Extension of the matrix Bartlett's formula to the third and fourth order and to noisy linear models with application to parameter estimation - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue IEEE Transactions on Signal Processing Année : 2005

Extension of the matrix Bartlett's formula to the third and fourth order and to noisy linear models with application to parameter estimation

Résumé

This paper focuses on the extension of the asymptotic covariance of the sample covariance (denoted Bartlett's formula) of linear processes to third- and fourth-order sample cumulant and to noisy linear processes. Closed-form expressions of the asymptotic covariance and cross-covariance of the sample second-, third- and fourth-order cumulants are derived in a relatively straightforward manner thanks to a matrix polyspectral representation and a symbolic calculus akin to a high level language. As an application of these extended formulae, we underscore the sensitivity of the asymptotic performance of estimated ARMA parameters by an arbitrary third- or fourth order-based algorithm with respect to the signal to noise ratio, the spectra of the linear process, and the colored additive noise.
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Dates et versions

hal-00446766 , version 1 (13-01-2010)
hal-00446766 , version 2 (30-05-2016)

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Jean-Pierre Delmas, Yann Meurisse. Extension of the matrix Bartlett's formula to the third and fourth order and to noisy linear models with application to parameter estimation. IEEE Transactions on Signal Processing, 2005, 53 (8), pp.2765 - 2776. ⟨10.1109/TSP.2005.850362⟩. ⟨hal-00446766v2⟩
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