TY - GEN

T1 - Model order selection rule for estimating the parameters of 2-D sinusoids in colored noise

AU - Kliger, Mark

AU - Francos, Joseph M.

PY - 2006/12/1

Y1 - 2006/12/1

N2 - We consider the problem of jointly estimating the number as well as the parameters of two-dimensional sinusoidal signals, observed in the presence of an additive colored noise field. In this framework we consider the problem of least squares estimation of the parameters of 2-D sinusoidal signals observed in the presence of an additive noise field, when the assumed number of sinusoids is incorrect. In the case where the number of sinusoidal signals is under-estimated we show the almost sure convergence of the least squares estimates to the parameters of the dominant sinusoids. In the case where the number of sinusoidal signals is over-estimated, the estimated parameter vector obtained by the least squares estimator contains a sub-vector that converges almost surely to the correct parameters of the sinusoids. Based on these results, we prove the strong consistency of a large family of model order selection rules.

AB - We consider the problem of jointly estimating the number as well as the parameters of two-dimensional sinusoidal signals, observed in the presence of an additive colored noise field. In this framework we consider the problem of least squares estimation of the parameters of 2-D sinusoidal signals observed in the presence of an additive noise field, when the assumed number of sinusoids is incorrect. In the case where the number of sinusoidal signals is under-estimated we show the almost sure convergence of the least squares estimates to the parameters of the dominant sinusoids. In the case where the number of sinusoidal signals is over-estimated, the estimated parameter vector obtained by the least squares estimator contains a sub-vector that converges almost surely to the correct parameters of the sinusoids. Based on these results, we prove the strong consistency of a large family of model order selection rules.

UR - http://www.scopus.com/inward/record.url?scp=33947654307&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33947654307

SN - 142440469X

SN - 9781424404698

T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

SP - III85-III88

BT - 2006 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings

T2 - 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006

Y2 - 14 May 2006 through 19 May 2006

ER -