Comparative Analysis of Mathematical Models of Tracking Radio Altimeters

Introduction. Tracking radio altimeters of low altitudes are widely used in civil aviation. These devises use periodic frequency modulated continuous wave (FMCW) signals, while altitude measurements are based on processing the beat signal processing. For this purpose, a closed automatic control loop is arranged to maintain the frequency of the beat signal at a fixed level by changing parameters of the transmitted signal (the frequency deviation or the modulation period). An alternative approach to arranging the tracking loop for altitude variations is based on the use of a phase locked loop (PLL), which adjusts the reference signal – a copy of the emitted signal – to obtain the maximum cross-correlation of the beat and reference signals. А comparative analysis of short-range radio altimeters with other currently known tracking radio altimeters for various types of frequency modulation of the transmitted signal seems to be a relevant research task.

Aim. An analysis of the influence of the type of frequency modulation on the accuracy of altitude estimation in a PLL-based radar altimeter, as well as a comparative analysis of this altimeter with other known tracking altimeters.

Materials and methods. Mathematical models of tracking radio altimeters are proposed, and a computer simulation of their performance is carried out for the case of altitude estimation over a smooth flat surface.

Results. The conducted comparative analysis of tracking radio altimeters confirmed the effectiveness of the PLL when processing signals of different frequency modulation type (sawtooth, triangular, and harmonic FM). Altitude estimates produced by PLL-based radar altimeters are unbiased, with their standard deviation not exceeding 3 cm for the signalto-noise ratio of greater than 10 dB and under the scenario parameters adopted in the work. The conducted comparison with other tracking altimeters showed that estimation errors of this radar altimeter are an order of magnitude smaller.

Conclusion. A PLL-based tracking radar altimeter can be used to estimate the height of the aircraft flight. The quality of altitude estimates produced by this device is higher than those produced by other known tracking radio altimeters. Further research and field tests will investigate the accuracy of altitude estimation when working over a rough surface.

1. Skolnik M. I. Radar handbook. 3rd ed. McGrawHill Education, 2008, 1328 p.

2. Radar Handbook. Ed. by M. I. Skolnik. 2nd ed. NY, McGraw-Hill, 1990, 1200 p.

3. Skolnik M. I. Introduction to Radar Systems. 2nd ed. NY, McGraw-Hill, 1980, 581 p.

4. Sosnovskii A. A., Khaimovich I. A. Radioelektronnoe oborudovanie letatel'nykh apparatov: sprav. [Aircraft Radio Equipment Handbook]. Moscow, Transport, 1987, 255 p. (In Russ.)

5. Sosnovskii A. A., Khaimovich A. I., Lutin E. A., Maksimov I. B. Aviatsionnaya radionavigatsiya: sprav. [Air Navigation Aids. Handbook]. Moscow, Transport, 1990, 264 p. (In Russ.)

6. Ostrovityanov R. V., Basalov F. A. Teoriya radiolokatsii protyazhennykh tselei [Theory of Radar of Extended Targets]. Moscow, Radio i svyaz', 1992, 232 p. (In Russ.)

7. Vidmar M. Design Improves 4.3 GHz Radio Altimeter Accuracy. Microwaves & RF. 2005, vol. 44, no. 6, pp. 57–70.

8. Reshma S., Midhunkrishna P. R., Joy S., Sreelal S., Vanidevi M. Improved Frequency Estimation Technique for FMCW Radar Altimeters. 2021 Intern. Conf. on Recent Trends on Electronics, Information, Communication & Technology (RTEICT). Bangalore, India, 27–28 Aug. 2021. IEEE, 2021, pp. 185–189. doi: 10.1109/RTEICT52294.2021.9573544

9. Zhukovskii A. P., Onoprienko E. I., Chizhov V. I. Teoreticheskie osnovy radiovysotometrii [Theory of Radio Altimetry]. Moscow, Sov. radio, 1979, 320 p. (In Russ.).

10. Tarasenkov A. A. The FM-Radio Range Sensor with Digital Tracking Loop. Sensors and Systems. 2019, no. 2, pp. 40–44.

11. Monakov A. A., Tarasenkov A. A. FMCW Radio Altimeter with the PLL to Adjust the Reference Signal. Pat. RU 207967 U1 G01S 13/34 (2021.08) H04L 25/03 (2021.08).

12. Roland E. Best Phase-Locked Loops. Design, Simulation and Applications. 4th ed. Ohio, Blacklick McGraw-Hill, 1999.

13. Shinnaka S. A New Frequency-Adaptive PhaseEstimation Method Based on a New PLL Structure for Single-Phase Signals. 2007 Power Conversion Conf. Nagoya, Japan, 2–5 Apr. 2007. IEEE, 2007, pp. 191– 198. doi: 10.1109/PCCON.2007.372967

14. Xu W., Huang C., Jiang H. Analyses and Enhancement of Linear Kalman-Filter-Based PhaseLocked Loop. IEEE Transactions on Instrumentation and Measurement. 2021, vol. 70, pp. 1–10, art. no. 6504510. doi: 10.1109/TIM.2021.3112776

15. Monakov A., Nesterov M. Statistical Properties of FMCW Radar Altimeter Signals Scattered from a Rough Cylindrical Surface. IEEE Transactions on Aerospace and Electronic Systems. 2017, vol. 53, no. 1, pp. 323–333. doi: 10.1109/TAES.2017.2650498

16. Chauhan A., Rout P., Singh K. M. Vibration Parameters Estimation using mHDFT Filter in PLL Technique. Intern. Conf. on Computational Performance Evaluation (ComPE), Shillong, India, 18 Sept. 2020. IEEE, 2020, pp. 649–653. doi: 10.1109/ ComPE49325.2020.9200039

17. Sithamparanathan K. Digital-PLL Assisted Frequency Estimation with Improved Error Variance. IEEE Global Telecommunications Conf., New Orleans, USA, 8 Dec. 2008. IEEE, 2008, pp. 1–5. doi: 10.1109/GLOCOM.2008.ECP.676

18. Oppenheim, A., Schafer R. Tsifrovaya obrabotka signalov [Digital Signal Processing]. Transl. by Boev S. F., 3d ed. Moscow, Tekhnosfera, 2012, 1049 p. (In Russ.)