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Analysis of Dual-Frequency Interferometry Applicability for Target Elevation Angle Measurement Using Two-Coordinate Radars

*Radio Physics and Radio Astronomy*, Vol. 28, #2, pp.143-157

**(2023)**(in Russian)

### V.G. Galushko, O.M. Vlasenko and E.V. Bulakh

Subject and Purpose. The study deals with the dual-frequency radio interferometry technique, which is based on the employment of two fairly close frequencies with the aim to remove ambiguity of the radar target elevation estimation using 2D-radar and eliminate 2 pm-uncertainty of the signal phase difference measurement. Analysis of random noise action on the accuracy of the elevation angle
estimation by the dual-frequency radio interferometry and assessment of practical applicability of the method make up the purpose of the paper.
Methods and Methodology. The noise action on the elevation angle measurement accuracy is examined through a series of analytical calculations with the use of statistical analysis methods. The noise in each receiving channel is modeled in terms of additive, statistically independent stationary Gaussian processes with zero mean values and equal variances. The calculation results are checked
via computer simulations with statistics estimations for 10 6 random noise realizations.
Results. A correct condition has been developed for the sector width where the target elevation angle is unambiguously estimated depending on the space separation of the antennas (baselines) and the frequency ratio. Expressions for elevation angle estimation errors have been obtained, showing that the error is mainly contributed by the faults in the determination of the ambiguity interval
number. A probability of the correct determination of the ambiguity interval number has been derived depending on the signal-to-noise ratio and the frequency difference, indicating that almost one hundred percent probability of the correct determination of the ambiguity interval number is only achieved when the signal-to-noise ratio exceeds 30 dB. A comparative analysis has been performed between the methods of dual-frequency interferometry and conventional phase-difference direction finding in the case of close X-band frequencies and the same sectors of survey.
Conclusions. The dual-frequency radio interferometry technique with close frequencies has been shown to outperform the standard phase-diff erence direction-fi nding method only when the signal-to-noise ratio is suffi ciently high (over 30 dB). In principle, the accuracy of the technique seems possible to improve by taking signifi cantly diff erent frequencies selected with regard to the scale
negotiation condition. However, it should be mentioned that the implementation of the relevant algorithm in practice is much more complicated than the conventional scheme with a single frequency and several antenna baselines.

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