TY - JOUR
T1 - Spectrum estimation of real vector wide sense stationary processes by the hybrid steepest descent method
AU - Slavakis, Konstantinos
AU - Yamada, Isao
AU - Sakaniwa, Kohichi
PY - 2002
Y1 - 2002
N2 - It is well-known that the unbiased estimate of the covariance matrix of a real vector wide sense stationary process is not necessarily positive semidefinite. By defining the real Hilbert space of all symmetric matrices, the conditions for a symmetric matrix to be positive definite, block Toeplitz, as well as to satisfy other design constraints, are formed as closed convex sets. This paper demonstrates that the problem of approximating the unbiased estimate of the covariance matrix of a real vector wide sense stationary process over the intersection of those closed convex sets in an optimal way can be resolved by the Hybrid Steepest Descent Method. An optimal solution is also provided even when inconsistent constraints are met, i.e., whenever the intersection of the closed convex sets is empty. The numerical results exhibit significant improvement of the proposed method over the standard estimates of the covariance matrix.
AB - It is well-known that the unbiased estimate of the covariance matrix of a real vector wide sense stationary process is not necessarily positive semidefinite. By defining the real Hilbert space of all symmetric matrices, the conditions for a symmetric matrix to be positive definite, block Toeplitz, as well as to satisfy other design constraints, are formed as closed convex sets. This paper demonstrates that the problem of approximating the unbiased estimate of the covariance matrix of a real vector wide sense stationary process over the intersection of those closed convex sets in an optimal way can be resolved by the Hybrid Steepest Descent Method. An optimal solution is also provided even when inconsistent constraints are met, i.e., whenever the intersection of the closed convex sets is empty. The numerical results exhibit significant improvement of the proposed method over the standard estimates of the covariance matrix.
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U2 - 10.1109/icassp.2002.5744055
DO - 10.1109/icassp.2002.5744055
M3 - Conference article
AN - SCOPUS:0036297232
SN - 1520-6149
VL - 2
SP - II/1357-II/1360
JO - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
JF - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
T2 - 2002 IEEE International Conference on Acoustic, Speech and Signal Processing
Y2 - 13 May 2002 through 17 May 2002
ER -