Abstract
In order to operate properly, the superresolution methods based on orthogonal subspace decomposition, such as multiple signal classification (MUSIC) or estimation of signal parameters by rotational invariance techniques (ESPRIT), need accurate estimation of the signal subspace dimension, that is, of the number of harmonic components that are superimposed and corrupted by noise. This estimation is particularly difficult when the S/N ratio is low and the statistical properties of the noise are unknown. Moreover, in some applications such as radar imagery, it is very important to avoid underestimation of the number of harmonic components which are associated to the target scattering centers. In this paper, we propose an effective method for the estimation of the signal subspace dimension which is able to operate against colored noise with performances superior to those exhibited by the classical information theoretic criteria of Akaike and Rissanen. The capabilities of the new method are demonstrated through computer simulations and it is proved that compared to three other methods it carries out the best trade-off from four points of view, S/N ratio in white noise, frequency band of colored noise, dynamic range of the harmonic component amplitudes, and computing time.
Highlights
There has been an increasing interest for many years in the field of superresolution methods, such as multiple signal classification (MUSIC) [1, 2] or estimation of signal parameters by rotational invariance techniques (ESPRIT) [3, 4]
The method we propose in this paper for the estimation of the signal subspace dimension performs the best tradeoff in terms of robustness to white noise, robustness to colored noise, dynamic range of the spectral components, and computing time
A new method is proposed in the paper for estimating the number of harmonic components in colored noise
Summary
There has been an increasing interest for many years in the field of superresolution methods, such as multiple signal classification (MUSIC) [1, 2] or estimation of signal parameters by rotational invariance techniques (ESPRIT) [3, 4]. When the noise statistics are unknown, other methods have been proposed, such as the Gerschgorin disk technique [9], known as the Gerschgorin disk estimator (GDE) criterion It makes use of a set of disks, whose centers and radii are both calculated from the autocorrelation matrix Σ. The method we propose in this paper for the estimation of the signal subspace dimension performs the best tradeoff in terms of robustness to white noise, robustness to colored noise, dynamic range of the spectral components, and computing time.
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