Skip to main content
Log in

Estimation of the energy spectrums of reflections in pulse doppler weather radars. Part 3. Statistical analysis of the reconstruction techniques of continuous spectrums of the reflections from meteorological objects

  • Published:
Radioelectronics and Communications Systems Aims and scope Submit manuscript

Abstract

This is the third paper in a series of papers dedicated to the peculiarities of estimation of the continuous energy spectrums of random processes of different nature, which are determined by their samples at discrete moments of time. In the article we justify the methodology and present the quantitative results of analytical and experimental investigation and comparison of statistical characteristics of classical and “parametric” methods of energy spectrums reconstruction for interperiod fluctuations of different nature reflections (including the ones from meteorological objects) in pulse radars. The methodology is followed by quantitative results which correspond to and obtained for a real-world “adaptive” case. Under the latter, a priori unknown echoes’ covariance matrix is replaced with different-kind estimates formed from finite-size training samples. Based on the results obtained, we substantiate the spectral estimation algorithms reasonable for utilization in different-purpose radars, in particular in pulse Doppler weather ones. Discussion of efficient ways for their practical implementation on a unified basis of adaptive lattice filters concludes the paper.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. D. I. Lekhovytskiy, D. V. Atamanskiy, D. S. Rachkov, A. V. Semeniaka, “Estimation of the energy spectrums of reflections in pulse Doppler weather radars. Part 1. Modifications of the spectral estimation algorithms,” Radioelectron. Commun. Syst. 58 (12), 523 (2015), DOI: 10.20535/S0021347015120018.

    Article  Google Scholar 

  2. D. I. Lekhovytskiy, D. V. Atamanskiy, D. S. Rachkov, A. V. Semeniaka, “Estimation of the energy spectrums of reflections in pulse Doppler weather radars. Part 2. Extreme performance,” Radioelectron. Commun. Syst. 59 (9), 379 (2016), DOI: 10.20535/S0021347016090016.

    Article  Google Scholar 

  3. I. S. Reed, J. D. Mallett, L. E. Brennan “Rapid convergence rate in adaptive arrays,” IEEE Trans. Aerosp. Electron. Syst. AES 10, No. 6, 853 (1974), DOI: 10.1109/TAES.1974.307893.

  4. Yu. I. Abramovich, A. I. Nevrev, “The analysis of adaptive maximization of signal-to-interference ratio, which uses the inversion of estimate of the correlation matrix,” Radiotekh. Elektron. 26, No. 12, 2558 (1981).

    Google Scholar 

  5. Yuri I. Abramovich, Nicholas K. Spencer, Ben A. Johnson, “Band-inverse TVAR covariance matrix estimation for adaptive detection,” IEEE Trans. Aerosp. Electron. Syst. 46, No. 1, 375 (2010), DOI: 10.1109/TAES.2010.5417169.

    Article  Google Scholar 

  6. D. Lekhovytskiy, Y. Abramovich, “Adaptive lattice filters for band-inverse (TAVR) covariance matrix approximations,” Proc. of Int. Radar Symp. IRS2009, 09–11 Sept. 2009, Hamburg, Germany (Hamburg, 2009), pp. 535–539.

    Google Scholar 

  7. D. I. Lekhovytskiy, Yu. I. Abramovich, G. A. Zhuga, D. S. Rachkov, “Band-diagonal regularization of ML estimates of the correlation matrices of Gaussian interferences in the adaptation algorithms of antenna arrays,” Applied Radio Electronics 9, No. 1, 107 (2010).

    Google Scholar 

  8. Yuri I. Abramovich, Nicholas K. Spencer, Alexei Y. Gorokhov, “A modified GLRT and AMF framework for adaptive detectors,” IEEE Trans. Aerosp. Electron. Syst. 43, No. 3, 1017 (2007), DOI: 10.1109/TAES.2007. 4383590.

    Article  Google Scholar 

  9. J. P. Burg, “A new analysis technique for time series data,” in: Modern Spectrum Analysis (IEEE Press, 1978) [ed. by D. G. Childers], pp. 42–48.

    Google Scholar 

  10. B. Friedlander, “Lattice filters for adaptive processing,” Proc. IEEE 70, No. 8, 829 (August 1982), DOI: 10.1109/PROC.1982.12407.

  11. B. Friedlander, “Lattice methods for spectral estimation,” Proc. IEEE 70, No. 9, 990 (1982), DOI: 10.1109/PROC.1982.12429.

