PGLA film and PGA fibers could provide ureteral stents with good compressive and tensile properties, respectively. In bicomponent stents, high film content led to high stiffness, while high fiber content resulted in poor compressional properties. To simplify the procedures to optimize the ratio of PGLA film and PGA fiber in the stents, a hierarchical support vector regression model (HSVRM) and particle swarm optimization (PSO) algorithm were used to construct relationships between the film-to-fiber weight ratio and the measured compressional/tensile properties of the stents. The experimental data and simulated data fit well, proving that the HSVRM could closely reflect the relationship between the component ratio and performance properties of the ureteral stents.A hierarchical support vector regression (SVR) model (HSVRM) was employed to correlate the compositions and mechanical properties of bicomponent stents composed of poly(lactic- Ureters are a pair of narrow thick-walled tubes that carry urine from kidneys to urinary bladders. Trauma, congenital malformation, tumor and calculi could obstruct ureters. Ureteral stents area type of tubular medical device that repairs the obstructed or impaired ureters. However, most ureteral stents currently on the market are non-biodegradable, with disadvantages such as causing ureteral infection, sedimentation of calculi, waist pain, abdominal discomfort, blood urine, stent breakage, urine return and other symptoms ,2. A secMuch attention has been paid to developing biodegradable ureteral stents, which can be degraded and subsequently discharged after recovery of the impaired ureter and, thus, help avoid a secondary surgery ,4. Howevet al. [et al. [et al. [Biodegradable synthetic polymers are widely used to prepare biomedical devices due to their consistent quality , in addiet al.  repaired [et al.  reconnec [et al. ,11,12 evet al. [et al. [et al. [In order to alleviate these problems mentioned above, two or more types of biodegradable synthetic polymers could be blended for the development of ureteral stents. Chew et al. ,14 demon [et al. ,16 fabri [et al.  investiget al. [It is difficult to complete the optimization experiments in the laboratory, as the processes are time consuming, expensive and labor intensive. Computational simulation could compensate by saving cost, time and labor. Using simulation, the mechanical properties of stents with different structures prepared under different conditions could be predicted, while the component ratio of PLA and PGLA and braiding parameters for the preparation of stents could be predicted as long as the required mechanical properties are proposed. A few examples have proven the effectiveness of simulation in the study of the mechanical properties of biomedical devices. Xiao et al.  presentset al. .In this paper, a hierarchical support vector regression (SVR) model (HSVRM) was proposed to simulate the braiding process of PGLA/PGA bicomponent ureteral stents. The primary and high-level SVR models were used to simulate the process of mixing and braiding and the process of thermal treatment, respectively. In order to obtain the optimal component proportion for the bicomponent ureteral stent, performance evaluation indices were defined; meanwhile, the particle swarm optimization (PSO) algorithm was used to get the optimal mixing ratio.This paper is organized as follows: ® Plus biostable polyurethane stent was selected as the control for the comparison of the mechanical properties. Three different stents . PGLA was a co-polymer of lactic acid/glycolic acid at a mole ratio of 1:9. The commercial 6Fr double pigtail Percuflexst stents  were brat stents . SubsequThe relationship between the properties of stents and each component was studied. The mechanical properties of the PLA/PGLA bicomponent stent are mainly attributed to that of the individual braided pure component stent (PCS) of PGA or PGLA. A particular mapping organization to quantify the relationship is demonstrated in As discussed above, mapping of the bicomponent stent preparation mainly consisted of two procedures, braiding mapping and thermal treatment mapping. The former can be modeled as a pure component model (PCM) and the latter as bicomponent model (BCM). By representing each mapping with a SVR model, a HSVRM could be obtained, as shown in n is the dimension of the performance indexes. We used Δl for radial deformation in the process of data sampling based on the experiments mentioned before and constructed a regression model for PCM using SVM [In PCM, the modulus of elasticity PGA and PGLA should be obtained from experimental data of PGA and PGLA, so mechanical properties of these two PCSs, PGA and PGLA, can be simulated via regressing the property data obtained from lab testing. sing SVM .b is the bias. For precursor fiber PGA, x is , K . Then, Equation (1) can be rewritten in the following form.With the solution of Equations (4) and (5), we introduce the inner product kernel function Most of the values of , and p is the proportion of the first component.For a bicomponent model, we can use the same means of SVR modeling, but it is worth noting that the independent variable Due to the influence of mechanical wear and the observation environment, the data obtained from sampling had noise, which may increase the complexity and affect the accuracy of modeling. Therefore, data preprocessing is necessary to obtain a smooth curve.x(n) has the form as follows.s (n)is the effective signal, v(n) is the noise signal. In order to obtain the optima estimation Ŝ of effective signal s, we need to design a filter to minimize the mean square error between S and Ŝ.We assume that an observation signal Ŝ is derived from Equation (9) is known as the Wiener filter [h(n). Then, the output of the linear filter is shown as follows.The process of r filter . The imph(n) should meet the following regular equation.xxR is the N order autocorrelation matrix of signal x(n) and xsr is the cross-correlation function vector of x(n) and S(n). If xxR is a non-singular matrix, we can obtain the following function from Formula (11).The minimum mean square error criterion The filter was applied to the obtained experiment data to achieve the smooth fitting data.Ideal ureteral stents should have high tensile modulus and strength, in addition to being biocompatible for convenient implantation ,23. DuriA suitable standard is of critical importance to the fabrication of bicomponent ureteral stents. To the best of our knowledge, there has been no standard to evaluate the mechanical properties of ureteral stents till now. In general, if the designed stent has the same compressional and tensile properties compared to a commercial non-biodegradable stent, it is acceptable. Being overly stiff, stents might cause discomfort due to high friction with adjacent tissues. The following performance indices are defined to measure the features of the ureteral stent.iE and commercial stent c,IE is known as sampling performance. It is formed as below:K is a constant greater than zero. We introduce a tolerance margin μ into the above formula. In other words, the performance of stents is optimal if the formula E = CE + μ can be satisfied. Σ is the covariance matrix of different mechanical properties. Therefore, when K=1, the formula Definition 1. Sampling point performance indicators: Under the same test conditions, the similarity of the mechanical properties of testing stent J of stents being tested is defined as the root-mean-square of the performance of all sampling points of stents being tested.N is the length of test data. Large J indicates that the mechanical properties of stents are close to the optimal performance of commercial stents. Definition 2. The performance of stents being tested: the performance evaluation function The performance evaluation function is strictly optimal. The optimized performance index can indicate consistency in the properties of the stents and the commercial stents throughout the testing process.cE, the problems in