idea is to use the new five parameters, which explicitly determine the target value. Relatively to the new parameters, the function takes the form suitable for application of the method of least squares.
This new method for locating of a radiation source in the homogeneous isotropic environment is easier and more accurate than the existing one. It does not require specifying the initial approximation or iterating.

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