The Design And Three-Dimensional Localization Of Small Size Ellipsoid Helix Array Based On Spherical Harmonics

In the ocean wave guide environment,the passive localization of the target in the threedimensional sound field space belongs to the technical difficulties in the field of underwater acoustics.The essence of passive localization is inverse problem solving and inversion is a way to solve the inverse problem.However,many parameters in the marine environment such as sound velocity profile,seawater depth and sediment layer parameters are uncertain.Therefore,these uncertainties will cause the decline or even collapse of localization performance if only using the inversion method.This paper refines target localization into a statistical inference problem from the perspective of information theory.The received acoustic wave data is modeled as random process,and geometrically described by Hilbert space,that is,represented by a set of complete orthogonal normalized basis such as spherical harmonics.This paper focuses on spherical harmonics decomposition methods.The inner product is used to transform the signal from the array element domain to the spherical harmonics domain.The inner product of the decomposition coefficient of the real sound field in the spherical harmonics domain and the decomposition coefficient of the copy sound field is used to realize the three-dimensional localization of the target.To achieve three-dimensional unambiguous localization of the target,an omnidirectional three-dimensional array is needed.In this paper,a small size ellipsoid Helix array is designed and fabricated.The designed array is a kind of omnidirectional three-dimensional array,and its special three-dimensional spatial structure can show the advantages combined with other arrays while used in the target localization.At the same time,the development of autonomous underwater vehicle(AUV)and unmanned surface vehicle(USV)has promoted the demand for small-aperture light arrays.This small size ellipsoid Helix array can satisfy this demand.In addition,the threedimensional unambiguous localization of the target not only requires that the receiving array has a three-dimensional space structure,but also requires that the position of the array element satisfies the basis function in Hilbert space such as the full sampling of spherical harmonics.Therefore,this paper designs an ellipsoid Helix array from the perspective of fully sampling spherical harmonics.In general,the number of target sound sources in the marine environment is relatively small.So the passive localization of underwater targets can also be regarded as a sparse reconstruction problem.This paper discretizes the search area and convert the passive localization problem into the problem of solving a linear equation,where the value to be solved in the vector or matrix corresponds to the signal strength of each discrete grid point.In this paper,the compressive sensing theory is extended to the spherical harmonics domain matching field,and the L1-SVD sparse reconstruction method of the spherical harmonics domain is proposed,which reduces the dimension of the sparse reconstruction under multiple snapshots.This paper mainly studies the spherical harmonics decomposition of the ellipsoid Helix array and the spherical harmonics domain matching field method based on sparse reconstruction.The three-dimensional localization of the target sound source is realized in the simulated waveguide environment,and the localization results of the matching field method in the array element domain under the same conditions are given for comparison.Finally,the muffler pool experiment was carried out to verify above theories.The results show that the spherical harmonics domain matching field is more tolerant than the array element domain matching field when environmental mismatch and noise interference exist.In addition,the spherical harmonics domain matching field method based on sparse reconstruction can effectively improve the resolution of localization and reduce the side lobes.