This paper addresses the application of measurement on goodness-of-fit (GoF) for amplitudes of radar clutter sample data against reference/theoretic parameterized probability density function (PDF). In general, various existing methods for this problem highly depend on empirical PDF parameters. This makes GoF assessments with these methods less perceivable and their accuracies are hard to control. A new method based on chi-squared type of measurement is proposed to overcome these difficulties. This method evaluates GoF by estimating the distance between the true PDF of the clutter data amplitude and the reference PDF. Hence the distance is statistically approximately independent with empirical PDF parameters. The new method has higher accuracy and symmetric property. It is especially useful for GoF comparison over multiple radar clutter data sets.
"A Modified Goodness-of-Fit Measurement for Radar Clutter Amplitude Statistics," Progress In Electromagnetics Research M,
Vol. 27, 151-165, 2012. doi:10.2528/PIERM12092104
1. Yueh, S. H., J. A. Kong, J. K. Jao, R. T. Shin, H. A. Zebker, T. Le Toan, and H. Ottl, "K-distribution and polarimetric terrain radar clutter," Progress In Electromagnetics Research, Vol. 3, 237-275, 1990.
2. Frery, A. C., H. J. Muller, C. C. F. Yanasse, and S. J. S. Sant'Anna, "A model for extremely heterogeneous clutter," IEEE Transactions on Geoscience and Remote Sensing, Vol. 35, No. 3, 648-659, 1997. doi:10.1109/36.581981
3. Tatarskii, V. I. and V. V. Tatarskii, "Statistical non-Gaussian model of sea surface with anisotropic spectrum for wave scattering theory. Part I," Progress In Electromagnetics Research, Vol. 22, 259-291, 1999.
4. Balleri, A. and A. Nehorai, "Maximum likelihood estimation for compound-Gaussian clutter with inverse gamma texture," IEEE Transactions on Aerospace and Electronic Systems, Vol. 43, No. 2, 775-779, 2007. doi:10.1109/TAES.2007.4285370
5. Younsi, A. and M. Nadour, "Performance of the adaptive normalized matched filter detection in compound-Gaussian clutter with inverse gamma texture model," Progress In Electromagnetics Research B, Vol. 32, 21-38, 2011. doi:10.2528/PIERB11051905
6. Habib, M. A., M. Barkat, B. Aissa, and T. A. Denidni, "Ca-Cfar detection performance of radar targets embedded in ``non centered Chi-2 Gamma" clutter," Progress In Electromagnetics Research, Vol. 88, 135-148, 2008. doi:10.2528/PIER08092203
7. Farshchian, M. and F. L. Posner, "The pareto distribution for low grazing angle and high resolution X-band sea clutter," 2010 IEEE Radar Conference, 789-793, 2010. doi:10.1109/RADAR.2010.5494513
8. 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
9. Li, , H. C., W. Hong, Y. R. Wu, and P. Z. Fan, "An efficient and flexible statistical model based on generalized Gamma distribution for amplitude SAR images," IEEE Transactions on Geoscience and Remote Sensing, Vol. 48, No. 6, 2711-2722, 2010. doi:10.1109/TGRS.2010.2041239
10. Balleri, A. and A. Nehorai, "Maximum likelihood estimation for compound-Gaussian clutter with inverse gamma texture," IEEE Transactions on Aerospace and Electronic Systems, Vol. 43, No. 2, 775-779, 2007. doi:10.1109/TAES.2007.4285370
11. Owolawi, P. A., "Rainfall rate probability density evaluation and mapping for the estimation of rain attenuation in South Africa and surrounding islands," Progress In Electromagnetics Research, Vol. 112, 155-181, 2011.
12. Kanellopoulos, J. D., A. D. Panagopoulos, and S. N. Livieratos, "Differential rain attenuation statistics including an accurate estimation of the e®ective slant path lengths," Progress In Electromagnetics Research, Vol. 28, 97-120, 2000. doi:10.2528/PIER99060503
13. Anastassopoulos, V., G. Lampropoulos, A. Drosopoulos, and M. Rey, "High resolution radar clutter statistics," IEEE Transactions on Aerospace and Electronic Systems, Vol. 35, No. 1, 43-60, 1999. doi:10.1109/7.745679
. Sokal, R. R. and F. J. Rohlf, Biometry: The Principles and Practice of Statistics in Biological Research, Freeman, New York, 1981.
15. Meyer, M. E. and D. V. Gokhale, "Kullback-Leibler information measure for studying convergence rates of densities and distributions," IEEE Transactions on Information Theory, Vol. 39, No. 4, 1401-1404, 1993. doi:10.1109/18.243456
16. Koehler, K. J. and K. Larntz, "An empirical investigation of goodness-of-fit statistics for sparse multinomials," Journal of the American Statistical Association, Vol. 75, No. 370, 336-344, 1980. doi:10.1080/01621459.1980.10477473
18., NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/.
19. Cha, S., "Comprehensive survey on distance/similarity measures between probability density functions," International Journal of Mathematical Models and Methods in Applied Sciences, Vol. 1, No. 4, 300-307, 2007.
20. Bar-Lev, S. K. and P. Enis, "On the classical choice of variance stabilizing transformations and an application for a Poisson variate," Biometrika, Vol. 75, No. 4, 803-804, 1988. doi:10.1093/biomet/75.4.803
21. Guan, Y., "Variance stabilizing transformations of poisson, binomial and negative binomial distributions," Statistics and Probability Letters, Vol. 79, No. 14, 1621-1629, 2009. doi:10.1016/j.spl.2009.04.010
22. Cherno, H. and E. L. Lehmann, "The use of maximum likelihood estimates in χ2 tests for goodness-of-fit," The Annals of Mathematical Statistics, Vol. 25, No. 3, 579-586, 1954. doi:10.1214/aoms/1177728726
23. Farina, A., F. Gini, M. V. Greco, and L. Verrazzani, "High resolution sea clutter data: Statistical analysis of recorded live data," IEE Proceedings | Radar, Sonar and Navigation, Vol. 144, No. 3, 121-130, Jun. 1997. doi:10.1163/156939398X00926
24. Arikan, F., "Statistics of simulated ocean clutter," Journal of Electromagnetic Waves and Applications, Vol. 12, No. 4, 499-526, 1998.