Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Statistical resolution limit for the multidimensional harmonic retrieval model: hypothesis test and Cramér-Rao Bound approaches | El Korso et al. EURASIP Journal on Advances in Signal Processing 2011 2011 12 http content 2011 1 12 o EURASIP Journal on Advances in Signal Processing a SpringerOpen Journal RESEARCH Open Access Statistical resolution limit for the multidimensional harmonic retrieval model hypothesis test and Cramér-Rao Bound approaches Mohammed Nabil El Korso Rémy Boyer Alexandre Renaux and Sylvie Marcos Abstract The statistical resolution limit SRL which is defined as the minimal separation between parameters to allow a correct resolvability is an important statistical tool to quantify the ultimate performance for parametric estimation problems. In this article we generalize the concept of the SRL to the multidimensional SRL MSRL applied to the multidimensional harmonic retrieval model. In this article we derive the SRL for the so-called multidimensional harmonic retrieval model using a generalization of the previously introduced SRL concepts that we call multidimensional SRL MSRL . We first derive the MSRL using an hypothesis test approach. This statistical test is shown to be asymptotically an uniformly most powerful test which is the strongest optimality statement that one could expect to obtain. Second we link the proposed asymptotic MSRL based on the hypothesis test approach to a new extension of the SRL based on the Cramér-Rao Bound approach. Thus a closed-form expression of the asymptotic MSRL is given and analyzed in the framework of the multidimensional harmonic retrieval model. Particularly it is proved that the optimal MSRL is obtained for equi-powered sources and or an equi-distributed number of sensors on each multi-way array. Keywords Statistical resolution limit Multidimensional harmonic retrieval Performance analysis Hypothesis test Cramér-Rao bound Parameter estimation Multidimensional signal processing Introduction The multidimensional harmonic retrieval problem is an important topic which arises in several applications 1 . The main .
