Bearing estimation using double frequency reassignment for a linear passive array
The paper demonstrates the use of frequency reassignment for bearing estimation. For this task, signals derived from a linear equispaced passive array are used. The presented method makes use of Fourier transformation based spatial spectrum estimation. It is further developed through the application of two-dimensional reassignment, which leads to obtaining highly concentrated energy distributions in the joint frequency-angle domain and sharp graphical imaging. The introduced method can be used for analysing, a priori, unknown signals of broadband, nonstationary, and/or multicomponent type. For such signals, the direction of arrival is obtained based upon the marginal energy distribution in the angle domain, through searching for arguments of its maxima. In the paper, bearing estimation of three popular types of sonar pulses, including linear and hyperbolic frequency modulated pulses, as well as no frequency modulation at all, is considered. The results of numerical experiments performed in the presence of additive white Gaussian noise are presented and compared to conventional digital sum-delay beamforming performed in the time domain. The root-mean-square error and the peak-to-average power ratio, also known as the crest factor, are introduced in order to estimate, respectively, the accuracy of the methods and the sharpness of the obtained energy distributions in the angle domain
- 1. F. Auger, P. Flandrin, Yu-Ting Lin, S. McLaughlin, S. Meignen, T. Oberlin, Hau-Tieng Wu, ”Time-frequency reassignment and synchrosqueezing: an overview”, IEEE Signal Proc. Mag., vol. 30, no. 6, pp. 32–41, 2013.
- 2. J.S. Byrnes, “Quadrature Mirror Filters, Low Crest Factor Arrays, Functions Achieving Optimal Uncertainty Principle Bounds, and Complete Orthonormal Sequences – A Unified Approach”, Applied and Computational Harmonic Analysis, vol. 1, no. 3, pp. 261–266, 1994.
- 3. Z . Chen, J. Su n, H. Hou, “Phase d i fference met hod for DOA estimation”, J. of Marine Science and Application, vol. 9, no.4, pp.445–450, 2010.
- 4. C. Chi, Z. Li, Q. Li, “Fast broadband beamforming using nonuniform Fast Fourier Transform for underwater real-time 3-d acoustical imaging”, IEEE J. Ocean. Eng., vol.41, no.2, pp.249–246, 2016.
- 5. K. Czarnecki, “The instantaneous frequency rate spectrogram”, Mech. Syst. Signal Process., vol. 66–67, pp.361–373, 2016.
- 6. K. Czarnecki, W. Leśniak, “The synchrosqueezing method in the bearing estimation of stationary signals for a passive sonar system with a towed array”, Hydroacoustics, vol. 18, pp. 41–46, 2015.
- 7. S.A. Fulop, K. Fitz, “Algorithms for computing the time-corrected instantaneous frequency (reassigned) spectrogram, with applications”, J. Acoust. Soc. Amer. (JASA), vol. 119, no. 1, pp.360–371, 2006.
- 8. V.A. Del Grosso, “Tables of the speed of sound in open ocean water (with Mediterranean Sea and Red Sea applicability)”, J. Acoust. Soc. Amer. (JASA), vol.53, no.5, pp.1384–1401, 1973.
- 9. S. Haykin, Radar array processing for angle of arrival estimation in Array Signal Processing, pp. 149–292, Prentice-Hall, 1985.
- 10. L.B. Jackson, H. Chien, “Frequency and bearing estimation by two-dimensional linear prediction”, proc. IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 4, pp. 665–668, 1979.
- 11. K. Kodera, C.D. Villedary, R. Gendrin, “A new method for the numerical analysis of non-stationary signals”, Phys. Earth Planet. In., vol.12, pp.142–150,1976.
- 12. H. Krim, M. Viberg, “Two decades of array signal processing research”, IEEE Signal Proc. Mag., vol. 13, no. 4, pp.67–94, 1996.
- 13. A. De Maio, Y. Huang, M. Piezzo, S. Zhang, A. Farina, “Design of Optimized Radar Codes with a Peak to Average Power Ratio Constraint”, IEEE Tran. Signal Process., vol. 59, no. 6, pp. 2683–2697, 2011.
- 14 . J. Marszal, Digital signal processing applied to the modernization of Polish Navy sonars, Polish Maritime Research, vol. 21, no. 2, pp. 65–75, 2014.
- 15. B. Maranda, “Efficient digital beamforming in the frequency domain”, J. Acoust. Soc. Amer., vol. 86, no. 5, pp. 1813–1819, 1989.
- 16. R.G. Pridham, R.A. Mucci, “Digital interpolation beamforming for low-pass and bandpass signals”, in Proceedings of the IEEE, vol. 67, no. 6, pp. 904–919, 1979.
- 17. M. Readhead, Calculations of the sound scattering of hyperbolic frequency modulated chirped pulses from fluid-filled spherical shell sonar targets, technical note, Maritime Operations Division, Defence Science and Technology Organisation, Australia, 2010.
- 18. P. Rudnick, “Digital Beamforming in the Frequency Domain”, J. Acoust. Soc. Amer., vol. 46, no. 5, pp. 1089–1090, 1969.
- 19. H . S l a b b e k o o r n , N . B o u t o n , I . Va n O p z e e l a n d , A . C o e r s , C . t e n Cate, A.N. Popper, “A noisy spring: the impact of globally rising underwater sound levels on fish”, Trends in Ecology & Evolution, vol. 25, no. 7, pp. 419–427, 2010.
- 20. W. Szymczak, E. Kozaczka, G. Grelowska, I. Gloza, and S. Kozaczka, “The shallow sea experiment with usage of linear hydrophone array”, The Journal of the Acoustical Society of America, vol. 133, no. 5, pp. 3439-3439, 2013.
- 21. E. Tuncer, B. Friedlander, Classical and Modern Direction of Arrival Estimation, Elsevier, Burlington, MA, 2009
- 22. J.R. Williams, “Fast beam-forming algorithm”, J. Acoust. Soc. Amer. (JASA), vol. 44, no. 5, pp. 1454–1455, 1968.
- 23. G. Grelowska, E. Kozaczka, S. Kozaczka, W. Szymczak, “Underwater Noise Generated by a Small Ship in the Shallow Sea”, Archives of Acoustics, vol. 39, no. 3, pp. 351–356, 2013.
- 24. G. Grelowska, “Study of seasonal acoustic properties of sea water in selected waters of the southern Baltic”, Polish Maritime Research, vol. 23, no. 1, pp. 25–30, 2016.
- 25. G. Grelowska, E. Kozaczka, S. Kozaczka, W. Szymczak, “Gdansk Bay sea bed sounding and classification of its results”, Polish Maritime Research, vol. 20, no. 3, pp. 45–50, 2013.