Sound speed profiles in high spatiotemporal resolution using multigrid three-dimensional variational method:a coastal experiment off northern Shandong Peninsula

It is essential to ac quire sound speed profiles(SSPs)in high-precision spatiotemporal resolution for undersea acoustic activities.However,conventional observation methods cannot obtain high-resolution SSPs.Besides,S SPs are complex and changeable in time and space,especially in coastal areas.We proposed a new space-time multigrid three-dimensional variational method with weak constraint term(referred to as STC-MG3DVar)to construct high-precision spatiotemporal resolution SSPs in coastal areas,in which sound velocity is defined as the analytical variable,and the Chen-Millero sound velocity empirical formula is introduced as a weak constraint term into the cost function of the STC-MG3DVar.The spatiotemporal correlation of sound velocity observations is taken into account in the STC-MG3DVar method,and the multi-scale information of sound velocity observations from long waves to short waves can be successively extracted.The weak constraint term can optimize sound velocity by the physical relationship between sound velocity and temperature-salinity to obtain more reasonable and accurate SSPs.To verify the accuracy of the STC-MG3DVar,SSPs observations and CTD observations(temperature observations,salinity observations)are obtained from field experiments in the northern coastal area of the Shandong Peninsula.The average root mean square error(RMSE)of the STC-MG3DVar-constructed SSPs is 0.132 m/s,and the STC-MG3DVar method can improve the SSPs construction accuracy over the space-time multigrid 3DVar without weak constraint term(ST-MG3DVar)by 10.14%and over the spatial multigrid 3DVar with weak constraint term(SC-MG3DVar)by 44.19%.With the advantage of the constraint term and the spatiotemporal correlation information,the proposed STC-MG3DVar method works better than the ST-MG3DVar and the SCMG3DVar in constructing high-precision spatiotemporal re solution SSPs.

Comprehensive Study of Inversion Methods for Sound Speed Profiles in the South China Sea

Traditional acquisition method of sound speed profiles using hydro-acoustic instruments is accurate but time-consuming and costly.To overcome this problem,some inversion methods have been developed over the last few decades.In this study,a comprehensive comparison of two inversion methods–the acoustic inversion method(AIM)and the satellite observation reconstruction method(SOR)–is presented.For AIM,the sound speed profile is first parameterized by the empirical orthogonal function(EOF)and the optimal parameters are searched by simulated annealing algorithm with respect to the cross-correlation function of the receiving signal and the simulation signal.For SOR,remotely sensed data are used to construct sound speed profiles.An experiment was conducted in the northeast of the South China Sea to verify the two methods.Both methods can obtain sound speed profiles quickly and cheaply.Compared with the sound speed profiles obtained by a conductivity-temperature-depth(CTD)instrument,the root-meansquare-error(RMSE)of AIM is 0.55 m s^(−1) and that of SOR is 1.71 m s^(−1).It is clear that AIM provides better inversion performance than SOR.Another primary benefit of AIM is that this method has no limitation to the inversion depth.The simulation results of sound propagation in regard to the inversed sound speed profiles show that the transmission losses of AIM and CTD are consistent and that of SOR is adversely affected by the inversion error of the sound speed and the inversion depth.But SOR has particular advantages in the inversion coverage.Together,all of these advantages make the AIM particularly valuable in practice.

Rapid environmental assessment in the South China Sea:Improved inversion of sound speed profile using remote sensing data

