| 1. IntroductionThe harmonic retrieval of sinusoidal signal embedded in noises is one of the major problems in spectral estimation fields, and the study on this problem has been in the whole course of spectral estimation. From classical periodogram to the subspace approaches with high resolving power, from the approaches based on the correlation to the approaches based on the cumulant, the harmonic retrieval goes through variety whirligigs. Many modern signal processing means have been applied to harmonic retrieval, such as nerve network,time-frequency analysis, mode recognition and adaptive technology. At the same time, harmonic retrieval methods are widely used in the areas such as radar, sonar, navigation, exploration, medical equipment, vibration and so on.The suppression ability to noises is used to weigh the performance of spectral estimation approaches in harmonic retrieval. At present, there are many cross-high-order spectral(CHOS) estimation approaches. These methods combined skillfully modern cross-spectral theories with some methods based on high-order cumulant so that we provided a new way to suppress noises, whose performance is more excellent. Methods based on cross-high-order cumulant can suppress uncorrelated colored noises and correlated Gauss noises, especially hold phase information, which has been proved. However, among majority cross-high- order spectral estimation approaches, the same part is that they all have used the extended characteristic equations. These approaches effectively improved spectral resolution and suppress the noises, while extended characteristic equation caused the false peaks in spectral estimation curve. To the worse situation, we can not know which peak is real signal peak. So this contradiction is the key issue to suppress the further improvement of harmonic retrieval ability. So if we can find a new CHOS approach with cleared false peaks, which will be an advancement in harmonic retrieval field. 2. Study on the methods of new CHOS estimation with cleared false peaksFirst, this paper introduced some basic conceptions and properties about high-order cumulant, high-order spectrum, cross-correlation function and cross-power spectrum, then took the advantages of modern cross-spectral and high-order-spectrum, combined them together skillfully, and then proposed some new conceptions, such as cross-high-order cumulant(CHOC), cross-high order-moment (CHOM) and CHOS, analyzed their properties and the abilities to reduce a noise. Secondly, based on the theory of modern CHOS estimation, the singular value decomposition natures of a sinusoidal matrix are studied. It is characteristic equations extended with accessorial roots that bring false peaks. The existing methods estimated the frequencies of sinusoidal signal via comparing the spectral peaks with false peaks, which can't clear out of accessorial roots, so false peaks exists all the same. If we can clear out of the accessorial roots, the false peaks will be suppressed. Then this paper put forward an algorithm which can eliminate the accessorial roots of the extended characteristic equation. This method solved the problem of false peaks in retrieval of harmonics in noise, and could compute and find the frequencies of harmonic signals directly. Several methods (WLS,SVD-TLS,LDLT ,QR and etc.) in CHOS estimation are brought about afterwards. Finally, simulations have shown that these methods can reduce the effects of hybrid colored noise and spectral density curve is smooth without false peaks. Moreover, they have higher precisions, especially the methods of QR and LDLT. Compared with other CHOS estimation methods, the algorithms mentioned above have completely cleared out of false peaks and this spectral estimation performance is much better. 3. ConclusionBased on the theories of modern CHOS estimation, this paper put forward cross-high-order spectral estimation approaches with cleared false peaks. Simulations have shown that these methods not only reduced the effect of hybrid noise and spe...
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