    Article  Google Scholar 

  12. C. F. N. Cowan, P. M. Grant, Adaptive Filters (Prentice Hall Inc., Englewood Cliffs, New Jersey, 1985).

    MATH  Google Scholar 

  13. A. V. Semeniaka, D. I. Lekhovytskiy, D. S. Rachkov, “Comparative analysis of Toeplitz covariance matrix estimation methods for space-time adaptive signal processing,” Proc. of IEEE CIE Int. Conf. on Radar, RADAR-2011, 24–27 Oct. 2011, Chengdu, China (IEEE, 2011), pp. 696–699, DOI: 10.1109/CIE-Radar.2011. 6159636.

    Google Scholar 

  14. N. A. J. Hastings, J. B. Peacock, Statistical Distributions (Butterworth and Co Ltd, London, 1975).

    MATH  Google Scholar 

  15. Ramon Nitzberg, “Application of maximum likelihood estimation of persymmetric covariance matrices to adaptive processing,” IEEE Trans. Aerosp. Electron. Syst. AES 16, No. 1, 124 (1980), DOI: 10.1109/TAES. 1980.308887.

    Article  Google Scholar 

  16. Yu. I. Abramovich, “The regularized method of adaptive optimization using the criterion of signal-to-interference ratio,” Radiotekh. Elektron. 26, No. 3, 543 (1981).

    Google Scholar 

  17. D. I. Lekhovytskiy, V. I. Zarytskiy, I. D. Rakov, et al. Methods of adaptive lattice filtration in the problems of space-time signal processing [in Russian] (RTI AS USSR, Moscow, 1987).

    Google Scholar 

  18. D. I. Lekhovytskiy, S. V. Polishko, G. A. Zhuga, “On the strategy of utilization of ML estimates of CM in multichannel systems of adaptive signal processing on the noise background,” Proc. of I Int. Sci. Conf. on Global Information Systems. Problems and Development Trends, 2006, Kharkiv–Tuapse, Ukraine (2006), pp. 444–445.

    Google Scholar 

  19. D. I. Lekhovytskiy, V. P. Riabukha, G. A. Zhuga, D. S. Rachkov, “Moving target selection in pulse radar stations. Part 3. Structures, parameters and efficiency of quasioptimal systems of interperiod processing of Gaussian signals on the background of Gaussian passive interferences,” Applied Radio Electronics 8, No. 2, 109 (2009).

    Google Scholar 

  20. D. I. Lekhovytskiy, V. P. Riabukha, G. A. Zhuga, V. N. Lavrentiev, “Experimental investigations of moving target selection systems based on adaptive lattice filters in the pulse radar stations with batch-to-batch staggering of pulse repetition times,” Applied Radio Electronics 7, No. 1, 3 (2008).

    Google Scholar 

  21. R. L. Stratonovich, Foundations of Adaptive Reception [in Russian] (Sov. Radio, Moscow, 1973).

    Google Scholar 

  22. Yuri I. Abramovich, Nicholas K. Spencer, Michael D. E. Turley, “Order estimation and discrimination between stationary and time-varying (TVAR) autoregressive models,” IEEE Trans. Signal Process. 55, No. 6, 2861 (2007), DOI: 10.1109/TSP.2007.893966.

    Article  MathSciNet  Google Scholar 

  23. B. Widrow, S. D. Stearns, Adaptive Signal Processing (Prentice Hall Inc., Englewood Cliffs, New Jersey, 1985).

    MATH  Google Scholar 

  24. R. A. Monzingo, T. W. Miller, Introduction to Adaptive Arrays (John Wiley & Sons, New York, 1980).

    Google Scholar 

  25. V. N. Kokin, A. V. Temerov, V. V. Fedinin, “The utilization of current estimate of the inverse correlation matrix of interferences in the adaptive detector,” Radiotekh. Elektron. 25, No. 7, 1540 (1980).

    Google Scholar 

  26. C. Giraudon, US Patent No. 3876947 (1975).

  27. V. A. Leksachenko, A. A. Shatalov, “The synthesis of multidimensional “whitening” filter using Gram-Schmidt method,” Radiotekh. Elektron. 21, No. 1, 112 (1976).

    Google Scholar 

  28. B. F. Bondarenko, V. P. Prokofiev, “The utilization of functional analysis techniques for the solution of synthesis problems for the system of space-time signal processing,” Radioelectron. Commun. Syst. 25, No. 7, 12 (1982).

    Google Scholar 

  29. Ya. D. Shirman, V. N. Manzhos, Theory and Techniques of Radiolocation Information Processing on the Noise Background [in Russian] (Radio i Svyaz’, Moscow, 1981).

