Spherical Harmonics Wavefield Decomposition And RKHS Three-dimensional Location In Waveguide

Target passive three dimensional location by receiving sound field data radiated from the target sources in the ocean waveguide environment has been a difficult problem to solve in underwater acoustic field.The scientific essence of target passive location is inverse problem solving.In other words,it is the process to estimate the location information of the target sources from the received data.Inversion is a method of inverse problem solving,by forward model fitting of forward problem,such as Matched field processing(MFP).However,MFP requires a huge amount of conditions which are difficult to be known concretely.That leads to a mismatch between the copy sound field which is generated from forward model and the received sound field.Further,this mismatch probably makes performance degrade,and even collapse.Therefore,the keys solutions of location problem are stability and robustness,and we also need turn it to inverse problem inference from inversion.The stability and robustness of the inference are ensured by completeness.Embarking from the theory of Hilbert space,this paper decomposes the wavefield in the complete infinite dimensional Hilbert space,and then a complete orthogonal sequence is obtained.The basic operation of decomposition is inner product.Under the Lebesgue measure,inner product turns to be equal almost everywhere rather than equal everywhere,so it has good robustness.Spherical harmonics decomposition and Reproducing Kernel Hilbert Space(RKHS)methods,are discussed in the paper.These two methods transform signal space to feature space and match the decomposition coefficients with the decomposition coefficients of the copy field in the feature space to achieve three-dimensional location.Three-dimensional location requires completeness of receiving data,so receiving array requires a variety of orientation.Hence,this paper adopts the spherical array as receiving array.The special spherically symmetric structure of spherical array can simplify the calculation of spherical harmonics decomposition and RKHS,but the positions of array elements on spherical array is not arbitrary,because they need meet the strict orthogonal condition.There are three main methods of laying array elements such as equal-angle sampling,Gaussian sampling and uniform sampling.This paper relies on the last method--uniform sampling,which needs the least number of array elements in the same condition.Under the acoustic source model of plane wave,the wavefield is decomposed into a set of complete spherical harmonic functions,and beamforming is done in the feature space spherical harmonic domain to estimate the direction of arrival(DOA)of the plane waves.Spherical harmonic domain signal processing is more efficient than array domain signal processing,and different receiving array structures can be united to the same signal processing framework.Under the acoustic source model of point source,the wavefield is decomposed into a set of complete spherical harmonic functions,and spherical Fourier coefficients are matched in spherical harmonic domain to achieve three-dimensional location of the targets.RKHS corresponds to a kernel function with reproducing property.Similar to spherical harmonics decomposition,wavefield can be decomposed into the kernel functions,and then decomposed coefficients are matched in the feature space to achieve three-dimensional location of the targets.The advantage of the RKHS method is that we can control the location results by changing the parameters of the kernel functions.Spherical harmonics decomposition and RKHS are studied in this paper.In simulation waveguide environment,DOA estimation and three-dimensional location estimation of target sources are achieved.Meanwhile,the results of these two methods are compared with the results of array domain matched field processing.There is no significant difference between the results of above two methods and array domain matched field processing without mismatch.Nonetheless,in the mismatch situation,the results of spherical harmonics decomposition and RKHS are superior to the results of array domain matched field processing.In the laboratory waveguide,a spherical array acoustic source location experiment is presented in final part,validating the above conclusions.