In the present research the optimizing approach to the determination of the parameters of an inaccessible point of an object is developed. The common issues are revealed and essential steps of their resolution are identified.
The essence of the problem is an objective contradiction between a requirement for the location of points A and B of the centers of the sighting tubes of optical devices in the same horizontal plane P1 and the lack of a real possibility to perform such to achieve this an identical one-level arrangement without error.
The aim of the study is to develop strategies for determining the position of an inaccessible point of an object in the minimum domain between intersecting sighting rays as well as an adaptive algorithm for determining the values of the parameters of an inaccessible point under the given absolute and relative errors.
To achieve this aim, the following problems are formulated and solved in the paper: 1. Develop strategies for determining the position of the inaccessible point of the object in the minimum domain between the intersecting sighting rays. 2. Develop an adaptive algorithm for determining the values of the parameters of an inaccessible point based on the specified absolute and relative errors.
In the proposed optimizing approach, the three-dimensional geometrical model with crossed directional rays for the determination of coordinates of the inaccessible point of an object is developed. It is discussed that points С and C', coordinated of which to be determined, locates in domain [CDM, CEM], [C'D'M, C'E'M] of the minimum distance ρmin between crossed directional rays.
The optimizing problem of the determination of coordinates of an inaccessible point of an object in space is reduced to a problem of the determination of the minimum distance between two crossed directional rays.
It’s known from the theory of function of multiple variables that function ρ = f (tC'D', tC'E') reaches its extremum ρmin when its partial derivatives by each variable are equal to zero.
Three strategies for selecting the position of the inaccessible point C (xC, yC, zC) in the found minimum region [CDM, CEM] are proposed. The required point C' (xC', yC', zC') can be located, for example, in the middle of the minimum segment [C'D'M, C'E'M].
The essence of the adaptive algorithm is in optimizing the variation of the initial values of data α, α', β, γ, γ', AB, at which the absolute and relative errors of the coordinates of the inaccessible point satisfy the error values set by the customer (0.0001-1.2%)
The proposed approach is verified using real experimental data.
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