the optimization of component proportion can be expressed in the following form.Currently, the optimization of component proportion is conducted using lab experiments, which is time consuming and not capable of predicting the performance properties of products. Therefore, constructing a reasonable model for optimizing the component proportion has a practical importance. According to Model (6) in Solving Equation (15) is a nonlinear optimization problem. Because of the complexity of the preparation process model and the performance evaluation function, it is unable to obtain the analytic solution of Equation (15). Therefore, it is not applicable to use traditional methods to calculate extreme points. Hereinafter, we will use the PSO algorithm to find out the optimal component proportion.i means a solution in B dimensional solution space. The flying speed of each particle is y = f(x), the higher the fitness, the more superior the status of the particle is. We mark the historical optimal status of each particle as bestg; the status update function of particle i is formed as follows.Particle swarm optimization was proposed by Kennedy and Eberhart . The kerHere, η is inertia weight and p is treated as the status of a particle. Thus, Equation (15) can be converted to a function optimization problem with one dimension. According to the definition of the fitness function, in order to calculate in a user-friendly manner, we use the opposite value of the performance index as our fitness function, which is shown as follows.The unknown proportion ratio In order to guarantee that the particle searching space is satisfied with constraint Equation (16), we introduce a penalty term into the above fitness function and obtain the following form.Here:We did lab experiments and related simulation to verify the effectiveness of the proposed model. Firstly, data obtained from lab experiments were smoothed by the Wiener filter, as introduced in in situ displacement and force using transducers. The testing procedures for the radial compressional properties are as follows:(1)Place a specimen with a length of 5 cm on the stand transversely;(2)Compress the specimen at a speed of 10 mm/min until 50% of its diameter. The maximum force is considered as the radial compressional force;(3)After a time period of 10 s, withdraw the probe at a speed of 10 mm/min. The percent of elastic recovery is defined as the ratio of the sum of immediate elastic deformation and delayed elastic deformation over the original diameter of the stent;(4)Each data point is obtained from three tests.Tensile properties of stents were tested according to the ISO 7998-1998 standard for testing the tensile property of artificial blood vessels. We made three sets of tests respectively of the radial compressive property and the axial tensile property of stents being tested. The radial compression properties were measured using a radial compression apparatus, which was specially designed and built . We compress the artificial blood vessel using a probe with a similar diameter and record the The axial tensile properties were measured on a Darong universal mechanical tester . It gave experimental results for tensile strength (MPa) and elongation at break (%) . All of x axis and the tensile stress as the y axis, a one-to-many unspecified reflection would be expected. However, the deformation of the sample is a function of time, and the sampling time is kept constant. Therefore, changes in two tensile and compressive properties can be converted to functions of time. From The time series of each stent regarding the axial tensile property and radial compression and their corresponding curve smoothed by the filter are shown in We magnify the area that contains violently-changed data points to demonstrate that after filtering, the curves become smoother. The nonlinear relation between strain and distortion can be easily observed from the experiment data. Therefore, if we use the linear fitting method, we would have lost many of the mechanical properties that needed to be considered.C and the kernel function coefficient g need to be determined. Here, we select the radial base function (RBF) as the kernel function and the parameter g as the kernel bandwidth. The penalty coefficient controls empirical risk and reaches a compromise between empirical risk and confidence range. The bigger C is, the higher the fitting degree is and the smaller the error is. However, we should also consider that being oversized may lead to an over-fitting of training data. Kernel bandwidth g controls the sensitivity of the SVM to the change of input data. The smaller this value, the less sensible SVM is in the change of input data. The optimal parameters of the one-component model and hierarchical mixture model from cross-validation are shown in According to the model in *p, we still need to determine PSO’s related parameters. The values of the related parameters are shown in Before using the PSO algorithm to obtain the optimal proportion ratio p only influences the inputs of the SVRMixed section in the HSVRM and is independent of the first layer SVR. In order to reduce the computational burden, SVRPGA and SVRPGLA generate 100 sets of mechanical properties of PGA and PGLA in accordance with the time series. The original searching problem can be converted to such a situation, that when two raw material components and related pure component stents and a set of reference mechanical property are given, we need to solve proportion ratio p* to minimize the fitness function. Because the stretching test and compression test are conducted independently, the covariance of these two mechanical properties is zero. In order to reduce the computational burden, we may as well assume that the covariance matrix ∑ = I.According to the analysis in p*. By operating the above optimizing process 10 times independently, the average property when the algorithm has good convergence is calculated and set as p* obtained from the PSO algorithm to produce urethral stents, the products can have uniform performances in the stretch interval  and the compression interval , respectively. The larger error in  is due to the tremendous changes of testing data and the higher risk of fitting in this section. From p. In order to evaluate the performance of the ureteral stents, a novel performance index was first defined based on the deviation in the properties of the commercial stent. Unlike the empirical method, the proposed performance index cannot only guarantee the terminal feature of the products, but also force the transition performance to converge to the reference performance. Furthermore, the PSO algorithm was employed to search the optimal ratio of the two components for the stent preparation. In this paper, we established an HSVRM to estimate the mechanical properties of PGLA/PGA bicomponent braided ureteral stents. In our simulations, the braiding process of each material was treated as a primary SVR, and the thermal treatment is replaced by a high level SVR with the input consisting of the materials and the PCSs mixed at the ratio In this work, we only considered static mechanical properties, which may not be adequate to characterize medical devices. In the future, dynamic performance properties will be investigated and simulated using improved models.


