Journal of Astronautics ›› 2014, Vol. 35 ›› Issue (3): 362-368.

### An Equivalent Algorithm for Fast Nonorthogonal Joint Diagonalization

ZHANG Jiang, ZHANG Hang

1. Communication Engineering Institute of PLA University of Science and Technology， Nanjing 210007，China
• Received:2012-01-20 Revised:2013-08-01 Online:2014-03-15 Published:2014-03-25

Abstract:

In view of the instantaneity requirement of parameter estimation of spatial source, an algorithm, named Equivalent Fast Joint Diagonalization (EFJD), is proposed in this paper. The EFJD algorithm, owns lower computational complexity and faster convergence and available for the parameter estimation of dynamic source. It reduces the computational complexity and accelerates the convergence of joint diagonalization by using two ways. Firstly, according to the situation that the number of matrices belonged to target matrix set is normally bigger than the rank of matrix, the number of matrices is reduced to the rank of matrix by using equivalent transformation, and the computational complexity in every iteration is decreased. Secondly, EFJD accelerates convergence by seeking a good initial value for iterative optimization algorithm. Mathematical derivation shows that EFJD can greatly reduce computational complexity , especially when the number of matrices belonged to the target set is much bigger than the rank of target matrices. Numerical simulations have shown that EFJD can not only reduce computational complexity of joint diagonalization but also improve the accuracy of joint diagonalization, compared with FFDiag.

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