特殊陣列下的快速波達方向估計
發(fā)布時間：2018-11-07 17:14
【摘要】：作為陣列信號處理的重要分支之一,波達方向(Direction of Arrival,DOA)估計技術具有廣泛的應用背景,其相關研究也一直是陣列信號處理領域的熱點。從問世至今,DOA估計經歷了從高分辨到超分辨的發(fā)展歷程,在估計性能日益完善的同時,如何降低計算量以便超分辨估計算法由理論走向工程應用逐漸成為另一個熱點問題。本文以均勻線陣(Uniform Linear Array,ULA)和互質陣為依托,針對常規(guī)波達方向估計計算量大的問題,提出三種降低計算量的快速算法,為超分辨估計算法工程化提供理論參考。本文的主要研究內容如下:首先,在充分研究基于L陣二維DOA估計的CESA算法后,提出了一種新的基于ULA的一維快速DOA估計算法。新算法在陣型上將ULA劃分成兩個陣元數(shù)相等的子陣,然后求子陣的前、后向互協(xié)方差矩陣并構造聯(lián)合互協(xié)方差矩陣,再對該矩陣的第一列向量線性操作以獲取信號子空間,最后構造多項式求根求得DOA。仿真實驗證明,該算法在保證估計精度可接受的同時有效降低了協(xié)方差矩陣計算和子空間分解的計算量。其次,在深入研究針對L陣二維DOA估計的CODE算法后,提出一種新的基于ULA的子空間快速估計算法。新算法先將ULA劃分成兩個子陣,然后將流型矩陣劃分成兩個存在旋轉不變關系的子矩陣,根據(jù)子陣互協(xié)方差矩陣與流型矩陣的對應關系,將互協(xié)方差矩陣也劃分成滿足旋轉不變性的兩個子矩陣,最后利用這兩個子矩陣求解出旋轉不變關系矩陣,繼而求出子空間、構造多項式求解DOA。新算法相對于CODE算法實現(xiàn)了估計精度的提高,同時有效降低了子空間獲取的計算量。最后,針對現(xiàn)階段較為熱點的互質陣提出了一種新的DOA快速估計算法,新算法利用互質陣部分均勻線性的特點將互質陣看成由兩個ULA子陣構成,然后分別根據(jù)root-MUSIC算法構造子陣多項式,之后利用子陣多項式構造互質陣的多項式,最后研究證明該互質陣多項式單位圓上的根就是待求的DOA對應的根。仿真實驗證明,新算法的估計精度和效率均高于求根MUSIC算法及現(xiàn)有的同類算法。
[Abstract]:As an important branch of array signal processing, DOA (Direction of Arrival,DOA) estimation technology has a wide application background, and its related research has been a hot spot in the field of array signal processing. Up to now, DOA estimation has gone through the development from high resolution to super resolution. While the performance of DOA estimation is becoming more and more perfect, how to reduce the computational complexity so that the super-resolution estimation algorithm can be applied from theory to engineering has gradually become another hot issue. In this paper, based on the uniform linear array (Uniform Linear Array,ULA) and the mutual mass matrix, three fast algorithms to reduce the computational complexity are proposed to solve the problem of large computational complexity in the conventional DOA estimation, which provides a theoretical reference for the engineering of the super-resolution estimation algorithm. The main contents of this paper are as follows: firstly, after fully studying the CESA algorithm based on L-matrix two-dimensional DOA estimation, a new one-dimensional fast DOA estimation algorithm based on ULA is proposed. The new algorithm divides ULA into two submatrices with equal number of elements in the matrix, then obtains the forward and backward cross-covariance matrix of the submatrix and constructs the joint cross-covariance matrix. Then the first column vector of the matrix is linearly operated to obtain the signal subspace. Finally, we construct polynomial to find the root of DOA.. Simulation results show that the proposed algorithm can effectively reduce the computational complexity of covariance matrix calculation and subspace decomposition while ensuring acceptable estimation accuracy. Secondly, after deeply studying the CODE algorithm for 2-D DOA estimation of L-matrix, a new fast subspace estimation algorithm based on ULA is proposed. The new algorithm first divides ULA into two submatrices, then divides the flow pattern matrix into two submatrices with rotation-invariant relations. According to the corresponding relationship between the submatrix cross-covariance matrix and the flow pattern matrix, the new algorithm divides the flow pattern matrix into two submatrices. The cross covariance matrix is also divided into two submatrices which satisfy the rotation invariance. Finally, the rotation invariant relation matrix is solved by using these two submatrices, and then the subspace is obtained, and the polynomial is constructed to solve the DOA.. Compared with the CODE algorithm, the new algorithm improves the estimation accuracy and reduces the computational complexity of subspace acquisition. Finally, a new DOA fast estimation algorithm is proposed for the hot mutual-prime matrix. The new algorithm takes advantage of the partial uniform linearity of the mutual-prime matrix to treat the matrix as two ULA subarrays. Then the submatrix polynomials are constructed according to the root-MUSIC algorithm, and then the polynomials of the coprime matrix are constructed by using the submatrix polynomials. Finally, it is proved that the roots on the unit circle of the coprime polynomials are the DOA corresponding roots to be solved. The simulation results show that the estimation accuracy and efficiency of the new algorithm are higher than that of the root seeking MUSIC algorithm and the existing similar algorithms.