As the sound signal of ships obtained by sensors contains other many significant characteristics of ships and called ship-radiated noise (SN), research into a denoising algorithm and its application has obtained great significance. Using the advantage of variational mode decomposition (VMD) combined with the correlation coefficient for denoising, a hybrid secondary denoising algorithm is proposed using secondary VMD combined with a correlation coefficient (CC). First, different kinds of simulation signals are decomposed into several bandwidth-limited intrinsic mode functions (IMFs) using VMD, where the decomposition number by VMD is equal to the number by empirical mode decomposition (EMD); then, the CCs between the IMFs and the simulation signal are calculated respectively. The noise IMFs are identified by the CC threshold and the rest of the IMFs are reconstructed in order to realize the first denoising process. Finally, secondary denoising of the simulation signal can be accomplished by repeating the above steps of decomposition, screening and reconstruction. The final denoising result is determined according to the CC threshold. The denoising effect is compared under the different signal-to-noise ratio and the time of decomposition by VMD. Experimental results show the validity of the proposed denoising algorithm using secondary VMD (2VMD) combined with CC compared to EMD denoising, ensemble EMD (EEMD) denoising, VMD denoising and cubic VMD (3VMD) denoising, as well as two denoising algorithms presented recently. The proposed denoising algorithm is applied to feature extraction and classification for SN signals, which can effectively improve the recognition rate of different kinds of ships. In the practical measuring process, measured signals are often mixed with noise and useless signal components which come from the surrounding complex environment and the measurement equipment itself. The time domain waveforms of the polluted signals are often different from those of original signals, and it is not easy to identify the original signal from the polluted signal. In the frequency domain, the bandwidth of the clear signal and the noisy signal also partially or even completely overlap. In this case, traditional spectrum analysis techniques and linear filtering algorithms cannot effectively eliminate noise. Therefore, the question of how to eliminate noise from the polluted signal must be solved in the signal processing field ,2.There is a kind of common denoising algorithm, the basic ideas of which is to extract components of signal obtained by one signal decomposition algorithm, identify and remove noise components by screening criteria, then reconstruct the useful components. For this kind of denoising algorithm, the focus is on selecting signal decomposition algorithm and noise-screening criteria. For instance, the wavelet denoising algorithm ,4 has beA kind of self-adaptive signal processing algorithm is empirical mode decomposition (EMD) ,7, origiAs a kind of non-recursive and self-adaptive signal-processing algorithm, variational mode decomposition (VMD) ,23,24, oIn this article, we proposed a new denoising algorithm for ship-radiated noise (SN) signals. We used VMD and CC to decompose the original signals into IMFs and identify noise IMFs, respectively; the decomposition number by VMD is equal to the number by EMD. According to the threshold of the CC, noise IMFs and useful IMFs can be distinguished effectively. Then, the first denoising can be realized by reconstructing useful IMFs. Secondary denoising can be accomplished by repeating the above steps of decomposition, mode-identification and reconstruction. The final result of denoising is determined according to the CC between IMFs and the original signal. Simulation results indicate that the proposed denoising algorithm based on the secondary VMD (2VMD) and CC is better than existing denoising ones. The proposed 2VMD denoising algorithm is used to feature extraction and classification for SN signals, which can effectively improve the recognition rate of different kinds of ships.The outline of the article is as follows. In the VMD algorithm, IMFs are defined as amplitude-modulated–frequency-modulated (AM–FM) signals, which are given by:The alternating direction multiplier method (ADMM) is used to obtain the saddle points, then the n = 0.Initialize Update the value of Judge whether or not The stop condition is as follows:Repeat the steps of updating parameters until the stopped condition is satisfied.The uniformly spaced distribution for initialization of center frequency is expressed as:In addition, The correlation coefficient (CC), as a parameter of statistical relationships, can measure the degree of dependence and correlation. In this paper, the formula of CC is shown as the following:A simulation example should make this easier to understand, with the simulation signals as follows:As can be seen in The denoising effects of different decomposition algorithms are compared. Therefore, two evaluation criteria for denoising algorithms are given as follows:Step 1:The target signal is decomposed by EMD, and the decomposition number by VMD is equal to the number by EMD;Step 2:Calculate the CCs between the original signal and IMFs by VMD, screen out the noise IMFs according to CC threshold. Through abundant simulation experiments, the CC threshold is fixed at 0.2 in this paper;Step 3:Reconstruct the useful IMFs by removing noise IMFs. After the reconstruction, the first denoising is completed;Step 4:Judge the times decomposition satisfies the 2VMD or not;Step 5:If 2VMD is not satisfied, the first reconstructed result is regarded as the input signal, then repeat Steps 1–3 to complete the whole denoising process; if it is satisfied, the reconstructed signal is regarded as the final denoising result.A 2VMD denoising algorithm using VMD and CC is designed in The line spectrum is the important information of the SN signals, and it provides a basis for ship detection and tracking. The periodic signal can be used as a line spectrum model. Therefore, three simulation experiments have been carried out in The simulation signal As seen in As seen in As seen in The simulation signal The simulation signal To further prove the suitability of the proposed 2VMD algorithm, the denoising effect is compared under different input SNRs and times of decomposition by VMD for the simulation signals in In recent research ,29, two First, three kinds of SN signals are performed by the proposed 2VMD denoising algorithm; then, the features of SN signals are extracted by the feature extraction algorithm in ; finallyThree kinds of SN signals, which are the same as the signals in , were reAccording to the research in , three kTo further prove the effectiveness of the proposed 2VMD denoising algorithm, the center frequencies of EIMF are classified by a support vector machine (SVM), and the polynomial kernel function is used for training and identifying. The classification results of train and test samples are shown in (1)A secondary VMD algorithm for denoising is put forward for the first time in this paper.(2)A novel denoising algorithm is proposed using 2VMD and CC for the SN signal in the field of underwater acoustic signal processing.(3)Compared with EMD and EEMD, the CCs between the simulation signal and its IMFs using VMD are closer to the true values. This shows that the VMD algorithm can better reflect the correlation.(4)Compared with EMD, EEMD and VMD denoising, the proposed denoising algorithm is a better denoising algorithm which has a high SNR and low RMSE by numerical simulations.(5)Compared with the different input SNRs and the times of decomposition by VMD, the proposed 2VMD denoising algorithm has high SNRs for different simulation signals, especially in the case of low-input SNRs. In addition, the proposed 2VMD denoising algorithm is superior to the two denoising algorithms presented recently in ,29.(6)Using the proposed 2VMD denoising algorithm and the feature extraction method in , the domIn order to achieve denoising of SN signals, a hybrid secondary denoising algorithm is proposed in this article. The proposed denoising algorithm employs 2VMD and CC. The target signal is decomposed using VMD, and the CC threshold is used to determine the useful IMFs. Through abundant simulation experiments and analytical comparisons, the proposed denoising algorithm demonstrated its superiority and the following contributions:


