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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)
E-mail: mvvad@mail.ru
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


Satellite radio navigation systems are currently used to determine with high accuracy the coordinates and the angular orientation of the aircraft and the equipment placed on them (in particular, on-board direction finding antennas). Under the conditions of loss of signals from satellite radio navigation systems, the coordinates and angular orientation of aircraft can be determined using onboard autonomous navigation sensors and systems (inertial, geomagnetic). However, the disadvantage of on-board autonomous navigation sensors and systems is the deterioration of the accuracy of determining navigation parameters with an increase in the time interval since the calibration of sensors or systems. The coordinates and the angular orientation of the aircraft, having in its composition a direction-finding antenna, an altimeter, a radio reference point and, if necessary, a radio rangefinder, can be determined by an angular-altimeter or an angular-altimeter-distance-measuring method in the presence of a ground reference point containing a reference source of radio emission, a direction finder and if necessary, a radio range finder.
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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