Minimum Eigenvalue Based 3-D AR Model Order Selection

This paper deals with the problem of three-dimensional autoregressive (3-D AR) model order estimation. Especially, we develop a practical algorithm to estimate the 3-D AR order (P1,P2,P3) corresponding to the quarter-space (QS) region of support. The proposed method is derived from the minimum description length (MDL) criterion and uses the minimum eigenvalue of the covariance matrix of the underlying 3-D Gaussian process. Numerical simulations are presented to illustrate the performances of the new proposed algorithm and compare it with a recently developed method

[1]  Mohamed Najim,et al.  3-D AR model order selection via rank test procedure , 2006, IEEE Transactions on Signal Processing.

[2]  J. Cadzow,et al.  Spectral estimation: An overdetermined rational model equation approach , 1982, Proceedings of the IEEE.

[3]  H. Akaike.  A new look at the statistical model identification , 1974 .

[4]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[5]  Byoungseon Choi.  An order-recursive algorithm to solve the 3-D Yule-Walker equations of causal 3-D AR models , 1999, IEEE Trans. Signal Process..

[6]  Brahim Aksasse,et al.  Two-dimensional autoregressive (2-D AR) model order estimation , 1999, IEEE Trans. Signal Process..

[7]  Thomas Kailath,et al.  Detection of signals by information theoretic criteria , 1985, IEEE Trans. Acoust. Speech Signal Process..

[8]  B. G. Quinn,et al.  The determination of the order of an autoregression , 1979 .

[9]  Brahim Aksasse,et al.  A rank test based approach to order estimation. I. 2-D AR models application , 1999, IEEE Trans. Signal Process..

[10]  E. Hannan,et al.  The determination of optimum structures for the state space representation of multivariate stochastic processes , 1982 .

[11]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[12]  Marc Hallin,et al.  Order Selection, Stochastic Complexity and Kullback-Leibler Information , 1996 .

[13]  Dimitris G. Manolakis,et al.  Three-dimensional linear prediction and its application to digital angiography , 1993, Multidimens. Syst. Signal Process..

[14]  D. Mitchell Wilkes,et al.  Robust and accurate ARX and ARMA model order estimation of non-Gaussian processes , 2002, IEEE Trans. Signal Process..

[15]  D. Mitchell Wilkes,et al.  ARMA model order estimation based on the eigenvalues of the covariance matrix , 1993, IEEE Trans. Signal Process..