Advances in acoustic technology and instrumentation now make it possible to explore marine resources. As a significant component of ocean exploration, underwater acoustic target tracking has aroused wide attention both in military and civil fields. Due to the complexity of the marine environment, numerous techniques have been proposed to obtain better tracking performance. In this paper, we survey over 100 papers ranging from innovative papers to the state-of-the-art in this field to present underwater tracking technologies. Not only the related knowledge of acoustic tracking instrument and tracking progress is clarified in detail, but also a novel taxonomy method is proposed. In this paper, algorithms for underwater acoustic target tracking are classified based on the methods used as: (1) instrument-assisted methods; (2) mode-based methods; (3) tracking optimization methods. These algorithms are compared and analyzed in the aspect of dimensions, numbers, and maneuvering of the tracking target, which is different from other survey papers. Meanwhile, challenges, countermeasures, and lessons learned are illustrated in this paper. With the exhaustion of land resources, humans have started shifting their focus to the exploitation and utilization of marine resources for the sake of achieving sustainable development . As a siA considerable amount of literature has investigated well the problem of target tracking in the terrestrial environment. Among them, the systems based on varieties of sensors can be adopted to detect and track the interested target . In 3],,3], the Due to the fact they are absorbed and attenuated significantly in the ocean, many detecting media such as electromagnetic waves and laser waves which can be used to implement terrestrial target tracking methods have poor performance in marine environments . As the This paper concentrates on a comprehensive survey of underwater target tracking algorithms and is organized as follows: In this section, related surveys about target tracking are introduced. In view of the fact that most survey papers are restricted to tracking based on WSNs, the difference between underwater acoustic target tracking and target tracking using WSNs is clarified. Moreover, compared to other surveys, the original contributions of this paper are illustrated.Communication issues: The underwater channel is a complex channel that is variable over time and space due to the characteristics of the transmission media and the environment [−2, resulting in frequent transmission loss. Therefore, robust data fusion techniques are needed in light of the packet loss phenomenon.ironment . The comironment . TherefoReal-time: In underwater tracking, the sensors are usually deployed in 3D-space and drift with the current. The tracking is highly dependent on the accuracy of the sensor positions, which poses more stringent real-time requirements for underwater acoustic tracking algorithms compared with those based on WSNs. The limited bandwidth results in low communication rates which also pose a great challenge for real-time underwater acoustic target tracking.Tracking mode: Unlike other modems, acoustic modems consume order of tens of Watts of energy during the transmitting process, and tens of milliwatts during receiving processes. The apparent asymmetry in power consumption makes it preferable for underwater acoustic tracking sensors to work in passive mode for energy-efficiency.To our knowledge, there are only a few review articles about target tracking, and they are all focused on target tracking based on WSNs. In , the autOur paper is the first review article centered on underwater target tracking. Many domestic and foreign scholars have thoroughly studied underwater target tracking and numerous papers have been published. Therefore, a survey on underwater target tracking is in need.We summarize the abundant related knowledge of underwater acoustic target tracking ranging from the acoustic tracking instrument to the process of tracking, which will provide readers with a comprehensive understanding of this research area.We provide an updated literature review of underwater acoustic target tracking algorithms and most of the papers which focus on a study of the underwater target tracking are included. A comprehensive comparison of these algorithms is provided according to the characteristics of the target such as numbers, dimensions, and maneuvering.Furthermore, the acoustic target tracking not only can be realized by WSNs but also can be dependent on TASA and acoustic imaging sensors which will be introduced in The existing review papers concentrate on target tracking algorithms based on WSNs. However, some tracking algorithms cannot be directly applied to underwater target tracking due to the special nature and complexity of the marine environment. Our article is the first paper providing a survey of acoustic tracking algorithms for underwater targets. Meanwhile, tracking instruments are not limited to UWSNs which are variations of WSNs, and TASA and acoustic imaging sensors are also included.To make readers understand the area easily, the basic structure of sensors used for tracking is clarified. Then the most common used acoustic tracking instruments including TASAs, UWSNs, and acoustic imaging sensors are introduced in this section.As is known to humans, acoustic waves are the only medium which can propagate over a long distance in seawater. As a result, people have been using sound waves to navigate, locate, track and recognize fixed or moving underwater targets. Devices with these functions are acoustic sensors. Compared to the tracking based on WSNs, the underwater acoustic tracking algorithms have to consider some special issues such as communication issues, improvement of real-time and tracking mode. However, the issues in tracking can be solved not only by effective algorithms but also by the tracking instruments. Recently, some researchers are focused on designing acoustic modems for sensors for underwater target tracking to solve the issues incurred by the underwater environment.The authors in  provide Traditionally, various types of TASAs have been used to complete the underwater target tracking task, for example, the hull-mounted array and towed array ,25,26. THowever, these tracking algorithms based on TASA have fatal flaws in some mission-critical scenarios because they need to be mounted on or towed by a submarine or a ship . The effNode localization. Due to the severe attenuation of electromagnetic waves, the global positioning system (GPS) is unable to provide localization service for the underwater sensor nodes. Effective node localization algorithms are in need and the accuracy of the node localization has a significant impact on tracking performance.Node cooperation. It defines how to communicate between nodes to reduce the amount of message transmitting.Position computation. Measurements obtained from underwater sensor nodes are severely interrupted by noise which cannot be ignored, therefore, how to use these noisy measurements to obtain the position of the target as close to the true one as possible becomes a challenging issue.Future-position estimation. Although this process is not necessary for every tracking algorithm, there are many algorithms that take into consideration this information that can be used to save energy consumption of sensor nodes by efficient node scheduling strategies.Energy management. Because the power of sensor nodes is limited, any tracking algorithms should achieve a good trade-off between tracking accuracy and energy consumption which directly determines the lifetime of the network.To address the aforementioned problems, UWSNs, variations of WSNs, are envisioned to enable applications for underwater target tracking. UWSNs have superiority over TASA in low-cost, self-organization, fault tolerance and rapid deployment . UWSNs cIn terrestrial WSNs, as a critical application, target tracking has been well studied and plenty of research results have been published ,34,35,36With the development of autonomous underwater vehicles (AUVs), incorporating TASA with UWSNs, a novel variation tracking system of USWNs has been proposed, which is composed of mobile sensor nodes such as the AUVs towing acoustic arrays ,38. Whether based on TASA or UWSNs, these