Optimal choice of Hankel-block-Hankel matrix shape in 2-D parameter estimation

Souleymen Sahnoun (1) , Konstantin Usevich (1) , Pierre Comon (1)

1 GIPSA-CICS - GIPSA - Communication Information and Complex Systems

In this paper we analyse the performance of 2-D ESPRIT method for estimating parameters of 2-D superimposed damped exponentials. 2-D ESPRIT algorithm is based on low-rank decomposition of a Hankel-block-Hankel matrix that is formed by the 2-D data. Through a first-order perturbation analysis, we derive expressions of the variance of the estimates in 2-D multiple-tones case. We also derive closed-form expressions of the variances of the complex modes, frequencies and damping factors estimates in the 2-D single-tone case. This analysis allows to define the optimal parameters used in the construction of the Hankel-block-Hankel matrix. A fast algorithm for calculating the SVD of Hankel-block-Hankel matrices is also used to enhance the computational complexity of the 2-D ESPRIT algorithm.

Mots clés: Frequency estimation; Hankel-block-Hankel matrix; 2-D ESPRIT; perturbation analysis

Domaines: Traitement du signal et de l'image [eess.SP]

Souleymen Sahnoun, Konstantin Usevich, Pierre Comon. Optimal choice of Hankel-block-Hankel matrix shape in 2-D parameter estimation. [Research Report] GIPSA-lab. 2016. ⟨hal-01288994v1⟩