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| − | + | Based on modulus property outlined in [28], the moduli of the elements in ��ux are [http://www.selleckchem.com/products/chir-99021-ct99021-hcl.html CHIR-99021 mouse] approximately equivalent to 1 in the case of noise disturbance, i.e., ||det(��ux)|?1|=�� with �š�0 (in the noise-free case, ��=0), while those in ��cx are far away from 1. Following this principle, the uncorrelated sources can be distinguished from the coherent sources. In order to construct the uncorrelated eigenvector matrix Tu?1, Ku column vectors corresponding to uncorrelated sources are extracted from T?1. Similarly, the remaining D column vectors corresponding to coherent sources are extracted to construct the matrix Tc?1. 3.2. 2-D Parameter Estimation for Uncorrelated Sources The estimation of Au is given by A^u=EsTu?1=[Cu[x,z]��ux?Cu[x,z]��uxM1Cu[y,z]��uy?Cu[y,z]��uyM2] (19) For the kth uncorrelated source, we have A^u,k=EsTu,k?1, where Tu,k?1 [https://en.wikipedia.org/wiki/Fleroxacin Fleroxacin] is the eigenvector of the kth uncorrelated source selected from Tu?1. With the definition of the exchange matrix Gl,n, A^u,k can be partitioned as A^u,k=[(A^u,k[x])T,(A^u,k[zx])T,(A^u,k[y])T,(A^u,k[zy])T]T (20) where A^u,k[x]=G2M1,1TA^u,k[x,z] (21) A^u,k[zx]=G2M1,2TA^u,k[x,z] (22) A^u,k[y]=G2M2,1TA^u,k[y,z] (23) A^u,k[zy]=G2M2,2TA^u,k[y,z] (24) with A^u,k[x,z] and A^u,k[y,z] the first 2M1 and the last 2M2 rows of A^u,k. Combining Equations (21) with (22) yields e^u,k[x]e^u,k[z]=(A^u,k[zx])?A^u,k[x]=[?cot��kcos?k+cot��ksin?ksin��kcos��k]+j[?cot��ksin?ksin��ksin��k] (25) In a similar way, by exploiting [http://www.selleckchem.com/products/Y-27632.html Y-27632 cell line] Equations (23) and (24), we have e^u,k[y]e^u,k[z]=(?A^u,k[zy])?A^u,k[y]=[?cot��ksin?k?cot��kcos?ksin��kcos��k]+j[cot��kcos?ksin��ksin��k] (26) According to Equations (25) and (26), we can obtain four real-valued equations: Re(e^u,k[x]/e^u,k[z])=?cot��kcos?k+cot��ksin?ksin��kcos��k, Im(e^u,k[x]/e^u,k[z])=?cot��ksin?ksin��ksin��k, Re(e^u,k[y]/e^u,k[z])=?cot��ksin?k?cot��kcos?ksin��kcos��k, Im(e^u,k[y]/e^u,k[z])=cot��kcos?ksin��ksin��k. Then, the closed-form estimation-formulas (i.e., coarse estimates) of azimuth angle, elevation angle, auxiliary polarization angle, and the polarization phase difference are given by ?^kcoarse={tan?1?Im(e^u,k[x]/e^u,k[z])Im(e^u,k[y]/e^u,k[z]),?if?(sin��k?Im(e^u,k[y]/e^u,k[z])��0)tan?1?Im(e^u,k[x]/e^u,k[z])Im(e^u,k[y]/e^u,k[z])+��,?if?(sin��k?Im(e^u,k[y]/e^u,k[z]) | |
Version du 30 décembre 2016 à 03:41
Based on modulus property outlined in [28], the moduli of the elements in ��ux are CHIR-99021 mouse approximately equivalent to 1 in the case of noise disturbance, i.e., ||det(��ux)|?1|=�� with �š�0 (in the noise-free case, ��=0), while those in ��cx are far away from 1. Following this principle, the uncorrelated sources can be distinguished from the coherent sources. In order to construct the uncorrelated eigenvector matrix Tu?1, Ku column vectors corresponding to uncorrelated sources are extracted from T?1. Similarly, the remaining D column vectors corresponding to coherent sources are extracted to construct the matrix Tc?1. 3.2. 2-D Parameter Estimation for Uncorrelated Sources The estimation of Au is given by A^u=EsTu?1=[Cu[x,z]��ux?Cu[x,z]��uxM1Cu[y,z]��uy?Cu[y,z]��uyM2] (19) For the kth uncorrelated source, we have A^u,k=EsTu,k?1, where Tu,k?1 Fleroxacin is the eigenvector of the kth uncorrelated source selected from Tu?1. With the definition of the exchange matrix Gl,n, A^u,k can be partitioned as A^u,k=[(A^u,k[x])T,(A^u,k[zx])T,(A^u,k[y])T,(A^u,k[zy])T]T (20) where A^u,k[x]=G2M1,1TA^u,k[x,z] (21) A^u,k[zx]=G2M1,2TA^u,k[x,z] (22) A^u,k[y]=G2M2,1TA^u,k[y,z] (23) A^u,k[zy]=G2M2,2TA^u,k[y,z] (24) with A^u,k[x,z] and A^u,k[y,z] the first 2M1 and the last 2M2 rows of A^u,k. Combining Equations (21) with (22) yields e^u,k[x]e^u,k[z]=(A^u,k[zx])?A^u,k[x]=[?cot��kcos?k+cot��ksin?ksin��kcos��k]+j[?cot��ksin?ksin��ksin��k] (25) In a similar way, by exploiting Y-27632 cell line Equations (23) and (24), we have e^u,k[y]e^u,k[z]=(?A^u,k[zy])?A^u,k[y]=[?cot��ksin?k?cot��kcos?ksin��kcos��k]+j[cot��kcos?ksin��ksin��k] (26) According to Equations (25) and (26), we can obtain four real-valued equations: Re(e^u,k[x]/e^u,k[z])=?cot��kcos?k+cot��ksin?ksin��kcos��k, Im(e^u,k[x]/e^u,k[z])=?cot��ksin?ksin��ksin��k, Re(e^u,k[y]/e^u,k[z])=?cot��ksin?k?cot��kcos?ksin��kcos��k, Im(e^u,k[y]/e^u,k[z])=cot��kcos?ksin��ksin��k. Then, the closed-form estimation-formulas (i.e., coarse estimates) of azimuth angle, elevation angle, auxiliary polarization angle, and the polarization phase difference are given by ?^kcoarse={tan?1?Im(e^u,k[x]/e^u,k[z])Im(e^u,k[y]/e^u,k[z]),?if?(sin��k?Im(e^u,k[y]/e^u,k[z])��0)tan?1?Im(e^u,k[x]/e^u,k[z])Im(e^u,k[y]/e^u,k[z])+��,?if?(sin��k?Im(e^u,k[y]/e^u,k[z])
