Estimation of 3-D frequencies by a New High-Resolution Spectral Analysis method

Abstract

Estimating frequencies of a sum of 3-D complex exponential (3-D SCE) model perturbed by an additive gaussian white noise is a problem which is imperative these last years. Indeed, the passage from 1D to 2-D or from 2-D to 3-D is not trivial and same problems which do not arise in the 1D case appear and they worth to be treated. We speak here about the pairing problem concerning the formation of pairs and triplets frequencies respectively. The high resolution spectral analysis methods such as the ACMP method (Algebraically Coupled Matrix Pencil), the MEMP method (Matrix Enhancement and Matrix Pencil) and the 3-D ESPRIT method (Estimation of Signal Parameters via Rotationnal Invariance Techniques) allow remedying to this problem. The proposed method overcomes the problem of the multiplicity of triplets frequencies of the 3-D ESPRIT method.