Research On The Low Frequency Calibration Of Finite-size Vector Sensor Array

The sound level radiated by submerged target becomes typically very low,thus compel the sonar array to make breakthroughs in its working frequency band,acting distance and anti-interference ability.Traditionally,the array for underwater acoustic surveillance are designed based on the half-wavelength spacing principle,its angular discrimination and array aperture are mutually restricted.Consequently,a low-frequency sonar array for target detection may be hundreds of meters,which will be not only inconvenient to use,but the cost of production and maintenance is also greatly improved.The emergence of acoustic vector sensor opens up a new way for the array design technology.A vector sensor can achieve frequency-independent directivity gain at one single space point,being very attractive in underwater applications.However,most of the existing vector sensor arrays are also based on the traditional design of half-wavelength spacing employed for hydrophone arrays.The proposed beamformer performance is still limited by array aperture,which failed to give full play to the ultra-wide band property of vector sensor.In the light of these situations,this paper proposes a finite size array design method whose inter-sensor spacing is much smaller than the wavelength.After the array performance analysis,this paper focuses on the low frequency array calibration problem.With the concept of multi-pole mode,this method utilizes the spatial differential theory to arrange vector sensors,thus a vector sensor array with very limited physical size can be built.Results illustrate that it can provide the same performance as traditional array with only 10% of its original size.The proposed finite size array is fundamentally the extension of vector sensor to higher order,which means that the resulting array is also frequency-independent.Thus,it is of great convenience to be applied to underwater low-frequency detections.Methods to overcome the platform scattering effect and to solve the low-frequency calibration problem in indoor water tank are proposed.The results of researches make it possible for this kind of array to realize in underwater acoustic field.The researches are divided into several parts as follows:(1)The finite size array design method and the array performance studyA broadband beamforming method is proposed for the finite size vector sensor array,which extracts multi-pole modes of different orders from the spatial differentials of the sound field.The vector sensors are used to replace the pressure difference operation,thus to achieve a desirable beam pattern,the order of spatial differential will be reduced.In other words,forthe same array configuration,using the vector sensors provides higher directivity than using the pressure sensor.Then,the array performance such as beampattern,array gain and array robustness are evaluated.Through the theoretical calculation and numerical illustration of these metrics,a proper way to choose array design parameters is also displayed.To evaluate the array performance for typical underwater circumstance,the receiving signal model using the normal mode theory had been established,and then the amplitude and phase distortion property caused by the shallow-water waveguide had been analyzed.Simulations and experimental tests show that due to the small array aperture,the waveguide effects are limited.In paper the beamformer distortion is also being considered in order to study the array performance in the presence of sensor gain and phase errors.It indicates that the mainlobe may be misoriented,sometimes even reversed because of the sensor errors.The results can also provide an array calibration precision reference for later work.(2)Model the acoustic scattering field for different nearby objects,and propose the corresponding system calibration method for finite size acoustic vector sensor arrayFor the spherical shell scattering problem,an exact solution can be achieved using analytical method,which is based on the partial wave expansion in terms of orthogonal functions and the adoption of classical boundary conditions.The difference between vector field and pressure field is deeply discussed,which indicates that the signal received by vector sensor may be asymmetric about the incident wave azimuth.For the thin circular plate,the Kirchhoff integral is used to generate the scattering field solution.And the characteristics of acoustic scattering for low frequency band are analyzed.The situations when the spherical shell and the thin circular plate coexist had also been studied by the Finite Element Method,and the characteristics for small grazing angle are summarized.Through these discussions,the acoustic scattering fields around any cylindrically symmetric objects can be modeled,which provide theoretical foundation for the receiving signals.Then,the optimal fitting idea is used to design the beamformer for arrays around scattering objects.The method establishes the relationship between the beampattern of the array output and the desired directivity pattern,thus resulting in an optimal weighting vector of the finite-size array.In the design procedure,the asymmetry property of the vector sensor is considered,and the feasibility of the algorithm is determined.This paper then proposes to combine the array measurement and calibration procedure together,regarding the array as a high order sensor,and taking its output beampattern as the evaluation guidance.Thus,the array can be calibrated in total.Finally,simulations and experimental results verify the correctness of the proposed method,which not only solve the problem about application ofvector sensor array,and also improve the array robustness.(3)Finite-size array calibration method in bounded space such as indoor water tank.For more times,we are focused to work at indoor water tank,which doesn't satisfy the far-field condition.In this paper,take into considering the bounded space restriction at low-frequency range,a calibration method for the finite size array is proposed.Transient state signal is modeled and analyzed to minimize the reflection effect of walls.And its efficiency has been shown by theoretical model and experimental tests.To correct the sound field distortion,the array manifold is reconstructed for the entire array in water tank space.The proposed method can calibrate the sensor consistence errors as well as remove the environmental factors.(4)Performed experiments at the outdoor environmentA prototype of finite size array consisting 5 vector sensors is designed to carry out the validation experiment.The array ability at target detection,direction-of arrival(DOA)estimation,and array gain are illustrated.Results show that the proposed array,whose physical size is less than 1m,can break the Rayleigh limit between array aperture and angular resolution,and realize the remote detection at low-frequency range,thus providing a new sight to underwater sonar design.