Method And Application Of Dual Quaternion Model Vector Antenna Array Signal

Under the framework of biquaternions and its beamspace, this dissertation mainly includes our researches on the modeling of the electromagnetic (EM) vector-sensor and its array, and its applications on the EM source signal processing.To describe the orthogonal relationships of each component in electromagnetic field, we used the pure biquatemion to describe the Maxwell’s Equations and deduce the pure biquatemion model of vector-sensors array. By analyzing the covariance matrix of the pure biquatemion model, we find that the covariance matrix can "natively" remove the correlated noise among the internal three electric antennas or among the internal three magnetic antennas, but cannot remove the correlated noise between the electric antenna and the magnetic antenna. Using the theory of the pure biquatemion matrix, we present the corresponding pure biquatemion multiple signals classification algorithm (PB-MUSIC). The analysis reveals that this algorithm can estimate the direction of arrival (DOA), given the EM source polarization parameters.To achieve the joint estimation of EM source DOA and polarization parameters, we discussed the beam-forming method in the pure biquatemion beamspace and established the corresponding model. The analysis reveals that the covariance matrix in this model can also enhance the robustness against the internal correlated noise in each vector-sensors array, and can reduce the storage space and the calculation amount of the eigenvalue decomposition. By building two different pure biquatemion beamspace, we present two different MUSIC algorithms based on the pure biquatemion beamspace, DOA-BB-MUSIC algorithm and DOA-P-BB-MUSIC algorithm. The analysis reveals that, the DOA-BB-MUSIC algorithm can decouple the DOA and the polarization parameters, and can make the blind estimation of DOA with no knowledge of polarization parameters, but it cannot estimate the polarization parameters. The DOA-P-BB-MUSIC algorithm uses Rayleigh criterion to decouple the DOA and the polarization parameters, and achieve the blind estimation of DOA and the estimation of polarization parameters, but the calculation amount is more than the DOA-BB-MUSIC algorithm. To whiten all of the colored noise or correlated noise that may exist between internal electric field and magnetic field, we present the according method in this pure biquatemion beamspace, and we also present DOA-PB-BB-MUSIC algorithm to estimate the DOA parameters in the colored noise or related noise environment. The theoretical analysis also reveals that, this algorithm can not only whiten all of the correlated noise between internal electric field and magnetic field, and it can also decouple the DOA and the polarization parameters, and achieve the blind estimation of DOA and the estimation of the polarization parameters. But since the algorithm needs an iterative solving process, the calculation amount is somewhat big.To reduce the calculation amount, we studied how to construct different biquaternion beamspace according to the colored noise or correlated noise between internal electric field and magnetic field that need to be decorrelated. And we present the DOA-GB-MUSIC algorithm. The analysis reveals that the DOA-GB-MUSIC algorithm can decouple the DOA and the polarization parameters, and achieve the blind estimation of DOA with no knowledge of the polarization parameters, but it cannot estimate the polarization parameters.We also discuss the adaptive beamforming problem under the framework of the biquaternion. We present the CAPON algorithm under the model of the pure biquaternion. We compared the algorithm with the traditional CAPON, and explained why the CAPON algorithm under the model of the pure biquaternion can enhance the robustness. And we theoretically proved that this algorithm under the model of the pure biquaternion cannot achieve beamforming with some specific polarization parameters. And to solve this problem, we present the robust CAPON algorithm.In general, the researches in this dissertation reveal that the biquaternion and its beamspace are tools which are very suitable for modeling and processing of vector-sensors array. The advantage that the biquaternion and its beamspace showed in EM source location and beam-forming makes us believe that they can be applied to more array signal processing tasks.