波導中波場球諧波分解和RKHS三維定位
發(fā)布時間：2018-11-11 19:02
【摘要】：在海洋波導環(huán)境中,通過接收目標聲源輻射的聲場數(shù)據(jù)來實現(xiàn)目標被動三維定位是水聲領域一直以來的研究難題。目標被動定位問題的本質是逆問題求解,即從接收到的數(shù)據(jù)中估計有關目標源的位置信息。逆問題求解的一種方法是反演,用正問題的前向模型擬合解決,例如匹配場處理(MatchedFieldProcessing,MFP)。然而MFP要求的條件太多,且條件難以確知,容易導致前向模型產(chǎn)生的拷貝聲場與接收聲場失配,從而使性能下降乃至崩潰。因而定位問題的關鍵是穩(wěn)定性和寬容性,需要將逆問題求解由反演轉向推斷。推斷的穩(wěn)定性和寬容性是由完備性作保證的。本文從希爾伯特空間理論出發(fā),在完備的無窮維希爾伯特空間中分解波場,獲得包含目標信息的完備正交歸一序列。分解的基本運算是內(nèi)積,在Lebesgue測度下,內(nèi)積放棄了處處相等的要求,轉向幾乎處處相等,更具寬容性。論文重點討論了球諧波分解和再生核希爾伯特空間(Reproducing Kernel Hilbert Space,RKHS)方法,通過內(nèi)積將信號空間變換到特征空間,將特征空間內(nèi)的分解系數(shù)與拷貝場的分解系數(shù)作內(nèi)積,實現(xiàn)目標三維定位。三維定位要求接收數(shù)據(jù)具備“完備性”,接收陣要求包含各種取向,本文采用球陣作為接收陣。球陣特殊的球對稱結構可以簡化球諧波分解和RKHS方法的計算。實際的球陣不是連續(xù)陣,需要合理布置陣元位置,以滿足球諧波的正交條件。球陣上陣元布放方法主要有三種:等角度采樣、高斯采樣和均勻采樣,本文采用相同條件下需要陣元數(shù)最少的均勻采樣。在平面波聲源模型下,將聲波場分解為完備的球諧波函數(shù)表示,在特征空間球諧域內(nèi)做波束形成,估計平面波到達角(direction of arrival,DOA)。球諧域信號處理相比陣元域計算效率更高,并且不同的接收陣結構可以用相同的信號處理框架統(tǒng)一起來。在點源模型下,聲波場也可以分解為球諧波函數(shù)表示,在球諧域內(nèi)對球Fourier系數(shù)做匹配,實現(xiàn)目標三維定位。RKHS中存在一個具有再生性的核函數(shù),與球諧波分解類似,聲波場可以用這個核函數(shù)作分解,在特征空間內(nèi)對分解系數(shù)做匹配,實現(xiàn)目標三維定位。球諧波分解和RKHS都是寬容的匹配場處理方法,而RKHS方法好處在于可以通過改變核函數(shù)參數(shù)來實現(xiàn)定位結果的核控制。本文研究了三維球陣球諧波分解和RKHS三維定位方法,在仿真波導環(huán)境中實現(xiàn)了目標聲源的到達角估計和三維位置估計,并與陣元域匹配場處理的結果作對比:不存在失配情況下,球諧波分解和RKHS方法與陣元域匹配場處理并無顯著差別;存在失配情況下,本文提出的兩種方法的結果要優(yōu)于陣元域匹配場處理。最后,在實驗室波導中,設計并實現(xiàn)了球陣聲源定位實驗驗證了上述結論。
[Abstract]:In the environment of ocean waveguide, it has been a difficult problem in underwater acoustic field to realize passive 3D localization of target by receiving acoustic field data from target sound source. The essence of passive target localization problem is to solve the inverse problem, that is, to estimate the location information of the target source from the received data. One method of inverse problem solving is inversion, which is solved by forward model fitting of forward problem, such as matching field processing (MatchedFieldProcessing,MFP). However, the MFP requires too many conditions and the conditions are difficult to be ascertained, which can easily lead to mismatch between the copy sound field generated by the forward model and the received sound field, which results in the degradation of the performance and even the collapse of the received sound field. Therefore, the stability and tolerance are the key to the localization problem, so it is necessary to change the inverse problem from inversion to inference. The stability and tolerance of inference are guaranteed by completeness. Based on Hilbert space theory, this paper decomposes the wave field in a complete infinite dimensional Hilbert space and obtains a complete orthogonal normalized sequence containing target information. The basic operation of decomposition is inner product. Under Lebesgue measure, inner product gives up the requirement of everywhere equality and turns to almost everywhere equality, which is more tolerant. This paper focuses on the spherical harmonic decomposition and the (Reproducing Kernel Hilbert Space,RKHS) method of reproducing kernel Hilbert space. The signal space is transformed into the feature space by the inner product, and the decomposition coefficient in the feature space and the decomposition coefficient of the copy field are internalized. Realize the three-dimensional positioning of the target. In this paper, the spherical array is used as the receiving array. The special spherical symmetric structure of spherical array can simplify the spherical harmonic decomposition and the calculation of RKHS method. The actual spherical array is not a continuous array, so it is necessary to arrange the position of the array elements reasonably to satisfy the orthogonal condition of spherical harmonics. There are three methods of array element placement in spherical array: equal angle sampling, Gao Si sampling and uniform sampling. In this paper, uniform sampling with the least number of elements is adopted under the same conditions. In the plane wave source model, the acoustic wave field is decomposed into a complete spherical harmonic function, beamforming is done in the spherical harmonic domain in the characteristic space, and the plane wave arrival angle (direction of arrival,DOA) is estimated. The spherical harmonic domain signal processing is more efficient than the array element domain computing efficiency, and different receiving array structures can be unified with the same signal processing framework. Under the point source model, the acoustic field can also be decomposed into spherical harmonic functions, and the spherical Fourier coefficients can be matched in the spherical harmonic domain to realize the three-dimensional positioning of the target. There exists a regenerative kernel function in RKHS, which is similar to the spherical harmonic decomposition. The acoustic field can be decomposed by this kernel function, and the decomposition coefficients can be matched in the feature space to realize the three-dimensional localization of the target. Spherical harmonic decomposition and RKHS are both tolerant matching field processing methods, but the advantage of RKHS method is that kernel control of location results can be realized by changing kernel function parameters. In this paper, three dimensional spherical harmonic decomposition and RKHS 3D positioning method are studied, and the angle of arrival and three dimensional position estimation of the target sound source are realized in the simulated waveguide environment. The results are compared with the results of array element domain matching field processing: without mismatch, there is no significant difference between spherical harmonic decomposition and RKHS method and array element domain matching field processing; In the case of mismatch, the results of the two methods proposed in this paper are better than that of matrix element domain matching field processing. Finally, the above conclusions are verified by designing and implementing the spherical array sound source localization experiment in the laboratory waveguide.