algorithms are non-visual tracking. The development and maturity of underwater acoustic imaging or video processing technology provide an alternative approach for underwater target visual tracking using acoustic imaging sensor. The most widely used acoustic imaging sensor is the looking forward sonar which is usually installed on the front of AUVs. The imaging sensor transmits acoustic signals to the underwater area of interest and processes the received back-scattering echoes. By using acoustic imaging techniques, an initial acoustic image of the real environment is obtained from the image sequences, the underwater target tracking can be realized by determining the target area in each frame image.In conclusion, there are diversified alternative acoustic tracking instruments for underwater target tracking. However, published survey articles are only centered on WSNs, which is not comprehensive. Therefore, in this paper, a classification, which is based on three commonly used underwater acoustic tracking instruments including the acoustic imaging sensor, TASA, and UWSNs, is proposed in The general process of target tracking including target detection, position determination, target model construction, state filtering and prediction is introduced in this section. For the integrity of the article, the process of tracking based on images is also covered. Target tracking refers to the process of processing the measurements obtained from sensors and maintaining an estimate of the current state of the target. The state mainly contains the position, velocity, and other kinematic components. The measurements refer to the observation information about the target, including direct distance estimation, slope distance, direction of arrival (DOA), received signal strength indication (RSSI), time of arrival (TOA) or time difference of arrival (TDOA), as well as the frequency difference between sensors caused by the Doppler frequency shift. When sensors detect the presence of the target, the observation information can be obtained by sampling the sensed signals . Then the position of the target can be computed mathematically by relating this information to the target state. Finally, the tracking process is completed by determining the position of the target at each step. Due to the existence of noise in measurements, an extra component, filtering process should be included to improve the tracking accuracy. Filtering algorithms are also used to predict the position of the target according to the target motion model to accelerate the tracking speed. The process described previously is the general tracking process in non-visual tracking which refers to using TASA or UWSNs.In visual tracking, which refers to using acoustic imaging sensors, the tracking process is a little different. Target tracking based on acoustic imaging sensors involves determining the exact location of the moving target in the next frame quickly by minimizing the search scope of the maneuvering, which can be summarized as shown in In conclusion, the tracking process both in visual tracking and non-visual tracking has some important components such as target detection, position determination, target model construction and state filtering and prediction.In visual tracking, this process means determining the existence of the moving target in the image sequences and describing the characteristics of the target . Currently, in the field of visual tracking, the commonly used moving target detection algorithms include background subtraction, frame difference, optical flow and mixture of the Gaussian model. Among varieties of target detection algorithms, background subtraction is the most frequently used one. The basic idea of it is to subtract the moving target from the difference image obtained by comparing the background image and the current image . Frame dDistinct from the detection based on images, target detection in non-visual tracking is much simpler. An acoustic sensor accuses the detection of the target when the received signal strength exceeds a predefined threshold. It is true that there are many other sophisticated algorithms for detecting targets accurately. More relevant information can be found in other articles.The process of position determination in visual tracking refers to locate the area of the target in each frame. After a target is correctly detected, the corresponding relationship between adjacent frames should be determined, which is also called target matching. Target matching is completed by the criterion that the center position and size of the same target changes little in consecutive frame images during a small sampling interval . While iContinuous positioning at the time sequence can also realize tracking tasks, and the corresponding velocity, as well as acceleration, can be obtained according to the position at several sampling instants. However, the state of the target always varies with time and measurements are corrupted by noise seriously, which results in tracking with continuous positioning having poor performance. Therefore, most of tracking algorithms adopt filtering techniques as the technology of state estimation and reducing the noise interference. Position determination algorithms are usually used to obtain the initial state of the target.k respectively. The transfer function Most of the target tracking problems are investigated based on a model, in other words, based on two descriptions. One is the target behavior represented by the dynamic motion model; the other is the observation of the target called the observation model. The establishment of underwater target dynamic motion model and observation model is the precondition of target tracking . The dynThe relationship between the measured bearings and the position of the target can be described as Equation (2) shows:The measurement function kν. The accuracy of target motion model directly affects the tracking precision. If the model is far different from the actual situation, it may lead to the divergence of the subsequent filtering process [The second term to the right of the Equation (3) represents the measurement noise  process . Howeverk can be represented as T as Equation (4) shows:y component as an example, the range change in y component and the velocity change in y component as Equations (5) and (6) show:In three-dimensional space, the state of a target at time Target tracking is a typical uncertainty problem. Due to the development of monitoring and anti-surveillance technologies as well as the improvement of target mobility, the problem of uncertainty in target tracking becomes more serious. The source of uncertainty mainly comes from the uncertainty of target motion represented by process noise, the uncertainty of the source of measurements (measurement noise) and the false noise incurred by multi-target and the dense cluttered environment. Therefore, the essence of target tracking is estimating and predicting the state of the target by filtering algorithms to eliminate the uncertainty associated with the target.According to the dynamic motion model and observation model established, how to choose the appropriate filtering algorithm or improve the existing ones to meet the specific requirements of the underwater target tracking is the key to designing target tracking algorithms. To this end, we will introduce the basic theory of filtering and the commonly used filtering algorithms in underwater target tracking:Bayesian filter: The core design idea of the Bayesian filter is obtaining the posterior probability by using observation data obtained at the current moment to correct the prior probability density function (PDF) [on (PDF) . Bayesiak, k, and the probability of the initial state of the target is assumed to be known. Since the state vector Let In linear conditions, the Bayesian filter can acquire the approximately optimal solution, namely the Kalman filter (KF). While in nonlinear conditions, the approximate optimal solution is hard to acquire owing to the infinite dimensional