Parameter Estimation Methods And Applications Based On Tensor Decomposition

In practical applications of modern signal processing,many signal types show the multidimensional data structure.However,the traditional methods can only unfold the multi-dimensional data into matrix or vector,which will destroy the original data in the multi-dimensional data structure and irreversibly lost this part of the structural information.But the tensor-decomposition-based methods do not have such problem.This is because the tensor decomposition model has the multi-linear data structure.It can not only retain the multidimensional structure information of signals,but also achieve the better performance than traditional matrix-based methods by using such structure information.Taking this as the research motivation,this dissertation introduces the tensor decomposition methods into the signal multi-parameter estimation field,and mainly studies the following five problems:Firstly,to solve the problem of the direction of arrival?DOA?estimation of the incident signal of the scalar sensor array,this dissertation proposes a Canonical Polyadic Decomposition?CPD?based L-shaped array 2D-DOA estimation algorithm,which can exploit the multi-rotation invariance of array structure.In the case of Vandermonde structural constraints,this algorithm has more relaxed application conditions than the classic ESPRIT algorithm.The CPD model has the uniqueness of decomposition under arbitrary permutation and scaling.By utilizing such property,the proposed algorithm can obtain the parameter estimation of spatial frequency with high precision.In addition,this dissertation adopts a new array representation with symmetrical structure and introduces the cross correlation matrix information to accomplish the pair-matching of two-dimensional angles.Secondly,to solve the problem of DOA estimation for coherent sources,this dissertation proposes a DOA estimation algorithm for uniform linear array based on Tucker decomposition.In the case of coherence with the incident signals,the existing methods tend to fail because the rank condition can not be satisfied.Under the circumstance,Tucker decomposition can still obtain the subspace estimation of the signal.And the subspace estimation performance of Tucker decomposition is superior to the traditional subspace methods based on matrix decomposition due to the utilization of structural information of the signals.Thirdly,to solve the spotlight Synthetic Aperture Radar?SAR?imaging problem for the target scatters with block sparse structure,this dissertation proposes a multi-mode sparse reconstruction algorithm based on Tucker decomposition.This algorithm can make full use of the Kronecker structure information of the SAR echo signal.When the sparsity is the same,the sparse reconstruction method based on Kronecker dictionary has a higher recovery bound than the classic matching pursuit method.In addition,the computational complexity analysis and numerical simulation experiments are carried out in terms of computing resource requirement.Both the theoretical analysis and simulation results indicate that the proposed algorithm requires much less computational resource than the existing methods.Fourthly,to solve the problem of partially polarized wave parameter estimation for Electromagnetic Vector Sensor?EMVS?array,this dissertation proposes a 2D-DOA estimation algorithm based on rank-?L₁,L₂,·?Block Component Decomposition?BCD?model.Not only does this model has the mode-n tensor rank similar to Tucker decomposition,but also it possesses the uniqueness of decomposition like CPD.This dissertation researches the rank condition of EMVS array model.The proposed algorithm can automatically accomplish the pair-matching of azimuth and elevation angles by means of the steering matrix estimated under the uniqueness of decomposition.Fifth,to solve the problem of fully polarized wave parameter estimation for EMVS array,this dissertation proposes a DOA-polarization joint estimation algorithm based on rank-?L,L,1?BCD model.Similar to the rank-?L₁,L₂,·?BCD model,the rank-?L,L,1?BCD model also has the uniqueness of decomposition.By utilizing such property,the proposed algorithm can achieve the array multi-parameter estimation and pair-matching.For each of the above algorithms,this dissertation has carried out several numerical simulations in each chapter to verify the effectiveness of the proposed algorithms.The experimental results and the theoretical analysis of each chapter are consistent.