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Аbout one of the methods of the decision of a problem of definition of coordinates in the system of spatial positioning of objects


V.P. Panov, V.V. Prikhodko, A.F. Kuzminsky

In this article the author considers the well-known method of solving the problem of determining the location of the receiving radio signals object from the four transmission of objects with the specified in the Cartesian system of spatial coordinates, proposed R. Bucher and D. Misra. The search coordinates in this method are determined according to the difference of time of arrival of the radio signals to a receiver from two different transmitters. The problem is reduced to solving a quadratic equation for a definition that has two values and through which are expressed linear coordinates . Choice of the correct solution is carried out with the involvement of additional information about the approximate location of the object. For the solution, obtained by R.Bucher and D.Misra, we considered two variants of the method of elimination of ambiguity without additional information involvement. In the first variant, the choice of the correct solution for is based on the use of a known method of successive approximations for the linearized in the vicinity of the search coordinates of nonlinear equations distances. The initial coordinates of the location of the object are used alternately decisions and , as the exact solution pick the one of the decisions for which the iterative process converges with the required accuracy. In the second variant of the expression for the search value receive directly through the solutions and . Both are discussed in this article variants can be used for the correct determination of the coordinates . Lack of an iterative process in the second variant makes it more preferable in comparison with the first.
June 24, 2020
May 29, 2020

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