پردازش آرايه‌اي بر مبناي مدل GARCH
محورهای موضوعی : مهندسی برق و کامپیوترهادی امیری 1 , حمیدرضا امین داور 2 , محمود کمره‌ای 3
1 - دانشگاه صنعتی امیرکبیر
2 - دانشگاه صنعتی امیرکبیر
3 - دانشگاه تهران
کلید واژه: پردازش سيگنال آرايه‌ايتخمين سمت ورودتخمين حداكثر احتمالGARCH Cramer-Rao Bound,
چکیده مقاله :
در مقاله حاضر، يك مدل جديد براي نويز جمع‌شونده براساس سريهاي زماني GARCH در پردازش سيگنال آرايه‌اي ارائه شده است. در بسياري از روشها بدلايلي همچون پيچيدگي‌هاي پياده‌سازي و محاسباتي توزيع احتمال نويز، گوسي فرض مي‌شود. بررسي‌‌ها و اندازه‌گيري‌هاي انجام گرفته براي نويز محيطي در كاربرد‌هاي مختلف، نشان از غيرگوسي بودن آن دارد و در شرايط واقعي كارايي روش‌هايي كه مبتني بر مدل گوسي نويز هستند، كاهش مي‌يابد. از مهمترين ويژگي‌هاي فرآيند نويز محيطي دنباله‌دار بودن (Heavy Tail) توزيع احتمال و تغيير ويژگي‌هاي آماري آن (مانند واريانس) در محيط مي‌باشد. از طرف ديگر فرآيند GARCH داراي خصوصيات مهمي همچون دنباله‌دار بودن توزيع احتمال و همچنين مدلسازي ناپايداري از طريق روابط بازگشتي بر روي واريانس شرطي است كه با توجه به ويژگي‌هاي اين فرآيند به نظر مي‌رسد كه مدل مناسبي براي نويز محيطي جمع‌شونده در كاربرد‌هاي پردازش آرايه‌اي باشد. در مقاله حاضر با استفاده از تخمين حداكثر احتمال ، روش جديد بكارگيري GARCH در پردازش آرايه‌اي ارائه و به كمك شبيه‌سازي در كاربرد آكوستيك زيرآب، كارايي اين روش در مقايسه با روشهاي ديگر به كمك خطاي تخمين سمت ورود اهداف در كنار معيار Cramer-Rao Bound اثبات شده است.
In this paper, we propose a new model for additive noise based on GARCH time-series in arraysignal processing. Due to the some reasons such as complex implementation and computational problems, probability distribution function of additive noise is assumed Gaussian. In the different applications, scrutiny and measurement of noise shows that noise can sometimes significantly non-Gaussian and thus the methods based on Gaussian noise will degrade in an actual conditions. Heavy-tail probability density function (PDF) and time-varying statistical characteristics (e.g.; variance) are the most features of the additive noise process. On the other hand, GARCH process has important properties such as heavy-tail PDF (as excess kurtosis) and volatility modeling through feedback mechanism onto conditional variance so that it seems the GARCH model is a good candidate for the additive noise model in the array processing applications. In this paper, we propose a new method based on GARCH using the maximum likelihood approach in array processing and verify the performance of this approach in the estimation of the Direction-of-Arrivals of sources against the other methods and using the Cramer-Rao Bound.
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