Modelación de distribuciones novedosas para la representación del Clutter de Radar
DOI:
https://doi.org/10.18041/entramado.2017v13n2.26227Palavras-chave:
Clutter de radar, Distribución Log-Weibull, Distribución Pearson, Distribución Lomax, Distribución LévyResumo
El clutter es una señal interferente causada por la reflexión de la emisión del radar sobre la superficie que rodea al blanco. Tradicionalmente, se han utilizado las distribuciones K, Weibull, Log-Normal, Rayleigh y Pareto para representar el comportamiento del clutter ; sin embargo, varios estudios han señalado la aplicación de otras alternativas novedosas que pudieran ser más adecuadas que las distribuciones tradicionales. Este artículo presenta la modelación de tres alternativas novedosas, las distribuciones Log-Weibull, Pearson (Lévy) y Lomax, en un conjunto de funciones informáticas de MATLAB. El código implementado permite un acceso fácil a la manipulación de las funciones de densidad y distribución, a la generación de variables aleatorias, al cálculo de los momentos y a la estimación de los parámetros de las distribuciones abordadas. La implementación está concebida para brindar a la comunidad de radares herramientas de simulación de la respuesta de los detectores de radar ante un amplio rango de condiciones de operación, lo cual permite la creación de nuevos mecanismos de procesamiento. Asimismo, se viabiliza el estudio del eco electromagnético que se obtiene de las superficies terrestres y marinas, con posibles aplicaciones medioambientales. El código creado formará parte de la librería MATE-CFAR 2 que incluirá varias distribuciones de clutter y detectores de radar.
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ABRAHAM, Douglas A.; PRESTON, John R. Statistical Analysis of Monostatic and Bistatic Echoes from ShipWreck. In: IEEE Journal of Oceanic Engineering. 2010. vol. 25, no. 1, p. 1-8 , doi: 10.1109/JOE.2014.2331533
AL-NOOR, Nadia H.; ALWAN, Shahad Saad. Non-Bayes, Bayes and Empirical Bayes Estimators for the Shape Parameter of Lomax Distribution. In: Mathematical Theory and Modeling. 2015. vol. 5, no. 2, p. 17-28.
ALZAATREH, Ayman; FAMOYE, Felix; LEE, Carl (2013). Weibull-Pareto Distribution and Its Applications. In: Communication in Statis-tics- Theory and Methods. 2013. vol. 42, no. 9, p. 1673-1691. doi: 10.1080/03610926.2011.599002
ATKINSON, Anthony B.; HARRISON, Allan J. Distribution of Personal Wealth in Britain. Cambridge: Cambridge University Press, 1978.
BAKER, Rose D. Application of some new Heavy-tailed Survival Distributions. Technical Report arXiv:1412.0952. 2014. Centre for Operational Research and Applied Statistics, University of Salford, United Kingdom.
CAI, Long; MA, Xiaochuan; HAO, Chengpeng; YANG, Xiaoguang. Performace Analysis of Distributed Fuzzy CA-CFAR Detector in Pearson Distributed Clutter. In: Sixth International Conference on Fuzzy Systems and Knowledge Discovery. (14-16 Aug: Tiajin, China). 2009.
CAI, Long; MA, Xiaochuan; YAN, Xiaoguang; HAO, Cehngpeng (2010). Some Analysis of Fuzzy CAGO/SO CFAR Detector in Non-Gaussian Background. In: IEEE 2nd International Workshop on Intelligent Systems and Applications. (22-23 May: Huei University, China). 2010.
CAMPBELL, Gregory; RATNAPARKHI, Makarand V. An application of Lomax distributions in receiver operating characteristic (ROC) curve analysis. Communications in Statistics–Theory Methods. 1993. vol. 22, no. 6, p. 681–1697.
CORBELLINI, Aldo; CROSATO, Lisa; GANUGI, Piero; MAZZOLI, Marco. Fitting Pareto II distributions on firm size: Statistical method-ology and economic puzzles. In: International Conference on Applied Stochastic Models and Data Analysis. (29 May - 31 Jun: Chania, Crete). 2007.
FARSHCHIAN, Masoud; POSNER, Fred L. (2010). The Pareto Distribution for Low Grazing Angle and High Resolution X-Band Sea Clutter. In: IEEE 2010 Radar Conference. (10-14 May: Washington DC, USA). 2010.
FIALKOWSKI, Joseph M.; GAUSS, Roger C.; DRUMHELLER, David M. Measurements and Modeling of Low-Frequency Near-Surface Scattering Statistics. In: IEEE Journal of Oceanic Engineering. 2004. vol. 29, no. 2, p. 197-214, doi: 10.1109/JOE.2004.828973
FINGAS, Merv. Handbook of Oil Spill Science and Technology. Wiley: New York, 2015.
