Nihat KABAOĞLU, Selçuk PAKER, Hakan Ali ÇIRPAN

3 boyutlu uzayda kaynak konumlandırması için en büyük olabilirlik yaklaşımı

Bu çalışmanın amacı, anten dizilimi ile aynı düzlemde bulunmayan 3 boyutlu uzayda bulunan kaynakların konumlarının kestirimidir. Kaynak konumları, 2 boyutlu dikdörtgen anten diziliminde toplanan verileri kullanan en büyük olabilirlik kestirimcisi ile belirlenmiştir. En büyük olabilirlik kestirimcisi, diğer kestirim yöntemlerine göre bir çok avantaja sahip olmasına rağmen işlemsel yoğunluğu olan bir algoritmadır. Bu işlemsel yoğunluk, çok boyutlu arama probleminden kaynaklanmaktadır. Karşılaşılan işlemsel yoğunluk, özyinelemeli beklenti en büyükleme algoritmasının ilgilenilen probleme uyarlanmasıyla ortadan kaldırılmıştır. Ayrıca, geliştirilen kestirimcinin başarımının incelenebilmesi için yansız bir kestirimci için alt sınırı oluşturan Cramer-Rao Sınırları çıkarılmıştır. Benzetim örneklerinden kullanılan yöntemin özellikle yüksek sinyal gürültü oranlarında oldukça iyi sonuçlar verdiği gözlemlenmiştir

Maximum likelihood approach for localization of sources in 3-D space

Various estimation methods have been proposed for localization of passive sources till now. Most of these studies assumed, sources were at the same plane with antenna array. This assumption may be inappropriate for some applications in real world. The goal of this study is to estimate unknown locations of sources that is not at same plane with antenna array but in 3-D space. Locations of the sources are determined by maximum likelihood estimator that uses data collected by a 2-D rectangular array. Maximum Likelihood Method is chosen as the estimator since it has better resolution performance than the conventional methods in the presence of less number and highly correlated source signal samples and low signal to noise ratio. Besides these superiorities, stability, asymptotic unbiasedness, asymptotic minimum variance properties and bringing no restrictions on the antenna array are the additional reasons for the decision of this method. Despite these advantages, Maximum Likelihood Estimator has computational complexity. This problem arises from multidimensional search problem. Computational complexity was overcome by adapting iterative Expectation Maximization algorithm to the problem at hand. Furthermore, Cramer-Rao bounds that is the lower bound of any unbiased estimator are derived for analyzing the accuracy performance of the proposed algorithm. It was observed that the proposed algorithm gave satisfactory results especially for high signal to noise ratios.

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