integral calculation. Then some sub-optimal algorithms are proposed such as the extended Kalman filter (EKF), the unscented Kalman filter (UKF) and the particle filter (PF).EKF: This filtering algorithm is developed based on the original KF formulation for nonlinear problems [problems . EKF adok is k + 1 can be represented as Equation (10) shows. The higher order is omitted here, where k + 1 is similar, represented as Equation (11) shows. The higher order is also omitted here.Assuming the estimated state of the target at time The second and higher order items are omitted in Equations (10) and (11) when the first order EKF is adopted, while the second order items should be kept in the second order EKF. Then the state estimation can be completed according to the basic KF. However, if the nonlinearity of the system is serious, tracking algorithms adopting EKF will result in large errors due to the loss of numerous information in the linearization process using Taylor series.UKF: Based on the unscented transform (UT), UKF approximates the nonlinear distribution using determined sample particles. Different from approximately linearizing the state, UT performs an approximation on the posterior PDF of the state by some determined symmetrical sampling points [g points . The meaPF: It is a sub-optimal algorithm of the Bayesian filter based on random sampling [sampling . Becausesampling , which ssampling  demonstrIn conclusion, when designing tracking algorithms, researchers should choose appropriate filtering algorithms according to the settled model and application scenarios. Therefore, in With the development of acoustic technology and tracking instrument, numerous research results have been applied into tracking underwater targets. To evaluate the state-of-the-art underwater acoustic target tracking algorithms, a classification criterion should be proposed and various algorithms should be compared and analyzed within the group with common characteristics. In this section, the classification of underwater acoustic target tracking algorithms is introduced. These algorithms can be classified based on the methods used such as instrument-assisted method, mode-based method, and the tracking optimization method. The categories of commonly used acoustic tracking instruments, namely, the acoustic imaging sensor, TASA, and UWSNs are put into the class called the instrument-assisted method. The mode-based method focuses on how to achieve better tracking results based on passive tracking and active tracking, which are classified according to the working mode of sensors. The tracking optimization method concentrates on improving the tracking accuracy and source consumption. In this paper, filtering techniques, arithmetic average, and the Sage-Husa model are taken as the noise-driven tracking optimization method. The sensor scheduling strategies and quantized methods are taken as the source-driven tracking optimization method. Taxonomy of underwater acoustic target tracking is illustrated in Instruments used to track underwater targets can be classified as acoustic imaging sensors, TASAs, and UWSNs. Based on the former, the kinematic state  and other features  of the target can be determined by images or video sequences, while the latter can only achieve motion tracking based on the acoustic echo signals. In this section, the algorithms based on different instruments are introduced. These algorithms are compared in the aspect of accuracy, complexity, and cost of tracking based on different instruments, as well as the strength and weakness of the corresponding tracking instrument.With the aid of visual analysis and the development of underwater imaging technologies, it is possible to realize underwater target tracking based on video or image sequences which are obtained by acoustic imaging sensors. Imaging sensors are not attractive compared with other acoustic sensors used in the underwater environment for their limited sensing range and poor visibility. Nevertheless, tracking based on visual data can also be an alternative method, especially in close-range tracking. Many approaches have been taken to overcome the limitations of tracking based on imaging sensors.In , the autThe proposed algorithm can be further used for fish abundance analysis and monitoring marine endangered species. However, the drawback of using a single imaging sensor is that it is unable to capture the interested target all the time due to the limited field of view (FOV) and abrupt motion of the target. Researchers in  developeIn some dark or murky underwater situations, the images obtained from imaging sensors cannot be used to complete detecting and tracking tasks. The authors in  are inspBased on the interested target being well detected by some vision-based target detection techniques such as feature-based detection and template-matching detection, the authors in  review tThe authors in  analyze The sound pressure hydrophone itself has no directivity so it is unable to determine the position of the target on its own. TASA usually uses sound pressure hydrophones forming a linear array model to obtain the bearing information of the target through the method of array signal processing. However, due to the cylindrical symmetry, single line array receivers have the problem of port-starboard ambiguity for tracking, which means generating a ghost track of the target symmetrically displaced with respect to the heading of the array as Although most algorithms adopt a heuristic approach to address the aforementioned problem , the autX1 and Y1 are known by deploying the towed array at a specific place. The central computer adopts data fusion technologies to process the measurements and then the state and trajectory of the target can be estimated by the filtering algorithm. After obtaining the definite bearing information of the target, the unobservability of the target still exists for the absence of range information especially for the single tracking platform towing or hull mounted the sensor array in passive mode. Some papers focus on designing a proper maneuvering plan for the tracking platform. Nevertheless, in , the autMoreover, when a sensor array is used to obtain the bearing information, the quality of tracking is highly dependent on the relative position between the interest target and the array. A target at the broadside brings the highest accurate bearing information, while at the end-fire will cause poor bearing resolutions. Therefore, the authors in  propose The matched-field processing (MFP) method is also can be applied to the area of underwater tracking. MFP determines the position of a target based on matching the complex acoustic field observed by a sensor array with the replica of an acoustic field computed numerically according to the acoustic prorogation model . The mosIn this section, different tracking algorithms based on TASA are reviewed. The problem of estimating the state of a target is assumed to be two-dimensional in , which iThe development of microelectromechanical devices and wireless technologies leads to the emergence of inexpensive small sensors equipped with sensing, processing and communication capabilities . UWSNs iIn , a trackA distributed smart sensor scheduling method is proposed to save energy at the level of sensors in . Each noAmong these energy-efficient tracking algorithms, the common characteristic is that not all measurements obtained in UWSNs are adopted or not all sensors work in active mode, which will surely reduce the accuracy of tracking. In , the autSince UWSNs consist of numerous sensors, the topology of these sensors will also have a great effect on the tracking performance . InadequRecently, the complex network theory is employed to solve the topology control problem of UWSNs . Based oPrevious topology control strategies are focused on UWSNs with stationary nodes, while for mobile networks, the problem is converted into optimizing the trajectories of sensors. The authors in  investigThe success of  lies in In this section, algorithms