基于双子段的信号频率和相位估计的算法研究

发布时间：2018-05-18 22:04

本文选题：双子段 + 相位差　；参考：《天津大学》2014年硕士论文

【摘要】：频率和相位参数估计在雷达、通信、语音处理、故障诊断等领域至关重要。该问题通常以复指数信号叠加白噪声背景作为数学模型,解决该问题离不开谱分析方法。现有的估计器都需借助内插、迭代等措施对DFT结果进行校正来确定真实频率和相位值,如最近出现的Candan估计器、CO估计器等。然而这些估计器在精度、计算复杂度及方差预测等方面难以较好地折中,表现在:(1)大多数内插估计器因估计原理做了数学理论近似,即使在无噪情况下也存在偏差;(2)有的估计器需要对很多DFT谱线综合计算,耗费了高复杂度;(3)大多数估计器没有推导出频率和相位估计方差的闭合理论表达式;(4)现有估计器在先估计频率的前提下,再依据频率估计结果去估计相位,这就引起误差扩散。为解决以上问题,本文提出双子段频率和相位估计法。该方法从apFFT的首、尾两个子分段提取其FFT峰值谱相位差而获得频率估计,对这两个子分段的DFT相位值进行对称补偿而获得相位估计。为提高性能,还提出频移补偿和迭代的措施对估计器做了改进。本文对提出的频率估计器和相位估计器做了理论证明和数值仿真。基于此而论证了本文估计器具有如下优势:(1)无论是频率估计器还是相位估计器,估计器生成过程都没有做数学上的理论近似,因而是无偏估计器;(2)估计器仅需提取前、后分段的单根峰值谱线的相位信息,做简单运算即可得估计结果,故计算复杂度低;(3)本文对估计器每一处理环节的参数方差都做了严格推导,最终导出了频率和相位估计方差的闭合理论表达式,及其两参数模型相位估计方差的克拉美罗限,故可以提供方差预测依据;(4)相位估计结果是通过对称补偿而得,不是依据频率估计结果得到,故不存在误差扩散问题。因而克服了现有估计器的主要缺陷。仿真实验不仅验证了该闭合表达式的正确性,还证明了在大多数频偏情况下,频率估计均方误差比apFFT/FFT相位差估计法和Candan估计器更接近于克拉美罗界,相位估计接近于两参数克拉美罗限,故本文方法具有更高的测量精度。
[Abstract]:The estimation of frequency and phase parameters is very important in radar, communication, speech processing and fault diagnosis. This problem is usually based on the complex exponential signal superimposed white noise background as a mathematical model, which can not be solved without spectral analysis method. The existing estimators need to calibrate the DFT results by means of interpolation, iteration and other measures to determine the true frequency and phase values, such as the recent Candan estimators and CO estimators. However, these estimators are difficult to make a good compromise in terms of accuracy, computational complexity and variance prediction. Even in the case of noise-free, there are some estimators that need to synthetically calculate many DFT lines. Most estimators do not derive the closed theoretical expression of frequency and phase estimation variance. The existing estimators estimate the frequency first and then estimate the phase according to the frequency estimation results, which leads to error diffusion. In order to solve the above problems, a method of frequency and phase estimation is proposed. In this method, the FFT peak spectrum phase difference is extracted from the first and last sub-sections of apFFT, and the frequency estimation is obtained. The DFT phase values of the two sub-segments are compensated symmetrically and the phase estimates are obtained. In order to improve the performance, the frequency shift compensation and iterative measures are proposed to improve the estimator. In this paper, the proposed frequency estimator and phase estimator are theoretically proved and numerically simulated. Based on this, it is proved that the estimator has the following advantages: 1: 1) whether it is a frequency estimator or a phase estimator, neither the estimator nor the phase estimator has a mathematical theoretical approximation, so the estimator is an unbiased estimator only needs to be extracted before the estimator is extracted. The phase information of a single peak line in the back segment can be estimated by a simple operation, so the computational complexity is low.) in this paper, the variance of the parameters in each processing link of the estimator is strictly deduced. Finally, the closed theoretical expression of frequency and phase estimation variance and the Clemero limit of phase estimation variance of two-parameter model are derived, which can provide the basis for variance prediction.) the result of phase estimation is obtained by symmetrical compensation. It is not based on the frequency estimation result, so there is no error diffusion problem. Therefore, the main defects of the existing estimators are overcome. Simulation experiments not only verify the correctness of the closed expression, but also prove that in most frequency offset cases, the mean square error of frequency estimation is closer to the Kelamero bound than the apFFT/FFT phase difference estimation and Candan estimator. The phase estimation is close to the two-parameter Crameiro limit, so the method in this paper has higher measurement accuracy.
【学位授予单位】：天津大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.23

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