350 rub
Journal Radioengineering №6 for 2020 г.
Article in number:
Bearing direction finding absolute errors with placement of the three-element antenna array on the unmanned vehicle
Type of article: scientific article
DOI: 10.18127/j00338486-202006(12)-05
UDC: 621.396.67
Keywords: To develop modern antenna arrays for direction finding the apparatus of Hallen's integral equations and Pocklington's integrodifferential equations are often used. They are used to perform an integer analysis of the distribution of currents in the elements of the antenna array. It is worth considering that these calculations are performed by solving a system of equations with complex unknowns of a rather high order for each discrete value of the azimuthal angle of the radio source in the confidence interval. Thus a restriction is placed on the use of the methods of integral and integro-differential equations used to correct experimentally measured bearings in real time. Due to radio deviation (reflection of radio waves from parts of the carrier) the bearing error can exceed (20…30)°. The theoretical account of the carrier body influence on direction finding errors usually comes down to the problem of diffraction of electromagnetic waves by conducting objects. First direction finding errors were analyzed for various angles of arrival of a wave without a carrier. Some negative asymmetry with respect to zero can be traced in the case of «even» azimuthal angles. For «odd» angles one can distinguish a characteristic region with a minimum absolute error for all calculated angles (from about 500 to 1200 MHz) in which the error does not exceed 1°. When placing the carrier for the «odd» analyzed angles the character of the command is the dependencies of absolute errors with the exception of 15° and 165° as close as possible to the «front» and «back» directions (0° and 180°). Starting from the frequencies of 100-150 MHz a sharp increase in the error to 5° is observed. These measurements show a very strong influence of the carrier on the error. Unfortunately in practice it is impossible to limit ourselves to theoretical calculations only. There is no mathematical model devoid of errors or inaccuracies. Also due to the limited computing and time resources the mathematical model has to be deliberately simplified. Both of the above factors negatively affect the accuracy of the calculation result. Because of this at the moment the development of algorithms for real-time computer correction of bearings measured in full-scale conditions remains relevant.
Authors:

A.S. Samodurov − Ph.D. (Eng.), Associate Professor, 

Design and Manufacture of Radio Department, 

FSBEI of HE «Voronezh State Technical University» (Voronezh, Russia)

E-mail: unaxel2000@mail.ru

D.S. Pogrebnoi − Bachelor of Science, Master Student,

Radioelectronic Devices and Systems Department, 

FSBEI of HE «Voronezh State Technical University» (Voronezh, Russia)

E-mail: denis2371@gmail.com

S.A. Antipov − Dr.Sc. (Phys.-Math.), Professor,

Physic Department, FSBEI of HE «Voronezh State Technical University» (Voronezh, Russia) Е-mail: ofrep@vorstu.ru

A.I. Klimov − Dr.Sc. (Eng.), Professor,

Design and Manufacture of Radio Department, FSBEI of HE «Voronezh State Technical University» (Voronezh, Russia)

Abstract:

To develop modern antenna arrays for direction finding, the apparatus of Hallen's integral equations and Pocklington's integrodifferential equations are often used. They are used to perform an integer analysis of the distribution of currents in the elements of the antenna array. It is worth considering that these calculations are performed by solving a system of equations with complex unknowns of a rather high order for each discrete value of the azimuthal angle of the radio source in the confidence interval. Thus, a restriction is placed on the use of the methods of integral and integro-differential equations used to correct experimentally measured bearings in real time.

Due to radio deviation (reflection of radio waves from parts of the carrier), the bearing error can exceed (20…30)°. The theoretical account of the carrier body influence on direction finding errors usually comes down to the problem of diffraction of electromagnetic waves by conducting objects.

First, direction finding errors were analyzed for various angles of arrival of a wave without a carrier. Some negative asymmetry with respect to zero can be traced in the case of «even» azimuthal angles. For «odd» angles, one can distinguish a characteristic region with a minimum absolute error for all calculated angles (from about 500 to 1200 MHz), in which the error does not exceed 1°.

