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噪声中的谐波恢复问题是信号处理领域的一个典型问题,在众多领域中有着广泛的应用。本文主要研究零均值乘性和加性噪声并存下的二维谐波信号频率估计问题,提出了一种基于数据矩阵的奇异值分解和子空间的旋转不变性的零均值乘性和加性噪声中的谐波频率的估计方法。乘性噪声为零均值情形下传统的估计方法往往难以直接应用或估计失效。本文利用谐波模型信号特征,通过对观测信号进行平方运算构造了一个数据矩阵。通过对数据矩阵的特征值进行理论分析,结合子空间旋转不变性,得到了零均值乘性和加性噪声中的谐波频率和数据矩阵之间的一种内在关系。这个性质可以用于零均值乘性和加性噪声并存下的二维谐波信号频率估计,并且所得的二维频率能自动配对。仿真实验验证了本文所提算法的有效性。 相似文献
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本文利用特殊四阶时间平均多矩谱对任意均值乘性噪声与任意均值加性噪声共存,并且乘性噪声之间相关、乘性噪声与加性噪声之间相互独立的噪声背景下的三次非线性耦合进行了分析,该方法能够有效地估计出观测信号中参于三次非线性耦合的频率和耦合产生的频率.并且该方法无需限制乘性噪声与加性噪声的颜色和分布.最后,文中把此方法拓广到二维,用此二维四阶时间平均多矩谱方法分析了二维三次非线性耦合问题,同样取得了良好的效果.仿真实验验证了文中结论. 相似文献
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对于零均值独立乘性噪声背景下二维谐波的三次非线性耦合估计问题,由于缺乏理论支持及有效的计算方法,至今尚无有效的解决办法.本文首先分析了不同的噪声模型对谐波耦合分析所产生的影响,通过对原始采样数据进行平方预处理,改变了采样信号的信噪模型,利用新模型下噪声的统计特性及噪声间的相关特性,通过定义一种特殊四阶时间平均矩,首次解决了零均值独立噪声背景下谐波频率的二维三次非线性耦合问题.数学推导了该特殊四阶时间平均矩的矩多谱,理论证明了相应估计子渐进无偏性和一致性.理论分析和试验结果表明,该方法用于二维谐波的三次耦合分析时,不再需要对噪声的统计特性及噪声间的相关特性作任何限制. 相似文献
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从通信和探测系统需要的频率估计出发,文中研究了实乘性和复加性随机噪声中复谐波的恢复问题,表明循环均值和循环相关函数可用来对不同分布的有色实乘性和复加性随机噪声中的谐波进行恢复,分别对于非零均值和零均值乘性噪声情形分析了循环估计量的性能.证明了循环估计量与一定意义下的最小二乘估计量渐近等价,并给出了循环估计量的大样本方差表达式.模拟结果验证了大样本性能分析. 相似文献
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从通信和探测系统需要的频率估计出发,文中研究了实乘性和复加性随机噪声中复谐波的恢复问题,表明循环均值和循环相关函数可用来对不同分布的有色实乘性和复加性随机噪声中的谐波进行恢复,分别对于非零均值和零均值乘性噪声情形分析了循环估计量的性能。证明了循环估计量与一定意义下的最小二乘估计量渐近等价,并给出了循环估计量的大样本方差表达式。模拟结果验证了大样本性能分析。 相似文献
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The problem of estimating the frequencies of harmonics in multiplicative and additive noise is addressed. The cyclic mean (CM) can be used if the multiplicative noise has nonzero mean; the cyclic variance (CV) can be used whether or not the multiplicative noise has zero mean. This paper answers the following question: under what conditions should we use the CV instead of the CM? The criteria used are the ease of detection and the accuracy of estimation. The CV is preferable to the CM if the coherent to noncoherent harmonic power ratio is less than a threshold that depends on the first four cumulants; when the noises are colored, this threshold becomes frequency dependent. Third- and fourth-order cyclic statistics are also studied, and it is shown that they will always be outperformed either by the CM or CV when the multiplicative noise is symmetric 相似文献
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By exploiting thvorable characteristics of a uniIbrm cross-array, a passive localization algorithm of narrowband sources in the spherical coordinates (azimuth, elevation and range) is proposed. Based on the properly chosen sensor outputs, we compute the third-order cyclic moment matrices, and exploit a pre-calibration technique to eliminate multiplicative noise. Then, we construct a parallel factor (PARAFAC) model, and adopt trilinear altemating least squares regression (TALS) to estimate three-dimensional (3-D) near-field parameters. The investigated algorithm is efficient in the sense that it can eliminate multiplicative noise and additive noise, provide the improved estimation accuracy, as well as avoid the parameter-pairing procedure. Simulation results are carried out to demonstrate the performance of the proposed algorithm. 相似文献
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Multiplicative noise causes smearing of spectral lines and thus hampers frequency estimation relying on conventional spectral analysis. In contrast, cyclic mean and correlation statistics have proved to be useful for harmonic retrieval in the presence of multiplicative and additive noise of arbitrary color and distribution. Performance analysis of cyclic estimators is carried through both for nonzero and zero mean multiplicative noises. Cyclic estimators are shown to be asymptotically equivalent to certain nonlinear least squares estimators, and are also compared with the maximum likelihood ones. Large sample variance expressions of the cyclic estimators are derived and compared with the corresponding Cramer-Rao bounds when the noises are white Gaussian. It is demonstrated that previously well established results on constant amplitude harmonics are special cases of the present analysis. Simulations not only validate the large sample performance analysis, but also provide concrete examples regarding relative statistical efficiency of the cyclic estimators 相似文献