GENTLE, James E. Random number generation and Monte Carlo methods. 2nd edition, Springer: New York, 2003 p. 102-109.
GINOS, Brenda F. Parameter Estimation for the Lognormal Distribution. Master of Science, Brigham Young University, Utah, USA. 2009.
GUPTA, Jaya; GARG, Mridula; GUPTA, Mahesh. The Lomax-Gumbel Distribution. In: Palestine Journal of Mathematics. 2016, vol. 5, no. 1, p. 35-42.
HASSAN, Amal S.; AL-GHAMDI, Amani S. Optimum step stress accelerated life testing for Lomax distribution. In: Journal of Applied Sciences Research. 2009. vol. 5, no. 12, p. 2153–2164.
ABDENOUR, Meziani Hilal; FAOUZI, Soltani. Performance analysis of some CFAR detectors in homogeneous Pearson-distributed clutter. In: Signal Processing. 2006, vol. 86, no. 8, p. 2115-2122. doi: 10.1016/j.sigpro.2006.02.036
HOLLAND, Oliver; GOLAUP, Assen; AGHVAMI, Hamid. Traffic Characteristics of Aggregated Module Downloads for Mobile Terminal Reconfiguration. In: IEE proceedings on Communications. 2006. vol. 153, no. 5, p. 683-690.
ISHII, Seishiro; SAYAMA, Syuji; MIZUTANI, Koichi. Effect of Changes in Sea-Surface State on Statistical Characteristics of Sea Clutter with X-band Radar. In: Wireless Engineering and Technology. 2011, vol. 2, no. 3, p. 175-183, doi: 10.4236/wet.2011.23025
JAE MYUNG, In Jae. Tutorial on Maximum Likelihood Estimation. In: Journal of Mathematical Psychology. 2003, vol. 47, no. 1, p. 90-100, doi: 10.1016/S0022-2496(02)00028-7
KURUOGLU, Ercan E. (2003). Analytical representation for positive alpha stable densities. In: IEEE International Conference in Acous-tics, Speech and Signal processing. 2003.
LEUNG, Sai W.; MINETT, James W.; SIU, Yu M. A fuzzy approach to signal integration. In: IEEE Transactions on Aerospace and Electronic Systems. 2002. vol. 38, no. 1, p. 346-351. doi: 10.1109/7.993258
LOMAX, K. S. Business failures: Another example of the analysis of failure data. In: Journal of the American Statistical Association. 1954, vol. 49, no. 268, p. 847–852.
MACHADO FERNÁNDEZ, José R. Estimation of the Relation between Weibull Distributed Sea clutter and the CA-CFAR Scale Factor. In: Journal of Tropical Engineering. 2015. vol. 25, no. 2, p. 19-28, doi: 10.15517/jte.v25i2.18209
MACHADO FERNÁNDEZ, José R.; BACALLAO VIDAL, Jesús C. Modelación de la Distribución K en MATLAB para Aplicaciones de Radar. In: Revista de Ingeniería Electrónica, Automática y Comunicaciones (RIELAC). 2016. vol. 37, no. 2, p. 54-66.
MACHADO FERNÁNDEZ, José R. Modelación de la Distribución Gamma en MATLAB para Aplicaciones de Radar. In: Ciencias Hol-guín. 2016a. vol. 22, no. 4, p. 1-17.
MACHADO FERNÁNDEZ, José R. Modelación de las Distribuciones Rayleigh y Exponencial en MATLAB para Aplicaciones de Radar. In: Telem@tica. 2016b. vol. 15, no. 2, p. 1-15.
MACHADO FERNÁNDEZ, José R. Distribuciones Estadísticas para Modelar Clutter Marino: Una Revisión (aceptado para publicación). In: Revista de Ingeniería Electrónica, Automática y Comunicaciones (RIELAC). 2017.
MACHADO FERNÁNDEZ, José R. Modelación de las Distribuciones Weibull y Log-Normal para Aplicaciones de Radar (aceptado para publicación). In: Ciencias Holguín. 2017a.
MACHADO FERNÁNDEZ, José R.; BACALLAO VIDAL, Jesús C. MATE-CFAR: Ambiente de Pruebas para Detectores CFAR en MATLAB. Telem@tica. 2014. vol. 13, no. 3, p. 86-98.
