An Improved Method for Diagonal Approximation of Matrix Inversion based on the Frequency Snapshot Model

In this paper, a more accurate diagonal approximation of the covariance matrix in the frequency domain is investigated. For this purpose, first, the frequency snapshot model approximation is revised and the imposed error between the approximated and true value is formulated. Then, the problem of inverse approximation of the matrix is introduced as the inverse function in matrix form is expanded via its correspondent Taylor series. Finally, by adding a scalar modification factor to this problem, the resultant optimization is solved to yield the optimal value of approximated inverse matrix. To indicate the convenience of this method, two different criteria, namely sorted eigenvalues trend and Forbinius distance, are utilized. The carried out simulations have confirmed that this method could improve the approximation up to 30%.

Keywords:

Frequency snapshot model , Diagonal Approximation , matrix Inversion , Taylor series