Complex perturbations in the profile and the sparsity of samples often limit the validity of rapid environmental assessment(REA)in the South China Sea(SCS).In this paper,the remote sensing data were used to estimate sound speed profile(SSP)with the self-organizing map(SOM)method in the SCS.First,the consistency of the empirical orthogonal functions was examined by using k-means clustering.The clustering results indicated that SSPs in the SCS have a similar perturbation nature,which means the inverted grid could be expanded to the entire SCS to deal with the problem of sparsity of the samples without statistical improbability.Second,a machine learning method was proposed that took advantage of the topological structure of SOM to significantly improve their accuracy.Validation revealed promising results,with a mean reconstruction error of 1.26 m/s,which is 1.16 m/s smaller than the traditional single empirical orthogonal function regression(sEOF-r)method.By violating the constraints of linear inversion,the topological structure of the SOM method showed a smaller error and better robustness in the SSP estimation.The improvements to enhance the accuracy and robustness of REA in the SCS were offered.These results suggested a potential utilization of REA in the SCS based on satellite data and provided a new approach for SSP estimation derived from sea surface data.

An improved algorithm based on equivalent sound velocity profile method at large incident angle

With the development of ultra-wide coverage technology,multibeam echo-sounder(MBES)system has put forward higher requirements for localization accuracy and computational efficiency of ray tracing method.The classical equivalent sound speed profile(ESSP)method replaces the measured sound velocity profile(SVP)with a simple constant gradient SVP,reducing the computational workload of beam positioning.However,in deep-sea environment,the depth measurement error of this method rapidly increases from the central beam to the edge beam.By analyzing the positioning error of the ESSP method at edge beam,it is discovered that the positioning error increases monotonically with the incident angle,and the relationship between them could be expressed by polynomial function.Therefore,an error correction algorithm based on polynomial fitting is obtained.The simulation experiment conducted on an inclined seafloor shows that the proposed algorithm exhibits comparable efficiency to the original ESSP method,while significantly improving bathymetry accuracy by nearly eight times in the edge beam.

Acoustic localization with multi-layer isogradient sound speed profile using TDOA and FDOA

In the underwater medium,the speed of sound varies with water depth,temperature,and salinity.The inhomogeneity of water leads to bending of sound rays,making the existing localization algorithms based on straightline propagation less precise.To realize high-precision node positioning in underwater acoustic sensor networks(UASNs),a multi-layer isogradient sound speed profile(SSP)model is developed using the linear segmentation approximation approach.Then,the sound ray tracking problem is converted into a polynomial root-searching problem.Based on the derived gradient of the signal’s Doppler shift at the sensor node,a novel underwater node localization algorithm is proposed using both the time difference of arrival(TDOA)and frequency difference of arrival(FDOA).Simulations are implemented to illustrate the effectiveness of the proposed algorithm.Compared with the traditional straight-line propagation method,the proposed algorithm can effectively handle the sound ray bending phenomenon.Estimation accuracy with different SSP modeling errors is also investigated.Overall,accurate and reliable node localization can be achieved.

Tracking of time-evolving sound speed profiles with an auto-regressive state-space model

An approach for time-evolving sound speed profiles tracking in shallow water is discussed. The inversion of time-evolving sound speed profiles is modeled as a state-space estimation problem, which includes a state equation for predicting the time-evolving sound speed profile and a measurement equation for incorporating local acoustic measurements. In the paper, auto-regression （AR） method is introduced to obtain a high-order AR evolution model of the sound speed field time variations, and the ensemble Kalman filter is utilized to track the sound speed field. To validate the approach, the accuracy in sound speed estimation is analyzed via a numerical implementation using the ASIAEX experimental environment and the sound velocity measurement data. Compared with traditional approaches based on the state evolution represented as a random walk, simulation results show the proposed AR method can effectively reduce the tracking errors of sound speed, and still keep good tracking performance at low signal-to-noise ratios.

A methodology to achieve the basis function for the expansion of sound speed profile

In order to evaluate the reliability and applicability of the Empirical Orthogonal Functions（EOFs）in the acoustic inversion of sound speed profile（SSP）and reduce EOF＇s dependence on the sample data,a methodology is proposed for the achievement of the basis functions for SSP＇s expansion.By analyzing the oceanographic dynamics which is the main cause of the SSP＇s variation,the basis functions are obtained naming the Hydrodynamic Normal Modes（HNMs）.The HNM basis functions are almost the same as those derived from the EOF method,while HNMs has less dependence on the amount of the sample data.HNMs method has a physically meaningful interpretation,and it could give out the physical parameters which determine the basis functions for the expansion of SSP,and this makes it possible to analyze and evaluate the trustiness and applicability of EOFs.

