本文選題：磁異常梯度 + 向下延拓　； 參考：《哈爾濱工程大學》2014年碩士論文

【摘要】：地磁輔助導航系統(tǒng)因其全天候、全地域、高隱蔽性等優(yōu)點,已經(jīng)成為慣性輔助導航系統(tǒng)中不可或缺的一部分。水下地磁輔助導航系統(tǒng)是基于水下地磁匹配原理進行導航定位的,其定位精度與水下地磁數(shù)據(jù)庫的精度有著直接的關系。位場延拓技術是構建水下地磁數(shù)據(jù)庫的有效手段。本文選取所含地磁信息更多的磁異常梯度數(shù)據(jù)作為研究對象,圍繞高精度、高效率等需求展開,重點研究了磁異常梯度數(shù)據(jù)向下延拓技術。由于位場向下延拓的不穩(wěn)定性,使得國內(nèi)外許多學者致力于尋求各種不同算法以解決這方面的問題。基于積分迭代的各種改進算法不僅有效地解決了位場大距離向下延拓的不穩(wěn)定性問題,而且在保證大距離向下延拓的前提下,使數(shù)據(jù)處理的精度和速度都得到了大幅度的提升。本文簡要介紹了地磁場要素及其基本構成,通過對磁異�？倧姸鹊慕榻B,引出了本文的研究對象——磁異常梯度。推導了磁異常梯度數(shù)據(jù)在空間域和頻率域上的位場延拓表達式,為后續(xù)的算法研究提供理論依據(jù)。通過對磁異常梯度延拓因子的變化分析,指出傳統(tǒng)的傅里葉變換方法在向下延拓過程中是不穩(wěn)定的。傳統(tǒng)的頻率域向下延拓迭代法是一種基于傅里葉變換的迭代法,在其進行數(shù)據(jù)迭代運算之前,需要利用傅里葉變換將空間域中的數(shù)據(jù)轉換到頻率域上,目的是減少計算量,提高計算速度。本文以提高計算速度為目的,通過研究發(fā)現(xiàn)Hartley變換保證了變換前后的信號熵和能量不變,而且作為一種實數(shù)域內(nèi)的變換,Hartley變換省去了傅里葉變換中虛數(shù)部分的運算,計算速度比傅里葉變換提高了很多。在研究了向下延拓迭代法后,本文利用Hartley變換代替傅里葉變換,提出了基于Hartley變換的向下延拓迭代法。最后應用理論模型仿真與實測數(shù)據(jù)對基于傅里葉變換的向下延拓迭代法和基于Hartley變換的向下延拓迭代法進行了對比試驗,結果表明基于Hartley變換的迭代法在保證向下延拓精度的同時可以將計算時間大幅縮小。針對基于Hartley變換的迭代法在抑制噪聲方面所表現(xiàn)出的不足,本文結合正則化理論,研究了磁異常梯度向下延拓正則化算法。論文首先介紹了經(jīng)典的Tikhonov正則化理論以及一些常用的正則化參數(shù)選取方法;通過正則化分析,定義了一種向下延拓正則化算子,該算子能夠保證向下延拓計算結果連續(xù)依賴于觀測數(shù)據(jù),利用曲率函數(shù)配合L-曲線法選擇了最優(yōu)正則化參數(shù);通過被添加噪聲的磁異常梯度數(shù)據(jù)對正則化算法進行了驗證,結果表明磁異常梯度向下延拓正則化算法對噪聲擁有更強的抑制能力,表現(xiàn)出了很好的自適應性;文章最后對兩種算法的適用范圍進行了討論。最后,為了滿足實際研究的需要,結合Matlab和VC++各自的特點,采用兩者混合編程的方式,設計了一個簡單的可用于實驗室內(nèi)研究的向下延拓軟件。該軟件可以通過對數(shù)據(jù)文件的加載,在輸入向下延拓深度并點擊對應的算法按鈕后,自動繪制出延拓深度位置處的磁異常梯度數(shù)據(jù)等值線圖。
[Abstract]:The geomagnetic auxiliary navigation system has become an integral part of the inertial navigation system because of its all-weather, whole region and high concealment. The underwater magnetic auxiliary navigation system is based on the principle of underwater geomagnetic matching, and its positioning accuracy has a direct relationship with the accuracy of underwater geomagnetic database. The extension technology is an effective means to construct underwater geomagnetic database. In this paper, more magnetic anomaly gradient data of geomagnetic information are selected as the research object, and the downward continuation technology of magnetic anomaly gradient data is focused on the high precision and high efficiency. A variety of different algorithms are sought to solve this problem. A variety of improved algorithms based on integral iteration not only effectively solve the instability problem of the large distance downward continuation of the bit field, but also make the accuracy and speed of data processing greatly improved on the premise of ensuring the large distance downward extension. In this paper, the elements of the geomagnetic field and its basic composition are introduced. By introducing the total intensity of magnetic anomalies, the object of this paper, magnetic anomaly gradient, is derived. The expression of the potential field extension of the magnetic anomaly gradient data in the spatial and frequency domains is derived, which provides a theoretical basis for the study of the subsequent algorithms. It is pointed out that the traditional Fourier transform method is unstable in the downward continuation process. The traditional frequency domain downward continuation iteration method is an iterative method based on Fourier transform. The Fourier transform is used to convert the data from the space domain to the frequency domain before the data iteration is performed. The purpose is to reduce the calculation. In order to improve the calculation speed, in order to improve the calculation speed, this paper finds that the Hartley transform ensures the entropy and energy of the signal before and after the transformation, and as a real domain transformation, the Hartley transform saves the operation of the imaginary part of the Fu Liye transform, and the calculation speed is much higher than that of the Fu Liye transform. After studying the downward continuation method, this paper uses the Hartley transform instead of Fu Liye transform, and proposes a downward continuation iterative method based on Hartley transformation. Finally, the theoretical model simulation and the measured data are used to compare the downward continuation iterative method based on the Fu Liye transformation and the downward continuation iterative method based on the Hartley transformation. It is shown that the iterative method based on Hartley transform can reduce the calculation time greatly while ensuring the downward continuation accuracy. In this paper, in this paper, the regularization algorithm for the downward continuation of magnetic anomaly gradient is studied in view of the deficiency of the iterative method based on Hartley transformation in reducing the noise. This paper first introduces the classical Ti. Khonov regularization theory and some commonly used regularized parameter selection methods; through regularization analysis, a downward continuation regularization operator is defined. The operator can ensure that the result of downward continuation depends on the observation data continuously. The optimal regularization parameter is selected by the curvature function combined with the L- curve method; by adding noise, the operator can choose the optimal regularization parameter. The magnetic anomaly gradient data is verified by the regularization algorithm. The results show that the magnetic anomaly gradient downward continuation regularization algorithm has a stronger suppression ability and shows good adaptability. Finally, the scope of application of the two algorithms is discussed. Finally, in order to meet the needs of the actual research, Matlab and VC++ are combined. A simple downward continuation software, which can be used in laboratory research, is designed by using the two mixed programming methods. The software can automatically draw the magnetic anomaly gradient data line at the depth position of the extension by loading the data file, and after the input downward extension depth and clicking the corresponding algorithm button. Figure.
【學位授予單位】：哈爾濱工程大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：TN96

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