本文選題：雙子段 + 相位差�。� 參考：《天津大學》2014年碩士論文

【摘要】：頻率和相位參數(shù)估計在雷達、通信、語音處理、故障診斷等領域至關重要。該問題通常以復指數(shù)信號疊加白噪聲背景作為數(shù)學模型,解決該問題離不開譜分析方法�，F(xiàn)有的估計器都需借助內(nèi)插、迭代等措施對DFT結果進行校正來確定真實頻率和相位值,如最近出現(xiàn)的Candan估計器、CO估計器等。然而這些估計器在精度、計算復雜度及方差預測等方面難以較好地折中,表現(xiàn)在:(1)大多數(shù)內(nèi)插估計器因估計原理做了數(shù)學理論近似,即使在無噪情況下也存在偏差;(2)有的估計器需要對很多DFT譜線綜合計算,耗費了高復雜度;(3)大多數(shù)估計器沒有推導出頻率和相位估計方差的閉合理論表達式;(4)現(xiàn)有估計器在先估計頻率的前提下,再依據(jù)頻率估計結果去估計相位,這就引起誤差擴散。為解決以上問題,本文提出雙子段頻率和相位估計法。該方法從apFFT的首、尾兩個子分段提取其FFT峰值譜相位差而獲得頻率估計,對這兩個子分段的DFT相位值進行對稱補償而獲得相位估計。為提高性能,還提出頻移補償和迭代的措施對估計器做了改進。本文對提出的頻率估計器和相位估計器做了理論證明和數(shù)值仿真�；诖硕撟C了本文估計器具有如下優(yōu)勢:(1)無論是頻率估計器還是相位估計器,估計器生成過程都沒有做數(shù)學上的理論近似,因而是無偏估計器;(2)估計器僅需提取前、后分段的單根峰值譜線的相位信息,做簡單運算即可得估計結果,故計算復雜度低;(3)本文對估計器每一處理環(huán)節(jié)的參數(shù)方差都做了嚴格推導,最終導出了頻率和相位估計方差的閉合理論表達式,及其兩參數(shù)模型相位估計方差的克拉美羅限,故可以提供方差預測依據(jù);(4)相位估計結果是通過對稱補償而得,不是依據(jù)頻率估計結果得到,故不存在誤差擴散問題。因而克服了現(xiàn)有估計器的主要缺陷。仿真實驗不僅驗證了該閉合表達式的正確性,還證明了在大多數(shù)頻偏情況下,頻率估計均方誤差比apFFT/FFT相位差估計法和Candan估計器更接近于克拉美羅界,相位估計接近于兩參數(shù)克拉美羅限,故本文方法具有更高的測量精度。
[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.
【學位授予單位】：天津大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：TN911.23

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