    Google Scholar 

  30. D. I. Lekhovytskiy, D. V. Atamanskiy, D. S. Rachkov, A. V. Semeniaka, “Spectral analysis of reflections in Doppler weather radars,” Proc. of XVII Int. Sci. and Tech. Conf. on Radiolocation, Navigation, Communications, Voronezh, 2011 (2011), pp. 1968–1979.

  31. D. I. Lekhovytskiy, V. P. Riabukha, G. A. Zhuga, D. S. Rachkov, A. V. Semeniaka, “Moving target selection in pulse radar stations. Part 5. Adaptive systems of interperiod processing of Gaussian signals on the background of Gaussian passive interferences,” Applied Radio Electronics 10, No. 4, 506 (2011).

    Google Scholar 

  32. V. Efremov, V. Laurukevich, D. Lekhovytsky, I. Vylegzhanin, B. Vovshin, “Results of theoretical and experimental investigations of meteorological formation power spectrum using “superresolution” methods,” Proc. of Int. Radar Symp. IRS2009, 09–11 Sept. 2009, Hamburg, Germany (Hamburg, 2009), pp. 777–784.

    Google Scholar 

  33. V. Laurukevich, A. Pushkov, I. Vylegzhanin, et al., “Estimation of energy, spectral and polarimetric characteristics of meteorological echoes in DMRL-C,” Proc. of Int. Radar Symp. IRS2011, 7–9 Sept. 2011, Leipzig, Germany (Leipzig, 2011), pp. 267–272.

    Google Scholar 

  34. V. Efremov, I. Vylegzhanin, B. Vovshin, “The new generation of Russian C-band meteorological radars. Technical features, operation modes and algorithms,” Proc. of Int. Radar Symp. IRS2011, 7–9 Sept. 2011, Leipzig, Germany (Leipzig, 2011), pp. 239–244.

    Google Scholar 

  35. D. I. Lekhovytskiy, D. S. Rachkov, A. V. Semeniaka, et al., “Statistical analysis of estimation accuracy of the meteorological formations parameters in pulsed Doppler weather radars with arbitrary staggering of pulse repetition intervals,” Proc. of Int. Radar Symp. IRS2011, 7–9 Sept. 2011, Leipzig, Germany (Leipzig, 2011), pp. 273–278.

    Google Scholar 

  36. V. Laurukevich, A. Pushkov, B. Vovshin, I. Vylegzhanin, “The results of field tests of russian meteorological radar ‘DMRL-C’,” Proc. of the IV Int. Radioelectronics Forum, Kharkiv, Ukraine (Kharkiv, 2011), Vol. 1, pp. 7–12.

    Google Scholar 

  37. J. P. Burg, D. G. Luenberger, D. L. Wenger, “Estimation of structured covariance matrices,” Proc. IEEE 70, No. 9, 963 (1982), DOI: 10.1109/PROC.1982.12427.

    Article  Google Scholar 

  38. D. I. Lekhovytskiy, D. S. Rachkov, A. V. Semeniaka, V. P. Riabukha, D. V. Atamanskiy, “Adaptive lattice filters. Part I. Theory of lattice structures,” Applied Radio Electronics 10, No. 4, 380 (2011).

    Google Scholar 

  39. D. I. Lekhovytskiy, D. S. Rachkov, A. V. Semeniaka, V. P. Riabukha, D. V. Atamanskiy, “Adaptive lattice filters. Part II. Tuning algorithms for ALF,” Applied Radio Electronics 10, No. 4, 405 (2011).

    Google Scholar 

  40. D. I. Lekhovytskiy, D. V. Atamanskiy, D. S. Rachkov, A. V. Semeniaka, “Improvement of accuracy of meteorological objects velocity unambiguous measurement in Doppler weather radars with staggered pulse repetition times,” Radioelectron. Commun. Syst. 58 (9), 385 (2015), DOI: 10.20535/S0021347015090010.

    Article  Google Scholar 

  41. D. I. Lekhovytskiy, “To the theory of adaptive signal processing in systems with centrally symmetric receive channels,” EURASIP J. Advances Signal Process. 33, 1 (2016), DOI: 10.1186/s13634-016-0329-z.

    Google Scholar 

  42. D. I. Lekhovytskiy, D. V. Atamanskiy, I. G. Kirillov, V. I. Zaritskiy, “Comparison of efficiency of adaptive processing in arbitrary and centrally symmetric phased array antennas,” Antennas 1, 30 (2000).