【學位授予單位】：哈爾濱工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN911.7
本文編號：2317024
[Abstract]:As an important branch of array signal processing, DOA (Direction of Arrival,DOA) estimation technology has a wide application background, and its related research has been a hot spot in the field of array signal processing. Up to now, DOA estimation has gone through the development from high resolution to super resolution. While the performance of DOA estimation is becoming more and more perfect, how to reduce the computational complexity so that the super-resolution estimation algorithm can be applied from theory to engineering has gradually become another hot issue. In this paper, based on the uniform linear array (Uniform Linear Array,ULA) and the mutual mass matrix, three fast algorithms to reduce the computational complexity are proposed to solve the problem of large computational complexity in the conventional DOA estimation, which provides a theoretical reference for the engineering of the super-resolution estimation algorithm. The main contents of this paper are as follows: firstly, after fully studying the CESA algorithm based on L-matrix two-dimensional DOA estimation, a new one-dimensional fast DOA estimation algorithm based on ULA is proposed. The new algorithm divides ULA into two submatrices with equal number of elements in the matrix, then obtains the forward and backward cross-covariance matrix of the submatrix and constructs the joint cross-covariance matrix. Then the first column vector of the matrix is linearly operated to obtain the signal subspace. Finally, we construct polynomial to find the root of DOA.. Simulation results show that the proposed algorithm can effectively reduce the computational complexity of covariance matrix calculation and subspace decomposition while ensuring acceptable estimation accuracy. Secondly, after deeply studying the CODE algorithm for 2-D DOA estimation of L-matrix, a new fast subspace estimation algorithm based on ULA is proposed. The new algorithm first divides ULA into two submatrices, then divides the flow pattern matrix into two submatrices with rotation-invariant relations. According to the corresponding relationship between the submatrix cross-covariance matrix and the flow pattern matrix, the new algorithm divides the flow pattern matrix into two submatrices. The cross covariance matrix is also divided into two submatrices which satisfy the rotation invariance. Finally, the rotation invariant relation matrix is solved by using these two submatrices, and then the subspace is obtained, and the polynomial is constructed to solve the DOA.. Compared with the CODE algorithm, the new algorithm improves the estimation accuracy and reduces the computational complexity of subspace acquisition. Finally, a new DOA fast estimation algorithm is proposed for the hot mutual-prime matrix. The new algorithm takes advantage of the partial uniform linearity of the mutual-prime matrix to treat the matrix as two ULA subarrays. Then the submatrix polynomials are constructed according to the root-MUSIC algorithm, and then the polynomials of the coprime matrix are constructed by using the submatrix polynomials. Finally, it is proved that the roots on the unit circle of the coprime polynomials are the DOA corresponding roots to be solved. The simulation results show that the estimation accuracy and efficiency of the new algorithm are higher than that of the root seeking MUSIC algorithm and the existing similar algorithms.
【學位授予單位】：哈爾濱工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN911.7
【引證文獻】
相關期刊論文 前1條
1 閆鋒剛;榮加加;劉帥;沈毅;金銘;;聯(lián)合互協(xié)方差矩陣的快速波達方向估計[J];系統(tǒng)工程與電子技術;2018年04期
，本文編號：2317024
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