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Article:

# Algorithm of determining the coordinates and angular orientation of direction-finder antennas on two flying machine with ground-base radio direction-finder

DOI 10.18127/j00338486-201909(13)-06

Keywords:

A.D. Vinogradov – Dr.Sc.(Eng.), Professor, Main Research Scientist, MESC «Zhukovsky–Gagarin Air Force Academy» (Voronezh)
A.Yu. Vostrov – Senior Designer, JSC «Concern «Sozvezdie» (Voronez)
E-mail: a.y.vostrov.1988@mail.ru
I.S. Dmitriev – Ph.D.(Eng.), Leading Research Scientist, JSC «Concern «Sozvezdie» (Voronez)
E-mail: dmiv@mail.ru

The spatial orientation of the i-th object is characterized by a column vector of 6 scalar values: coordinates and orientation angles: .
In a mathematically correct formulation, the problem of estimating the spatial orientation of the i-th and j-th air objects direction-finding antennas from measured azimuth and elevation, altitudes and distances is a statistical problem of estimating an unknown 12-dimensional parameter on which depends N-dimensional random variable density distribution – a observation vector from its one-time sampling.
The conditional distribution density of the observation vector ν with a centered Gaussian error distribution law is
,
where the observation vector ν contains the objects heights value and their mutual azimuth and elevation and/or range with ground mark; K – is the covariance matrix of the elements of the observation vector ; – vector of observation errors, – analytical expression of the vector of observation through the elements of the state vector.
From the likelihood function, obtained an expression for the object direction-finding antenna spatial orientation errors covariance matrix according to the Rao–Cramer inequality. Using these expressions, constructed MSE magnitude dependence graphs of determining the spatial orientation parameters of a pair air objects direction-finding antennas, depending on their relative orientation with respect to the reference sources of radio emission.
The smallest standard deviation of spatial orientation parameters of the objects direction-finding antennas by the angular-height method can be obtained when they are located near the reference sources of radio emission. To provide with high accuracy the determination of the objects coordinates and orientation angles away from the reference sources of radio emission, it is necessary to use an angular-height-distance measuring method for determining the orientation parameters.
Article contains 5 drawings, 1 table and references to 21 sources of the information.

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