Basis functions for shallow-water temperature profiles based on the internal-wave eigenmodes

The shallow-water temperature profile is typically parameterized using a few empirical orthogonal function(EOF)coefficients.However,when the experimental area is poorly known or highly variable,the adaptability of the EOFs will be significantly reduced.In this study,a new set of basis functions,generated by combining the internal-wave eigenmodes with the average temperature gradient,is developed for characterizing the temperature perturbations.Temperature profiles recorded by a thermistor chain in the South China Sea in 2015 are processed and analyzed.Compared to the EOFs,the new set of basis functions has higher reconstruction accuracy and adaptability;it is also more stable in ocean regions that have internal waves.

An improved positioning model of deep-seafloor datum point at large incidence angle

The inhomogeneous sound speed in seawater causes refraction of sound waves,and the elimination of the refraction effect is essential to the accuracy of underwater acoustic positioning.The raytracing method is an indispensable tool for effectively handling problems.However,this method has a conflict between localization accuracy and computational quantity.The equivalent sound speed profile(ESSP)method uses a simple sound speed profile(SSP)instead of the actual complex SSP,which can improve positioning precision but with residual error.The residual error is especially non-negligible in deep water and at large beam incidence angles.By analyzing the residual error of the ESSP method through a simulation,an empirical formula of error is presented.The data collected in the sailing circle mode(large incidence angle)of the South China Sea are used for verification.The experiments show that compared to the ESSP method,the improved algorithm has higher positioning precision and is more efficient than the ray-tracing method.

TOA positioning algorithm of LBL system for underwater target based on PSO

For the underwater long baseline(LBL)positioning systems,the traditional distance intersection algorithm simplifies the sound speed to a constant,and calculates the underwa-ter target position parameters with a nonlinear iteration.However,due to the complex underwater environment,the sound speed changes with time and space,and then the acoustic propagation path is actually a curve,which inevitably causes some errors to the traditional distance intersection positioning algorithm.To reduce the position error caused by the uncertain underwater sound speed,a new time of arrival(TOA)intersection underwater positioning algorithm of LBL system is proposed.Firstly,combined with the vertical layered model of the underwater sound speed,an implicit positioning model of TOA intersection is constructed through the constant gradient acoustic ray tracing.And then an optimization function based on the overall TOA residual square sum is advanced to solve the position parameters for the underwater target.Moreover,the particle swarm optimization(PSO)algorithm is replaced with the tra-ditional nonlinear least square method to optimize the implicit positioning model of TOA intersection.Compared with the traditional distance intersection positioning model,the TOA intersec-tion positioning model is more suitable for the engineering practice and the optimization algorithm is more effective.Simulation results show that the proposed methods in this paper can effectively improve the positioning accuracy for the underwater target.

声速剖面EOF重构的实测数据采样深度研究

经验正交函数(experiential orthogonal functions,EOF)是重构声速剖面(sound speed profile,SSP)的一种有效方法,利用部分实测数据结合历史剖面资料可以重构当前位置的声速剖面。针对实测数据的采样深度难以确定这一问题,本文介绍了一种基于历史声速剖面资料的实测数据采样深度选取方法,根据EOF空间函数的方差贡献率确定数据量,进而采用EOF算法重构全海深声速剖面。实验结果表明:采用该方法得到的数据重构的声速剖面与实测声速剖面具有较好的一致性,基于常梯度声线跟踪法得到的水深数据能够满足0.25%倍水深限差,有效波束比达到了100%,为实际测量作业中声剖数据的采样深度提供了参考。