TY - GEN
T1 - Estimation of rank deficient covariance matrices with Kronecker structure
AU - Castaneda, Mario H.
AU - Nossek, Josef A.
PY - 2014
Y1 - 2014
N2 - Given a set of observations, the estimation of covariance matrices is required in the analysis of many applications. To this end, any know structure of the covariance matrix can be taken into account. For instance, in case of separable processes, the covariance matrix is given by the Kronecker product of two factor matrices. Assuming the covariance matrix is full rank, the maximum likelihood (ML) estimate in this case leads to an iterative algorithm known as the flip-flop algorithm in the literature. In this work, we first generalize the flip-flop algorithm to the case when the covariance matrix is rank deficient, which happens to be the case in several situations. In addition, we propose a non-iterative estimation approach which incurs in a performance loss compared to the ML estimate, but at the expense of less complexity.
AB - Given a set of observations, the estimation of covariance matrices is required in the analysis of many applications. To this end, any know structure of the covariance matrix can be taken into account. For instance, in case of separable processes, the covariance matrix is given by the Kronecker product of two factor matrices. Assuming the covariance matrix is full rank, the maximum likelihood (ML) estimate in this case leads to an iterative algorithm known as the flip-flop algorithm in the literature. In this work, we first generalize the flip-flop algorithm to the case when the covariance matrix is rank deficient, which happens to be the case in several situations. In addition, we propose a non-iterative estimation approach which incurs in a performance loss compared to the ML estimate, but at the expense of less complexity.
KW - Kronecker product
KW - covariance matrix estimation
KW - flip-flop algorithm
KW - separable processes
UR - http://www.scopus.com/inward/record.url?scp=84905234956&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2014.6853625
DO - 10.1109/ICASSP.2014.6853625
M3 - Conference contribution
AN - SCOPUS:84905234956
SN - 9781479928927
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 394
EP - 398
BT - 2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
Y2 - 4 May 2014 through 9 May 2014
ER -