When placing the carrier for the «odd» analyzed angles, the character of the command is the dependencies of absolute errors, with the exception of 15° and 165°, as close as possible to the «front» and «back» directions (0° and 180°). Starting from the frequencies of 100-150 MHz, a sharp increase in the error to 5° is observed. These measurements show a very strong influence of the carrier on the error.

Unfortunately, in practice it is impossible to limit ourselves to theoretical calculations only. There is no mathematical model devoid of errors or inaccuracies. Also, due to the limited computing and time resources, the mathematical model has to be deliberately simplified. Both of the above factors negatively affect the accuracy of the calculation result. Because of this, at the moment, the development of algorithms for real-time computer correction of bearings, measured in full-scale conditions, remains relevant.

Pages: 24-29
References
  1. Jianzhi Li, Bo Ai, Ruisi He On 3D cluster-based channel modeling for large-scale array communitations. IEEE transactions on wireless communications. 2019. V. 18. № 10. DOI: 10.1109/TWC.2019.2930694.
  2. Chirkov O.N. Matematicheskaja model' vzveshennoj ocenki kanala radiosvjazi dlja mnogoantennyh OFDM-sistem. Vestnik Voronezhskogo gosudarstvennogo tehnicheskogo universiteta. 2019. T. 15. № 4. S. 49−54 (In Russian).
  3. Zang J.W., Alvarez Melcon A., Gomez Diaz J.S. Nonreciprocal phased-array antennas. Physical review applied. 2019. V. 12. № 5.  DOI: 10.1103/PhysRevApplied.12.054008.
  4. Muratov A.V., Nikolaev V.I., Nosova L.A., Samodurov A.S. Chislennyj analiz pelengacionnyh harakteristik kol'cevoj vibratornoj antennoj reshetki, ustanovlennoj na bortu vertoleta. Teorija i tehnika radiosvjazi. Voronezh: «Koncern «Sozvezdie». 2015. № 4. S. 30−35  (In Russian).
  5. Ashihmin A.V., Razinkin K.A., Samodurov A.S. Chislennyj analiz pelengacionnyh harakteristik kol'cevoj vibratornoj antennoj reshetki, ustanovlennoj na bortu samoleta. Vestnik Voronezhskogo gosudarstvennogo tehnicheskogo universiteta. 2005. T. 1. № 11. S. 154−159 (In Russian).
  6. Bobylkin I.S., Muratov A.V., Nosova L.A., Samodurov A.S. Razrabotka pelengacionnoj antennoj reshetki raspolozhennoj na bortu bespilotnogo letatel'nogo apparata. Vestnik Voronezhskogo gosudarstvennogo tehnicheskogo universiteta. 2015. T. 11. № 6. S. 133−135 (In Russian).
  7. Mollai S., Farzaneh F. Compact cross form antenna arrays intended for wideband two-dimensional interferometric direction finding including the channel phase tracking error. AEU-international journal of electronics and communications. 2018. V. 83. Р. 558-565. DOI: 10.1016/j.aeue.2017.10.030.
  8. Ashihmin A.V., Razinkin K.A., Samodurov A.S. Obosnovanie vozmozhnosti ispol'zovanija uproshhennoj jelektrodinamicheskoj modeli samoleta v vide sovokupnosti konusa i cilindra. Vestnik Voronezhskogo gosudarstvennogo tehnicheskogo universiteta. 2005. T. 1.  № 11. S. 34−39 (In Russian).
  9. Pirogov A.A., Buslaev A.B., Kostjukov A.S. Razrabotka modelej i algoritmov proektirovanija cifrovyh ustrojstv s ispol'zovaniem  programmiruemyh logicheskih integral'nyh shem. Vestnik Voronezhskogo gosudarstvennogo tehnicheskogo universiteta. 2018. T. 14. № 4. S. 88−95 (In Russian).
  10. Lee Jung-Hoon, Lee Jong-Hwan, Woo Jong-Myung. Method for obtaining three- and four-element array spacing for interferometer direction-finding system. IEEE antennas and wireless propagation letters. 2016. V. 15. Р. 897−900.
Date of receipt: 17 марта 2020 г.