Modeling And Parameters Estimation Of Electromagnetic Vector Sensor Arrays Based On Geometric Algebra

Comparing with traditional scalar antenna arrays, electromagnetic(EM) vector sensor arrays can record multidimensional information of the EM wave signal. One of the research topics in this field is how to use those information sufficiently and effectively. This dissertation focuses on utilizing the powerful mathematical technique, Geometric Algebra, to establish the models of EM vector sensor arrays, and study the estimations of parameters under multidimensional case. The main work of the dissertation contains modeling EM vector sensor array signal with geometric algebra, DOA estimation, polarization estimation and polarization coherent sourses identification. The detailed work is summarized as the following:Firstly, geometric algebra system is introduced in detail, especially the geometric algebra of three dimensional vector space(G3), the geometric algebra of four dimensional vector space(G4), the geometric algebra of complex three dimensional vector space(CG3), and their operation rules, including the fundamental analysis tools of their matrices.Secondly, introduce the DOA estimation algorithm of vector sensor arrays based on G3(G3-MUSIC). Since G3-MUSIC does not take full advantages of second-order statistics information of the received signal, an improved parameter estimation algorithm based on G3 is proposed(G3v-MUSIC). The algoritm decouples direction parameters and polarization parameters through Rayleigh-entropy, so that it could achieve the DOA estimation of polarized independent sources blindly without knowing their polarization forms. In general statistical circumstance, G3v-MUSIC algorithm performes better than G3-MUSIC in DOA estimation thanks to the more utilization of the second-order statistics information.Thirdly, from the standpoint of clarifying the relationship between conventional complex unit j and geometric algebra, an EM vector sensor array model based on G4 is proposed, so does DOA estimation algorithm(G4-MUSIC). The performance analysis of G4-MUSIC is discussed on various aspects including the low rank approximation properties of covrance matrix, the decorrelation properties to local correlated noise, and the orthogonality of G4 vector. For G4-MUSIC cannot estimate polarization parameters, a modified G4-MUSIC is proposed to estimate azimuth and elevation angles of the incident signals, as well as their polarization parameters.Fourthly, the spatial smoothing decoherence algorithm is introduced to process polarized coherent sourses based on EM vector sensor arrays. Given the stringent requirements of spatial smoothing algorithm to array space structures, the model of vector sensor array and the MUSIC algorithm for DOA estimation based on CG3 is proposed. The covariance matrix of CG3-MUSIC can identify(up to) three polarized coherent sourses automatically for the incoherence of polarization steering vectors. Although CG3-MUSIC deals with the coherent sourses with a limitied number, nevertheless, it does not use any space structures information of the vector sensor array. The proposed algorithm can apply to any vector sensor arrays with arbitrary space structures when the number of polarized coherent sourses is small.