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Generalized Unitary Joint Diagonalization Algorithm Based on Approximate Givens Rotations
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DOI：10.1109/LSP.2023.3342705.png)
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Like the Joint Diagonalization of a unique set of matrices, Generalized Joint Diagonalization is an algebraic problem encountered in different applications such as data fusion and blind source separation. This letter proposes a new generalized unitary joint diagonalization approach based on the Jacobi iterative scheme using Givens rotations and simplified criterion, introducing three approximations. These approximations allowed us to reach a simultaneous estimation of different parameters. The first appears in the simplified criterion composed of entries doubly affected by the Givens rotations. The second approximation is in the Givens parameter using a small amplitude angle. The last approximation resides in keeping only the first order of transformed entries. Numerical experiments, including examples of joint blind audio source separation, are provided. The results show the effectiveness of the developed algorithm as compared to existing ones. The simultaneous estimation of different Givens rotations improves the algorithm's computation complexity and convergence rate.
Keyword:
Jacobian matrices
Mathematical models
Covariance matrices
Approximation algorithms
Convergence
Signal processing algorithms
Estimation
Generalized unitary joint diagonalization (GUJD)
Givens rotations
Jacobi iterative algorithm
joint blind source separation (JBSS)
期刊
IF:
9.6
论文数:
1.1W
被引数:
1.7W
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