The Robustness Design And Three-dimensional Localization Of Helix Array Based On Spherical Harmonics In Waveguide

The active and passive source localization problem is not only hot but also the difficulty in the underwater acoustic studies.The passive source localization problem attempts to determine the position of source using the array received data composed by signals radiated by source and noises,and in fact,this is an inference problem.Moreover,the active source localization has to solve the effective illumination issue.The difficulty in these issues is the uncertainty characteristic of signal in underwater waveguide.As a result,only using inversion to solve the inverse problem will lead to degradation of performance.The key of the inverse problem is the robustness and stability of solution.From the point of view of statistics and information theory,we can model the received data as stochastic process,and the statistics of localization is the estimator.Considering the position of source or target can only be one point in every moment,in the mathematical sense,the position is a Dirac delta function.This is the natural property of localization.In order to let the localization result approach the delta function,which means the result of location is zeros except the target location,we describe the geometry of this stochastic processes in Hilbert space,which means we represent the stochastic processes using a complete orthonormal basis function,such as Spherical Harmonic.We associate the inference problem with the precious orthogonality of basis function in Hilbert space to enlarge the applicable area of Hilbert space theory.And we design the localization algorithm to approach the delta function and improve the accuracy and robustness of localization result.The Dirac delta function can be compounded of infinity but countable basis functions,such as the Spherical Harmonic on 2-Sphere.In order to obtain enough basis function,the receive array need to possess the completeness to obtain the projection of acoustics function in different Spherical Harmonic.The ocean is a depth bounded but range unbounded,three-dimensional waveguide,so the location of target is also three-dimensional.We need the three-dimensional array with different orientation to solve this problem.At the same time,the position of sensors need to have the ability to sample different Spherical Harmonic.In this paper,we proposed two criterions for three-dimensional array design.Combined with the representation of acoustics filed using Spherical Harmonic,we design the array from the aspect of the Spherical Harmonic decomposition performance and disturbance-resistant to solve the localization problem.The first criterion requires the position of sensors should satisfy the orthogonality among different Spherical Harmonic to improve the accuracy of coefficient of acoustic field.And the second criterion attends to reduce the effect of sensor position mismatch on the accuracy of coefficient.Moreover,these criterions can be applied to any three-dimension arrays,and we design the DNA dual helix array in this paper.The passive localization will be much difficult when the signal radiated by source drowned by noises and interference.In this situation,we need consider the active localization.One of the advantage of active localization problem is we can focus the energy radiated by transmit array to the target and minimize the energy on other position,i.e.effective illumination.The effective illumination can reduce the reverberation to improve signal to reverberation ratio and signal to noise ratio,and as a result,improve the performance of localization result using interaction and iteration of transmit and receiving.However,the effective illumination is also an inference problem because we can't get the exact information of waveguide.And the interaction and iteration of transmit and receiving also need to be resolved.In this paper,we design a mix array consisted of transmit array and receiving array based on the design of helix receiving array.The transmit array is the major structure and every transmit sensor surrounded by a dual helix array for receiving.And we can guide the transmit signal based on the received signal and the acoustics model.The performance will improve using the interaction between transmit and receiving.