    Google Scholar 

  43. V. P. Riabukha, “Adaptive systems of radar stations noise protection. Part 1. Correlation automatic compensators based on stochastic gradient adaptation algorithms,” Applied Radio Electronics 15, No. 1, 11 (2016).

    Google Scholar 

  44. D. I. Lekhovytskiy, “Thirty years experience in development of adaptive lattice filters theory, techniques and testing in Kharkiv,” Proc. of VIII Int. Conf. on Antenna Theory and Techniques, ICATT2011, 20–23 Sept. 2011, Kyiv, Ukraine (IEEE, 2011), pp. 51–56, DOI: 10.1109/ICATT.2011.6170713.

    Google Scholar 

  45. A. H. Sayed, Fundamentals of Adaptive Filtering (John Wiley and Sons Inc., NJ, Hoboken, 2003).

  46. V. I. Djigan, Adaptive Signal Filtering [in Russian] (Tehnosfera, Moscow, 2013).

    Google Scholar 

  47. Dmytro S. Rachkov, David I. Lekhovytskiy, Andrii V. Semeniaka, Boris M. Vovshin, Uladzimir U. Laurukevich, “Lattice implementation of ‘superresolving’ methods for meteorological objects spectra estimation,” Proc. of 15th Int. Radar Symp. IRS 2014, 16–18 June 2014, Gdansk, Poland (IEEE, 2014), pp. 35–38, DOI: 10.1109/IRS.2014.6869229.

    Google Scholar 

  48. Dmytro S. Rachkov, David I. Lekhovytskiy, “Lattice-filter-based unified structure of system for interperiod processing of weather radar signals,” Proc. of IEEE Int. Radar Conf., 10–15 May 2015, Arlington, USA (IEEE, 2015), pp. 1234–1239, DOI: 10.1109/RADAR.2015.7131183.

    Google Scholar 

  49. David I. Lekhovytskiy, Dmytro S. Rachkov, Andrii V. Semeniaka, “K-rank modification of adaptive lattice filter parameters,” Proc. of IEEE Int. Radar Conf., 10–15 May 2015, Arlington, USA (IEEE, 2015), pp. 127–132, DOI: 10.1109/RADAR.2015.7130983.

    Google Scholar 

  50. D. I. Lekhovytskiy, V. P. Riabukha, D. S. Rachkov, A. V. Semeniaka, “Recursive algorithms of adaptive lattice filters adjustment,” Tehnologiya i Konstruirovanie v Elektronnoi Apparature 2–3, 26 (2016), DOI: 10.15222/TKEA2016.2-3.26.

    Google Scholar 

  51. H. Lev-Ari, T. Kailath, “Schur and Levinson algorithms for nonstationary processes,” Proc. of IEEE Int. Conf. on Acoustic, Speech and Signal Processing, ICASSP, 30 Mar.–1 Apr. 1981, Atlanta, CA, USA (IEEE, 1981), pp. 860–864, DOI: 10.1109/ICASSP.1981.1171194.

    Google Scholar 

  52. K. C. Sharman, T. S. Durrani, “Spatial lattice filter for high-resolution spectral analysis of array data,” IEE Proc. F: Commun. Radar Signal Process. 130, No. 3, 279 (1983), DOI: 10.1049/ip-f-1:19830047.

    Google Scholar 

  53. Dmytro S. Rachkov, David I. Lekhovytskiy, Andrii V. Semeniaka, Viacheslav P. Riabukha, Dmytro V. Atamanskiy, “Lattice-filter-based ground clutter canceller for pulse Doppler weather radar,” Proc. of 15th Int. Radar Symp. IRS 2014, 16–18 June 2014, Gdansk, Poland (IEEE, 2014), pp. 215–219, DOI: 10.1109/IRS.2014. 6869251.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to D. I. Lekhovytskiy.

Additional information

Original Russian Text © D.I. Lekhovytskiy, D.V. Atamanskiy, D.S. Rachkov, A.V. Semeniaka, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radioelektronika, 2017, Vol. 60, No. 2, pp. 59–96.

ORCID: 0000-0001-7519-3239

ORCID: 0000-0002-8705-8584

ORCID: 0000-0002-9329-1294

ORCID: 0000-0002-1170-6151

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lekhovytskiy, D.I., Atamanskiy, D.V., Rachkov, D.S. et al. Estimation of the energy spectrums of reflections in pulse doppler weather radars. Part 3. Statistical analysis of the reconstruction techniques of continuous spectrums of the reflections from meteorological objects. Radioelectron.Commun.Syst. 60, 47–79 (2017). https://doi.org/10.3103/S0735272717020017

Download citation

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0735272717020017

Navigation