波导中波场球谐波分解和RKHS三维定位
发布时间：2018-11-11 19:02
【摘要】：在海洋波导环境中,通过接收目标声源辐射的声场数据来实现目标被动三维定位是水声领域一直以来的研究难题。目标被动定位问题的本质是逆问题求解,即从接收到的数据中估计有关目标源的位置信息。逆问题求解的一种方法是反演,用正问题的前向模型拟合解决,例如匹配场处理(MatchedFieldProcessing,MFP)。然而MFP要求的条件太多,且条件难以确知,容易导致前向模型产生的拷贝声场与接收声场失配,从而使性能下降乃至崩溃。因而定位问题的关键是稳定性和宽容性,需要将逆问题求解由反演转向推断。推断的稳定性和宽容性是由完备性作保证的。本文从希尔伯特空间理论出发,在完备的无穷维希尔伯特空间中分解波场,获得包含目标信息的完备正交归一序列。分解的基本运算是内积,在Lebesgue测度下,内积放弃了处处相等的要求,转向几乎处处相等,更具宽容性。论文重点讨论了球谐波分解和再生核希尔伯特空间(Reproducing Kernel Hilbert Space,RKHS)方法,通过内积将信号空间变换到特征空间,将特征空间内的分解系数与拷贝场的分解系数作内积,实现目标三维定位。三维定位要求接收数据具备“完备性”,接收阵要求包含各种取向,本文采用球阵作为接收阵。球阵特殊的球对称结构可以简化球谐波分解和RKHS方法的计算。实际的球阵不是连续阵,需要合理布置阵元位置,以满足球谐波的正交条件。球阵上阵元布放方法主要有三种:等角度采样、高斯采样和均匀采样,本文采用相同条件下需要阵元数最少的均匀采样。在平面波声源模型下,将声波场分解为完备的球谐波函数表示,在特征空间球谐域内做波束形成,估计平面波到达角(direction of arrival,DOA)。球谐域信号处理相比阵元域计算效率更高,并且不同的接收阵结构可以用相同的信号处理框架统一起来。在点源模型下,声波场也可以分解为球谐波函数表示,在球谐域内对球Fourier系数做匹配,实现目标三维定位。RKHS中存在一个具有再生性的核函数,与球谐波分解类似,声波场可以用这个核函数作分解,在特征空间内对分解系数做匹配,实现目标三维定位。球谐波分解和RKHS都是宽容的匹配场处理方法,而RKHS方法好处在于可以通过改变核函数参数来实现定位结果的核控制。本文研究了三维球阵球谐波分解和RKHS三维定位方法,在仿真波导环境中实现了目标声源的到达角估计和三维位置估计,并与阵元域匹配场处理的结果作对比:不存在失配情况下,球谐波分解和RKHS方法与阵元域匹配场处理并无显著差别;存在失配情况下,本文提出的两种方法的结果要优于阵元域匹配场处理。最后,在实验室波导中,设计并实现了球阵声源定位实验验证了上述结论。
[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.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN911.7
本文编号：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.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN911.7
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