基于改进遗传算法的矩阵联合对角化
doi: 10.3724/SP.J.1146.2005.00724
Joint Diagonalization of Matrix Based on Improved Genetic Algorithm
-
摘要: 该文首先将矩阵联合对角化问题化简成一个只含有特征矩阵的优化问题，为了便于求解，文中将待求特征矩阵的每一列向量进行参数化处理，并利用改进的遗传算法寻找最优的新参数。算法改进了染色体的选择，交叉和变异概率，并在交叉算子和变异算子中引入了模拟退火技术，最后结合梯度算法进行局部寻优。计算机仿真结果验证了该算法的正确性和有效性。Abstract: The paper simplifies the joint diagonalization of matrices into optimization problem which only includes the eigen matrix. For solving the problem conveniently, each row vector of the eigen matrix is parameterized, then utilizes the improved genetic algorithm to get the optimal parameter. The algorithm improves the choose of chromosome and probability of cross with variation, introduces simulated anneal technology into operator of crossing and variation. Finally it unifies the gradient algorithm to seek local optimality. The simulation result verify the algorithm.
-
Vanderveen A J and Paulraj A. An analytical constant modulus algorithm. IEEE Trans. on Signal Proc., 1996, 44(5): 1135-1155.[2]Vanderveen A J, Vanderveen M C and Paulraj A. Joint angle and delay estimation using shift-invariance techniques[J].IEEE Trans. on Signal Proc.1998, 46(2):405-418[3]Belouchrani A, Abed-Meraim K, Cardoso J F and Moulines E. A blind source separation technique using second-order statistics[J].IEEE Trans. on Signal Proc.1997, 45(2):434-444[4]Sidiropolus N D, Giannakis G B, and Bro R. Parallel factor analysis in sensor array processing[J].IEEE Trans. on Signal Proc.1999, 44(3):2377-2388[5]Wax M and Sheinvald J. A least squares approach to joint diagonalization. IEEE Trans. on Signal Proc., 1997, 4(2): 52- 53.[6]VanderVeen A J. Joint diagonalization via subspace fitting technique[J].Proc 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 01.2001, 5:2773-2776[7]Moler C and Stewart G W. An algorithm for generalized matrix eigenvalue problems. SIAM Journal on Numerical Analysis, 1973, 241-256.[8]Cardoso J F and Souloumiac A. Blind beamforming for non- Gaussian signals[J].IEE Proc. Radar and Signal Processing.1993, 140(6):362-370[9]Yeredor A. Non-orthogonal joint diagonalization in the least squares sense with application in blind source separation[J].IEEE Trans. on Signal Proc.2002, 50(7):1545-1553[10]王永良, 陈辉, 彭应宁, 万群. 空间谱估计理论与算法. 北京: 清华大学出版社, 2004: 168-173.[11]李敏强, 寇纪凇, 林丹, 李书全. 遗传算法的基本理论与应用. 北京: 科学出版社, 2003: 56-78. -
计量
- 文章访问数: 3254
- HTML全文浏览量: 96
- PDF下载量: 779
- 被引次数: 0
下载:
