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本文深入研究Shore提出的最小交叉熵(MCE)谱分析理论,得出了自相关阵和交叉熵、功率谱和交叉熵的关系式及用先验谱和自相关新信息表示的连续MCE谱公式,证明了MCE谱是有约束ME谱而ME谱是先验谱等效的AR谱阶数不大于自相关新信息个数时的MCE谱,并证明了Shore谱是本文给出的MCE谱的离散近似。然后,本文提出了MCE谱的快速递归算法,它无须求解非线性方程组,而是逐阶地交叉地计算逼近先验谱和后验谱的ME谱,因此,它不仅有MEM的快速性,而且充分使用了十分宝贵的先验信息,也可以说,它把MEM拓广于计算MCE谱。最后,本文例示了计算机模拟结果,它与理论分析有良好的一致。
In this paper, the theory of minimum cross entropy (MCE) analysis proposed by Shore is studied in depth. The relation between autocorrelation matrix and cross entropy, power spectrum and cross entropy and the formula of continuous MCE spectrum represented by Apriori spectrum and autocorrelation information , It is proved that the MCE spectrum is a constrained ME spectrum and the ME spectrum is the MCE spectrum when the AR spectral rank of the prior spectrum is not greater than the number of new autocorrelation information and it is proved that the Shore spectrum is the MCE spectrum given in this article Discrete approximation. Then, this paper proposes a fast recursive algorithm for MCE spectrum. It does not need to solve the nonlinear equations, but crosses the ME spectra approaching the prior and posterior spectra step by step. Therefore, it not only has the rapidity of MEM, but also Full use of a very valuable prior information, it can be said that it expand the MEM to calculate MCE spectrum. Finally, this article illustrates the computer simulation results, which is in good agreement with the theoretical analysis.