V.A. Ufaev – Dr.Sc.(Eng.), Senior Research Scientist, 

MESC «Zhukovsky–Gagarin Air Force Academy» (Voronezh)

E-mail: Andreyuff@mail.ru

On the basis of the hypothesis of equality of the measured and true values of the amplitude of the field strength, an algebraic solution for estimating the unknown coordinates and the energy parameter of the radiator is obtained.

Initially, by compiling and solving a redefined system of linear equations by pseudo-rotation of matrices, the coordinates of the emitter are determined under the assumption of independence of the distance to the reference point from the coordinates of the emitter. Then make and solve the square equation concerning distance to a reference point with the subsequent estimation of coordinates and an energy parameter.

The ambiguity of the algebraic solution is resolved by comparing the maximum likelihood functional and choosing the parameters at which its maximum is reached.

According to the simulation of a cellular-type system in multiplicative noise, the results of algebraic solutions by the maximum likelihood method and the calculated ones are close, except for a special zone where anomalous changes occur due to the limitations of the coordinate determination method.

Algebraic solutions for maximum likelihood estimation provide an increase in the calculation speed of about 500 times.

The proposed principle can be used in solving the ambiguity of algebraic solutions in systems of difference-rangefinder type and in the inverse problem of self-positioning of the receiving point by the amplitude of the electromagnetic field of beacons with a known location.

The article contains 4 figures, a list of references from 9 sources.

1. Ufaev V.A., Afanasev V.I., Razinkov S.N. Otsenka koordinat istochnika radioizlucheniya na osnove izmerenii amplitudy elektromagnitnogo polya. Radiotekhnika. 2003. № 10. S. 71−76. (In Russian).
2. Ufaev V.A. Sposoby opredeleniya mestopolozheniya i prostranstvennoi identifikatsii istochnikov radioizluchenii: Monografiya. Voronezh: Izd-vo «Tsifrovaya poligrafiya». 2019. 430 s. (In Russian).
3. Bulychev Yu.G., Burlai I.V., Kritskii Ya.V. Kompleksnaya optimizatsiya obrabotki izmerenii uglomernykh sistem. Radiotekhnika. 2002. № 4. S. 11−15. (In Russian).
4. Shcherbachyov V.A. Zamknutye resheniya pri opredelenii koordinat v raspredelennoi raznostno-dalnomernoi sisteme. Radiotekhnika. 2013. № 4. S. 4−8. (In Russian).
5. Grudinskaya G.P. Rasprostranenie radiovoln. M.: Vysshaya shkola. 1975. 280 s. (In Russian).
6. Bukov V.N. Vlozhennye sistemy. Analiticheskii podkhod k analizu i sintezu matrichnykh sistem. Kaluga: Izd-vo nauchn. lit-ry N.F. Bochkaryovoi. 2006. 720 s. (In Russian).
7. Falkovich S.E. Otsenka parametrov signala. M.: Sov. radio. 1970. 336 s. (In Russian).
8. Zaezdnyi A.M. Osnovy raschetov po statisticheskoi radiotekhnike. M.: Svyaz. 1969. 447 s. (In Russian).
9. Pat. RF № 2405166. Sposob opredeleniya mestopolozheniya peredatchika perenosnym pelengatorom. Rospatent, byul. № 33.27.11.2010. (In Russian).