based on different tracking instruments are reviewed. These algorithms are all oriented at or devoted to solving the inherent flaws of tracking instruments. For example, UWSNs have the limited resources, therefore, considerable papers are focused on the limitation. To make readers easier to select the appropriate tracking instrument, we compare these papers in the aspect of precision, complexity, and cost of tracking based on different instruments, as well as the strength and weakness of the corresponding tracking instrument in According to the working mode of tracking sensors, tracking algorithms can be categorized into passive tracking and activity tracking. In the former, the tracker can only estimate the state of the target by the signal directly emitted from the target. In general, the obtained measurement is the relative bearing of the target to the tracker. While in the latter, the extra range information about the target can be acquired by the time of arrival (TOA) or time difference of arrival (TDOA) because these echoes reflected from the target are produced by the tracker. In other words, active tracking contains both transmitters and receivers while the passive tracking only includes receivers. In this section, algorithms based on different tracking mode are introduce and compared in tracking precision. The technology and measurements adopted in every algorithm are also summarized.The problem of tracking using passive measurements can be formulated as bearings-only tracking (BOT) which is a technology of determining the state of a target solely through measurements obtained from the signals originated from the target. Due to the inherent nonlinearity between the passive measurements and the state of the target, the design of a reliable and robust algorithm for BOT is still a challenge.In , since tThe passively acquired bearing measurements of the targets are often corrupted by noise. If these bearing or azimuth measurements are directly used to compute the position of the target , even smThe tracking performance can be improved by a higher order of pre-processor; however, it is at the cost of bringing the extra computation complexity and time. The optimal number of the order is left for future work.The BOT has the problem of unobservability before the single observing platform making a maneuvering. Like the work in  which elThe BOT problem existing in most passive tracking scenarios poses a great challenge in multi-target tracking and trace across processing . To addrRecently, measurements in passive tracking are not limited to bearing measurements anymore, and it can contain the time-delay measurement obtained by hearing the emitted signals arriving at different sensors as  shows. HUnknown environmental factors such as water depth, salinity, and currents pose great challenges for underwater target tracking . FurtherThe extra range information about the target is obtained by using multiple detecting platforms in ,75 or utThe tracking algorithms based on active tracking are aimed at estimating the state of the target according to the bearings and range information provided by the echoes from the target, and the echoes are originated from the system itself. Therefore, systems of active tracking contain transmitters and receivers. However, systems containing active sources have poor governance in anti-submarine warfare (ASW) due to the concealment. The position of the target is also easily obtained because of the available range information provided by active measurements. Therefore, the tracking algorithm based on active measurements is not the attractive research center of the underwater tracking area, especially in their applications in ASW. There are few papers researching the active tracking.In , a multiIn , a bistaSE and SL denote the strength of the signal received by the receiver and that transmitted by the transmitter respectively. eL represents the level of noise out of beam-former and nNrd is related to the ability of receivers to recognize noise. TL1 and TL2 represent the transmission loss from the transmitter to the target and that from the target to the receiver respectively. The range information is implicit in the transmission loss TL1 and TL2:In Equation (12), In , the autLike , the autReferences ,81 shareIn this section, various algorithms based on tracking mode (passive and active) are introduced in detail. Now, we compare them in the aspect of tracking precision in According to the tracking instrument and tracking mode, researchers have proposed numerous algorithms to improve the tracking accuracy and stability. However, other optimization methods have also been investigated for further improvement. Here, we take the filtering techniques, arithmetic average, and Sage-Husa model as the tracking optimization methods driven by the noise. The filtering techniques such as KF, EKF, UKF, and PF are used to estimate the state of the target and decrease the interference of noise on the tracking performance. That’s why we take the filtering techniques as the tracking optimization methods. The sensor scheduling strategies and quantized methods are the subcategories of the tracking optimization methods driven by the limited source.k. The estimation of The filter algorithm plays an important role in the tracking process for reducing the noise interference. In most tracking problems, the target is usually described by the state space model which includes the state and observation equation. Assuming KF: It is a recursive estimation method based on the state space model, which is aimed at producing estimates with high accuracy by a set of low-level and redundant measurements. However, KF is only suitable for tracking the target with linear motion and moving in the environment white Gaussian noise. Therefore, EKF and UKF, variations of KF, are developed for solving the nonlinear problem.The algorithm named 3DUTT is employed to determine the location of the target with the trilateration in . HoweverSince bearing measurements have a nonlinear relationship with the state of the target, vast literature considers adopting EKF and PF in some bearing-only tracking cases ,85,86. HThe existing range-based tracking algorithms usually locate the target by the distance to some sensing nodes, and the distance is obtained by multiplying the speed of the acoustic wave by the traveling time. However, the sound speed is not constant in underwater environments, which results in the range-based tracking algorithms having poor tracking performance. To address the aforementioned problem, an isogradient sound speed profile (SSP) is adopted in  to formuAn adaptive KF is proposed for tracking underwater maneuvering target in . The algBased on the concept that the collective estimation is better than the single estimation, a novel tracking approach based on UKF is proposed for BOT problem in , which iConsidering the complexity of PF, the authors in  address PF: A two-stage PF-based technique is proposed for tracking multi-target based on passive tracking in [cking in . CompareFor the problem of tracking targets with weak signals, a tracking algorithm is proposed for underwater targets by combining PF with track-before-detect which is named as PF-TBD in . The metThere are some papers proposing PF-based tracking algorithms for WSNs ,92. The Tracking underwater targets with video sequences is a great challenge due to the complex background. A new algorithm combining the real-time of Mean Shift and the robustness of PF is proposed in . The traFrom the above introduction of various tracking algorithms based on different filtering selections, we know that the EKF, UKF, and PF are commonly used filters in underwater target tracking because the target model of underwater targets is usually nonlinear and the noise is non-Gaussian. By analyzing data collected from the looking forward sonar, the authors in  compare Because of the complexity of the marine environment, the acquired measurements are usually corrupted seriously by noise, and the measuring error