In this paper, sequential parametric detection problem is addressed for non-Gaussian correlated clutter. It is well known that the assumption of normally distributed clutter leads, mostly, to analytical expressions of the threshold as well the distribution of detection statistic. Nevertheless, due to the resolution improvement of recent sensing instruments such as high resolution radar, the Gaussian assumption is unrealistic since the clutter is nonhomogeneous. As a consequence, using non-Gaussian assumption of the clutter prevents, mostly, of obtaining analytical expressions of the threshold and the distribution of detection statistics. In this work, we overcome this issue by use of the so called bootstrap techniques for dependent data. Numerical simulations reveal that our proposed method outperforms the classical and sequential non-bootstrap based detection schemes in terms of probability of detection and selects the optimum sample size needed to achieve the required detection performances.
Mohammed Nabil El Korso,
Abdelhak M. Zoubir,
"Bootstrap Based Sequential Detection in Non-Gaussian Correlated Clutter," Progress In Electromagnetics Research C,
Vol. 81, 125-140, 2018. doi:10.2528/PIERC17111608
1. Watts, S., "Radar clutter and multipath propagation," IEE Proceedings F (Radar and Signal Processing), Vol. 138, 73-74, IET, 1991. doi:10.1049/ip-f-2.1991.0011
2. Park, S., E. Serpedin, and K. Qaraqe, "Gaussian assumption: The least favorable but the most useful," IEEE Signal Processing Magazine, Vol. 30, No. 3, 183-186, 2013. doi:10.1109/MSP.2013.2238691
3. Greco, M., F. Gini, and M. Rangaswamy, "Statistical analysis of measured polarimetric clutter data at different range resolutions," Proceedings of the IEE, Radar Sonar and Navigation, Vol. 153, No. 6, 473-481, 2006. doi:10.1049/ip-rsn:20060045
4. Conte, E., A. De Maio, and C. Galdi, "Statistical analysis of real clutter at different range resolutions," IEEE Transactions on Aerospace and Electronic Systems, Vol. 40, No. 3, 903-918, 2004. doi:10.1109/TAES.2004.1337463
5. Carretero-Moya, J., J. Gismero-Menoyo, A. Blanco-del Campo, and A. Asensio-Lopez, "Statistical analysis of a high-resolution sea-clutter database," IEEE Transactions on Geoscience and Remote Sensing, Vol. 48, No. 4, 2024-2037, 2010. doi:10.1109/TGRS.2009.2033193
6. Ward, K. D., S. Watts, and R. J. Tough, Sea Clutter: Scattering, the K Distribution and Radar Performance, Vol. 20, IET, 2006. doi:10.1049/PBRA020E
7. Conte, E., M. Longo, and M. Lops, "Modelling and simulation of non-rayleigh radar clutter," IEE Proceedings F, Radar and Signal Processing, Vol. 138, 121-130, IET, 1991. doi:10.1049/ip-f-2.1991.0018
8. Gini, F., "A cumulant-based adaptive technique for coherent radar detection in a mixture of kdistributed clutter and gaussian disturbance," IEEE Transactions on Signal Processing, Vol. 45, No. 6, 1507-1519, 1997. doi:10.1109/78.599993
9. Ward, K., "Compound representation of high resolution sea clutter," Electronics Letters, Vol. 17, No. 16, 561-563, 1981. doi:10.1049/el:19810394
10. Lampropoulos, G., A. Drosopoulos, N. Rey, et al. "High resolution radar clutter statistics," IEEE Transactions on Aerospace and Electronic Systems, Vol. 35, No. 1, 43-60, 1999. doi:10.1109/7.745679
11. Rangaswamy, M., D. D. Weiner, and A. Ozturk, "Non-gaussian random vector identification using spherically invariant random processes," IEEE Transactions on Aerospace and Electronic Systems, Vol. 29, No. 1, 111-124, 1993. doi:10.1109/7.249117
12. Conte, E., M. Lops, and G. Ricci, "Asymptotically optimum radar detection in compound-gaussian clutter," IEEE Transactions on Aerospace and Electronic Systems, Vol. 31, No. 2, 617-625, 1995. doi:10.1109/7.381910
13. Gini, F. and M. Greco, "Suboptimum approach to adaptive coherent radar detection in compound-Gaussian clutter," IEEE Transactions on Aerospace and Electronic Systems, Vol. 35, No. 3, 1095-1104, 1999. doi:10.1109/7.784077