MACHADO FERNÁNDEZ, José R.; BACALLAO VIDAL, Jesús C. Improved Shape Parameter Estimation in K Clutter with Neural Net-works and Deep Learning. In: International Journal of Interactive Multimedia and Artificial Intelligence. 2016a. vol. 3, no. 7, p. 96-103. doi: 10.9781/ijimai.2016.3714
MACHADO FERNÁNDEZ, José R.; BACALLAO VIDAL, Jesús C. Improved Shape Parameter Estimation in Pareto Distributed Clutter with Neural Networks. In: International Journal of Artificial Intelligence and Interactive Multimedia. 2016b. vol. 4, no. 8, p. 7-11. doi: 10.9781/ijimai.2016.421
MACHADO FERNÁNDEZ, José R.; BACALLAO VIDAL, Jesús C. Optimal Selection of the CA-CFAR Adjustment Factor for K Power Sea Clutter with Statistical Variations. In: Ciencia e Ingeniería Neogranadina. 2016c. vol. 27, no. 1, p. 61-76. doi: 10.18359/rcin.1714
MACHADO FERNÁNDEZ, José R.; BACALLAO VIDAL, Jesús C.; Chávez Ferry, Nelson. A Neural Network Approach to Weibull Dis-tributed Sea Clutter Parameter’s Estimation. In: Inteligencia Artificial. 2015. vol. 18, no. 56, p. 3-13. doi: 10.4114/ia.v18i56.1090
MACHADO FERNÁNDEZ, José R.; SÁNCHEZ RAMS, Roberto C. Implementación de un Detector de Promediación de Clutter (CA-CFAR) usando VHDL. Telem@tica. 2016. vol. 15, no. 2, p. 52-61.
MALEVERGNE, Yannick; PISARENKO, Vladilen; SORNETTE, Didier. Empirical Distributions of Stock Returns: between the Stretched Exponential and the Power Law. In: Quantitative Finance. 2005. vol. 5, no. 4, p. 379-401.
MCLAUGHLIN, Michael P. Compendium of Common Probability Distributions, 2014. p. 47.
MENG, Xiandong; FENG, Ganzhong; XUE, Hua; HE, Zhiming. Wideband Radar Target Detection Theory in Coherent K Distributed Clutter. In: Research Journal of Applied Sciences, Engineering and Technology. 2013. vol. 5, no. 5, p. 1528-1532.
MEZIANI ABEDNOUR, Hilal; SOLTANI, Faouzi. Generalised Decentralised Fuzzy CA-CFAR Detector in Pearson Distributed Clutter. In: IEEE 10th International Conference on Signal Processing. 2010. p. 1915-1918
NIKIAS, Chrysostomos L.; SHAO, Min (1995). Signal processing with alpha-stable distributions and applications. Wiley: New York, 1995.
O’CONNOR, Andrew N. Probability Distributions Used in Reliability Engineering. University of Maryland: USA, 2011. p. 34, 116.
PIERCE, Robert D. RCS characterisation using the alpha stable distribution. In: IEEE 1996 National Radar Conference. (13-16 May: Michigan, USA). 1996.
PIERCE, Robert D. Application of the positive alpha stable distribution. In: IEEE Signal Processing Workshop on Higher-Order Statis-tics, Alberta, Canada. (21-23 Jul: Alberta, Canada). 1997.
MURTHY, D. N. Prabhakar; XIE, Min; JIANG, Renyan. Weibull Models. Wiley: New York, 2004.
PRESTON, John R.; ABRAHAM, Douglas A. Statistical Analysis of Multistatic Echoes From a Shipwreck in the Malta Plateau. In: IEEE Journal of Oceanic Engineering. 2015. vol. 40, no. 3, p. 643-656. doi: 10.1109/JOE.2014.2331533
QI, Cong-hui; ZHAO, Zhi-qin. Electromagnetic Scattering and Statistic Analysis of Clutter from Oil Contaminated Sea Surface. In: Radi-oengineering. 2015. vol. 24, no. 1, p. 87-92, doi: 10.13164/re.2015.0087
RINNE, Horst. The Weibull Distribution A Handbook. CRC Press: London, 2009.
ROSENBERG, Luke; BOCQUET, Stephen. Application of the Pareto Plus Noise Distribution to Medium Grazing Angle Sea-Clutter. In: IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing. 2015, vol. 8, no. 1, p. 255-261, doi: 10.1109/JSTARS.2014.2347957
ROTH, Michael. On the Multivariate t Distribution. Technical Report LiTH-ISY-R-3059. 2013. Department of Electrical Engineering, Linkopings Universitet, Germany.
