A New Method for Estimating the Number of Harmonic Components in Noise with Application in High Resolution Radar
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A New Method for Estimating the Number of Harmonic Components in Noise with Application in High Resolution Radar Emanuel Radoi Laboratoire E3I2, Ecole Nationale Sup´erieure des Ing´enieurs des Etudes et Techniques d’Armement (ENSIETA), 2 rue Franc¸ois Verny, 29806 Brest, France Email: [email protected]
Andre´ Quinquis Laboratoire E3I2, Ecole Nationale Sup´erieure des Ing´enieurs des Etudes et Techniques d’Armement (ENSIETA), 2 rue Franc¸ois Verny, 29806 Brest, France Email: [email protected] Received 18 February 2003; Revised 8 December 2003; Recommended for Publication by Bjorn Ottersten 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. Keywords and phrases: superresolution methods, subspace projection, discriminant function, high-resolution radar.
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INTRODUCTION
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]. They have been conceived to overcome the limitations of the Fourier-transform-based techniques, which are mainly related to the resolution achieved, especially when the number of available samples is reduced, and to the choice of the weighting windows, which controls the sidelobe level. Furthermore, there is always a tradeoff to do between the spatial (spectral, temporal, or angular) resolution and the dynamic resolution. The most effective classes of superresolution methods divide the observation space into two orthogonal subspaces (the so-called signal subspace and noise subspace) and are based on the autocorrelation matrix eigenanalysis. In conjunction with signal subspace dimension estimation criteria,
they are well known to provide performances close to the Cramer-Rao bound [5]. Akaike information criteri
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