D.D. Gabrielyan – Honored Scientist of RF, Dr.Sc.(Eng.), Professor, Deputy Head on Science of STC,  FSUE «RNIIRS» FRPC

N.Yu. Vorobev – Head of Department, 

FSUE «RNIIRS» FRPC

A.N. Gorbachev – Leading Engineer, 

FSUE «RNIIRS» FRPC

V.I. Demchenko – Ph.D.(Eng.), Head of Scientific and Thechnical Complex, 

FSUE «RNIIRS» FRPC

A.A. Saranov – Deputy Head of Department, 

FSUE «RNIIRS» FRPC

D.S. Fedorov – Engineer of the 1st category,  FSUE «RNIIRS» FRPC

The article discusses the use of the least squares method to generalize the applied problems in the development of radio systems and algorithms for their operation. The main areas where least squares method are widely used: The generalized problem of the synthesis of radiation pattern in accordance with the purpose and performance characteristics of the radio systems. Application of the least squares method in the tasks of generalized processing of angle observations of satellites performed in receiving radio systems.

A common approach for both directions is the use of quadratic functionals, the form of which is associated with solvable problems. For the first direction, the article considers from a unified point of view the solution problems of the synthesis of amplitude-phase distribution for a given complex radiation pattern for flat antenna arrays with an arbitrary border, an antenna arrays with radiators located on an arbitrary line, and for correcting amplitude-phase distribution with a deviation radiating aperture from the given. The square of the difference between a given and a formed radiation pattern is used as a functional. The required solution is determined from the condition of minimizing the functional by the parameters of the amplitude-phase distribution.

The second direction is connected with the processing of angle measurements carried out for radio-emitting objects with known coordinates, in particular a satellite. Within the framework of this direction, the tasks of specifying the orbital parameters of the satellite with the known topocentric coordinates of the radio systems and of specifying the orientation of the angular system of the radio systems with the known parameters of the orbit of the satellite are being solved. As for the first direction, the solution of problems is connected with the formation of a quadratic functional and its minimization by the corresponding parameters of the orbit or Euler angles, which determine the position of the angular system in space.

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