14. Sangston, K. J., F. Gini, M. V. Greco, and A. Farina, "Structures for radar detection in compound gaussian clutter," IEEE Transactions on Aerospace and Electronic Systems, Vol. 35, No. 2, 445-458, 1999. doi:10.1109/7.766928
15. Conte, E., A. De Maio, and G. Ricci, "Recursive estimation of the covariance matrix of a compound-Gaussian process and its application to adaptive CFAR detection," IEEE Transactions on Signal Processing, Vol. 50, No. 8, 1908-1915, 2002. doi:10.1109/TSP.2002.800412
16. Gini, F. and M. Greco, "Covariance matrix estimation for cfar detection in correlated heavy tailed clutter," Signal Processing, Vol. 82, No. 12, 1847-1859, 2002. doi:10.1016/S0165-1684(02)00315-8
17. Pascal, F., P. Forster, J.-P. Ovarlez, and P. Larzabal, "Performance analysis of covariance matrix estimates in impulsive noise," IEEE Transactions on Signal Processing, Vol. 56, No. 6, 2206-2217, 2008. doi:10.1109/TSP.2007.914311
18. Boukaba, T., A. M. Zoubir, and D. Berkani, "Parametric detection in non-stationary correlated clutter using a sequential approach," Digital Signal Processing, Vol. 36, 69-81, 2015. doi:10.1016/j.dsp.2014.10.003
19. Ramakrishnan, D. and J. Krolik, "Adaptive radar detection in doubly nonstationary autoregressive doppler spread clutter," IEEE Transactions on Aerospace and Electronic Systems, Vol. 45, No. 2, 484-501, 2009. doi:10.1109/TAES.2009.5089536
20. Dong, Y., "Parametric adaptive matched filter and its modified version,", Defense Science and Technology Organization South Australia, 2006.
21. Wald, A., Sequential Analysis, Courier Dover Publications, 1947.
22. Zoubir, A. M. and D. R. Iskander, Bootstrap Techniques for Signal Processing, Cambridge University Press, 2004. doi:10.1017/CBO9780511536717
23. Chernick, M. R., Bootstrap Methods: A Practitioner’s Guide, Wiley-Interscience, 1999.
24. Chernick, M. R., W. Gonz´alez-Manteiga, R. M. Crujeiras, and E. B. Barrios, "Bootstrap methods," International Encyclopedia of Statistical Science, 169-174, Springer, 2011. doi:10.1007/978-3-642-04898-2_150
25. Zoubir, A. M. and D. R. Iskandler, "Bootstrap methods and applications," IEEE Signal Processing Magazine, Vol. 24, No. 4, 10-19, 2007. doi:10.1109/MSP.2007.4286560
26. Suratman, F. Y. and A. M. Zoubir, "Bootstrap based sequential probability ratio tests," IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 6352-6356, IEEE, 2013.
27. Nagaoka, S. and O. Amai, "A method for establishing a separation in air traffic control using a radar estimation accuracy of close approach probability," J. Japan Ins. Navigation, Vol. 82, 53-60, 1990. doi:10.9749/jin.82.53
28. Nagaoka, S. and O. Amai, "Estimation accuracy of close approach probability for establishing a radar separation minimum," The Journal of Navigation, Vol. 44, No. 1, 110-121, 1991. doi:10.1017/S0373463300009784
29. Krolik, J., G. Niezgoda, and D. Swingler, "A bootstrap approach for evaluating source localization performance on real sensor array data," IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 1281-1284, IEEE, 1991.
30. Bohme, J. and D. Maiwald, "Multiple wideband signal detection and tracking from towed array data," IFAC Proceedings, Vol. 27, No. 8, 107-112, 1994. doi:10.1016/S1474-6670(17)47700-7
31. Debes, C., C. Weiss, A. M. Zoubir, and M. G. Amin, "Distributed target detection in through-the-wall radar imaging using the bootstrap," IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 3530-3533, IEEE, 2000.
32. Walck, C., "Hand book on statistical distributions for experimentalists," Tech. Rep., Particle Physics Group, University of Stockholm, 1996.
33. Basseville, M., "Distance measures for signal processing and pattern recognition," Signal Processing, Vol. 18, No. 4, 349-369, 1989. doi:10.1016/0165-1684(89)90079-0
34. Martinez, W. L. and A. R. Martinez, Computational Statistics Handbook with MATLAB, Vol. 22, CRC Press, 2007.
35. Davison, A. C. and D. V. Hinkley, Bootstrap Methods and Their Application, Vol. 1, Cambridge University Press, 1997. doi:10.1017/CBO9780511802843
36. Efron, B. and R. J. Tibshirani, An Introduction to the Bootstrap, CRC Press, 1994.