【學位授予單位】：浙江大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN911.7
本文編號：2325822
[Abstract]:In the environment of ocean waveguide, it has been a difficult problem in underwater acoustic field to realize passive 3D localization of target by receiving acoustic field data from target sound source. The essence of passive target localization problem is to solve the inverse problem, that is, to estimate the location information of the target source from the received data. One method of inverse problem solving is inversion, which is solved by forward model fitting of forward problem, such as matching field processing (MatchedFieldProcessing,MFP). However, the MFP requires too many conditions and the conditions are difficult to be ascertained, which can easily lead to mismatch between the copy sound field generated by the forward model and the received sound field, which results in the degradation of the performance and even the collapse of the received sound field. Therefore, the stability and tolerance are the key to the localization problem, so it is necessary to change the inverse problem from inversion to inference. The stability and tolerance of inference are guaranteed by completeness. Based on Hilbert space theory, this paper decomposes the wave field in a complete infinite dimensional Hilbert space and obtains a complete orthogonal normalized sequence containing target information. The basic operation of decomposition is inner product. Under Lebesgue measure, inner product gives up the requirement of everywhere equality and turns to almost everywhere equality, which is more tolerant. This paper focuses on the spherical harmonic decomposition and the (Reproducing Kernel Hilbert Space,RKHS) method of reproducing kernel Hilbert space. The signal space is transformed into the feature space by the inner product, and the decomposition coefficient in the feature space and the decomposition coefficient of the copy field are internalized. Realize the three-dimensional positioning of the target. In this paper, the spherical array is used as the receiving array. The special spherical symmetric structure of spherical array can simplify the spherical harmonic decomposition and the calculation of RKHS method. The actual spherical array is not a continuous array, so it is necessary to arrange the position of the array elements reasonably to satisfy the orthogonal condition of spherical harmonics. There are three methods of array element placement in spherical array: equal angle sampling, Gao Si sampling and uniform sampling. In this paper, uniform sampling with the least number of elements is adopted under the same conditions. In the plane wave source model, the acoustic wave field is decomposed into a complete spherical harmonic function, beamforming is done in the spherical harmonic domain in the characteristic space, and the plane wave arrival angle (direction of arrival,DOA) is estimated. The spherical harmonic domain signal processing is more efficient than the array element domain computing efficiency, and different receiving array structures can be unified with the same signal processing framework. Under the point source model, the acoustic field can also be decomposed into spherical harmonic functions, and the spherical Fourier coefficients can be matched in the spherical harmonic domain to realize the three-dimensional positioning of the target. There exists a regenerative kernel function in RKHS, which is similar to the spherical harmonic decomposition. The acoustic field can be decomposed by this kernel function, and the decomposition coefficients can be matched in the feature space to realize the three-dimensional localization of the target. Spherical harmonic decomposition and RKHS are both tolerant matching field processing methods, but the advantage of RKHS method is that kernel control of location results can be realized by changing kernel function parameters. In this paper, three dimensional spherical harmonic decomposition and RKHS 3D positioning method are studied, and the angle of arrival and three dimensional position estimation of the target sound source are realized in the simulated waveguide environment. The results are compared with the results of array element domain matching field processing: without mismatch, there is no significant difference between spherical harmonic decomposition and RKHS method and array element domain matching field processing; In the case of mismatch, the results of the two methods proposed in this paper are better than that of matrix element domain matching field processing. Finally, the above conclusions are verified by designing and implementing the spherical array sound source localization experiment in the laboratory waveguide.
【學位授予單位】：浙江大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN911.7
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