SAYAMA, Shuji; ISHII, Seishiro. Amplitude Statistics of Ground Clutter from Town and Hill Observed by S-band Radar. In: IEEJ Trans-actions Fundamentals and Materials. 2011. vol. 131, no. 11, p. 916-923, doi: 10.1541/ieejfms.131.916
SAYAMA, Shuji; ISHII, Seishiro. Amplitude Statistics of Sea Clutter by MDL Principle. In: IEEJ Transactions Fundamentals and Materi-als. 2011. vol. 132, no. 10, p. 886-892, doi: 10.1541/ieejfms.132.886
SAYAMA, Shuji; ISHII, Seishiro. Suppression of Log-Normal Distributed Weather Clutter Observed by an S-Band Radar. In: Wireless Engineering and Technology. 2013. vol. 4, no. 3, p. 125-133, doi: 10.4236/wet.2013.43019
SAYAMA, S.; SEKINE, M. Weibull, Log-Weibull and K-Distributed Ground Clutter Modelling Analyzed by AIC. In: IEEE Transactions on Aerospace and Electronic Systems. 2001, vol. 37, no. 3, p. 1108-1113, doi: 10.1109/7.953262
SCHOENECKER, Steven; WILLETT, Peter; BAR SHALOM, Yaakov. The Effect of K-Distributed Clutter on Trackability. In: IEEE Trans-actions on Signal Processing. 2016. vol. 64, no. 2, p. 475-484, doi: 10.1109/TSP.2015.2478745
SEKINE, Matsuo; MUSHA, Toshimitsu. Log-Weibull Distributed Sea Clutter. In: IEE Proceedings. 1980. vol. 127, no. 3, p. 225-228, doi: 10.1049/ip-f-1:19800033
SHAKEEL, Muhammad; REHMAT, Nazia; AHSAN UL HAQ, Muhammad. Comparison of the Robust Parameters Estimation Methods for the Two-Paramaters Lomax Distribution. In: Cogent Mathematics. 2017. vol 4, no. 1, p. 1-11, doi: 10.1080/23311835.2017.1279397
TAHIR, Muhammad H.; CORDEIRO, Gauss M.; MANSOOR, Abbasi; ZUBAIR, Muhammad. The Weibull-Lomax Distribution: Properties and Applications. In: Hacettepe Journal of Mathematics and Statistics. 2015. vol. 44, no. 2, p. 461-480. doi: 10.15672/HJMS.2014147465
TSAKALIDE, Panagiotis.; TRINCI, F.; NIKIAS, Chrysostomos L. Performance assessment of CFAR processors in Pearson-distributed clutter. In: IEEE Transactions on Aerospace and Electronic Systems. 2000. vol. 36, no. 4, p. 1377-1386, doi: 10.1109/7.892685
WALCK, Christian. On Moments and their Estimation. Internal Note SUF-PFY/91-01. Particle Physics Group, Deparment of Physics, University of Stockholm: Stockholm, Sweden, 1991.
WALCK, Christian. Hand-book on Statistical Distributions for Experimentalists. Particle Physics Group, University of Stockholm: Stock-holm, Sweden, 2007. p. 53.
WARD, Keith; TOUGH, Robert; WATTS, Simon. Sea Clutter Scattering, the K Distribution and Radar Performance. 2nd edition, The Institution of Engineering and Technology: London, United Kingdom, 2013.
WEINBERG, Graham V. Assessing the Pareto Fit to High Resolution High Grazing Angle Sea Clutter. In: IET Electronics Letters. 2011a. vol. 47, no. 1, p. 516-517.
WEINBERG, Graham V. An Investigation of the Pareto Distribution as a Model for High Grazing Angle Clutter. DSTO-TR-2525. 2011b. Electronic Warfare and Radar Division, Defence Science and Technology Organization: Edinburgh, South Australia.
WEINBERG, Graham V. Constant False Alarm Rate Detectors for Pareto Clutter Models. In: IET Radar, Sonar and navigation. 2013. vol. 7, no. 2, p. 153-163, doi: 10.1049/iet-rsn.2011.0374.
WEINBERG, Graham V. Constant False Alarm Rate Detection in Pareto Distributed Clutter: Further Results and Optimality Issues. In: Contemporary Engineering Sciences. 2014. vol. 7, no. 6, p. 231-261, doi: dx.doi.org/10.12988/ces.2014.3737
WEINBERG, Graham V. Formulation of a Generalised Switching CFAR with application to X-Band Maritime Surveillance Radar. In: Springer Plus. 2015. vol. 4, no. 574, p. 1-13.
ZHU, Difei; SUN, Jiaxiu (2014). Empirical Distributions of Stock Returns and Applications in Value at Risk. (Master of Science in Fi-nance), South China Normal University, China.