may result in large tracking error even employing filtering techniques. In , a novelZ(1), Z(2) and Z(3) denote the measurements acquired at the time instant 1, 2 and 3 respectively. The corresponding pre-processing result is represented by Z′(1), Z′(2) and Z′(3). Z1p(1) and Z1p(2) denote the 1-step predictor measurement of Z(1) and Z(2) respectively: The detailed computation process can be seen in Equation (15), where Z1p(1) and Z1p(2) in Equation (15) can be computed by taking an average of one-step differences of previous N measurements as follows:N can be chosen according to the real application. In Equation (16), the negative index measurements refer to the measurements stored before the start of the algorithm.The 1-step predictor measurement Traditional arithmetic average as previously mentioned is not applied to the time-varying system because the coefficient is same. In , a statiIn general, underwater target tracking is realized by multiple sensors in which case the communication issues are inevitable. Due to the limited communication bandwidth in underwater channel, the amount of transmission message is restricted. The most effective way to reduce the length of communication message is quantization, which means compressing the raw measurements or state estimation into several bits of data. However, the quantized procedure degrades the performance of tracking accuracy for the loss of information. Recently, some studies are focused on addressing the problem of improving tracking performance with optimal quantization. The acoustic sensors used for underwater target tracking are equipped with limited energy and communication capability, which motivated the presence of effective sensor scheduling strategies. Tracking optimization means not only improving tracking accuracy but also considering the source constraints. Therefore, source-driven optimization methods including sensor scheduling strategies and quantized methods are presented here.Due to the limited energy source of sensors, effective sensor scheduling strategies are important for robust tracking by avoiding node failure incurred by energy exhaustion. An adaptive scheduling strategy is presented to increase the energy efficiency of each sensor node in . HoweverTo reduce the energy, only part of sensors need to participate into tracking. In general, in 3D underwater environment, four sensors can determine the position of one target. Therefore, some researches are focused on designing the sensor scheduling strategies which can select the most informative sensors from the candidate ones located within the sensing region of the target. In , only 60Although the raw measurements can provide more accurate information about the target, the limited communication bandwidth and energy make quantized measurements preferable in underwater environment. There is a large amount of papers focus on quantizer design in WSNs ,69. On tIn this section, we present a comparison between all algorithms mentioned before and the challenges in underwater target tracking, including low target detection probability, sound speed variation, eliminating PS ambiguity as well as the balance between tracking accuracy and energy consumption are illustrated. Countermeasures for the mentioned challenges are also presented. The lessons learned about designing the underwater acoustic tracking algorithms also are introduced for readers’ reference.Underwater target tracking plays a crucial part in modern civil and military systems. Therefore, numerous research results have been reported. Due to the special characteristics of the marine environment, the acoustic wave becomes the only appropriate carrier to realize underwater target tracking. In this paper, we make a comprehensive study of the underwater acoustic target tracking algorithms and propose a new taxonomy based on the methods used, namely, instrument-assisted method, mode-based method, and tracking optimization method. The varieties of underwater target tracking algorithms introduced in Different from the tables in Due to the special and complex underwater environment characteristics, the acoustic wave becomes the only suitable carrier for realizing underwater target tracking. However, the problem of acoustic communication and the complexity of the marine environment pose great challenges to target tracking:The low target detection probability: Due to the complexity of the underwater environment, tracking using imaging sensors has the problem of low contrast and visibility which even makes it hard for humans to detect the presence of a target. Tracking using acoustic echoes also has difficulty in detecting due to the attenuation of the acoustic waves.Sound speed variation: Many tracking algorithms based on distance measurements obtained by TDOA or TOA assume that the acoustic waves are transmitted at a constant speed in the marine environment, which is impractical and results in large tracking errors, especially in trilateration. Therefore, how to construct a stable and accurate sound speed model is a challenge.PS ambiguity: When using a sensor array to realize underwater target tracking, PS ambiguity appears due to the structural symmetry of the array. Because the ambiguity makes tracking algorithms more complicated and results in noticeable performance degradation, the process of removing such artifacts is dispensable.The balance between tracking accuracy and energy consumption: If USWNs are exploited for tracking, the energy consumption is a key factor. However, as Improve low target detection probability: In most tracking systems, the target is always at a large distance relative to the detecting sensors. With the development of acoustic concealment technology, detecting and tracking targets with low SNR has become an urgent problem. Compared with detect-before-track (DBT), TBD is the feasible technology to solve the problem [ problem . Aimed a problem , which t problem . In addi problem  to realiSound speed model: The undefined parameters in water environments such as depth, temperature, and salinity variations have an obvious impact on the sound speed change. The relationship between sound speed variation and these factors is complicated. The authors in [thors in  adopt onthors in  to constthors in , which ithors in  have demthors in .Eliminate PS ambiguity: There are some papers focused on addressing this problem using a multiline array, e.g., twin array and triplet array [et array ,111. Nevet array  propose Keep a balance between energy consumption and tracking accuracy: The authors in [thors in ,66 consiDesigning effective underwater target tracking algorithms should take many factors into account especially the effect of the marine environment. Therefore, many additional measures should be employed. Here we list some lessons based.The medium used in underwater target tracking is acoustic waves; however, the tracking instruments can be varied, as Due to the complexity of the marine environment, errors are inevitable in tracking results. Designing a calibration method and choosing proper filter algorithms can reduce the error. The authors in  design aWith the increasing interest in the exploration of marine resources, underwater target tracking technology has aroused wide attention. Due to the specificity and complexity of the marine environment, acoustic waves have become the most widely used medium for tracking underwater targets. Numerous research papers have reported their tracking results. In this paper, we survey many acoustic tracking algorithms based on a new taxonomy, namely, instrument-assisted methods, mode-based methods, and tracking optimization methods. The contributions of this paper include: (1) It is the first review article about underwater acoustic target tracking; (2) the relevant knowledge is clarified in detail, which makes it easier for the readers to understand the area of underwater target tracking; (3) comprehensive comparisons have been made to make the readers quickly find a suitable method to improve tracking performance; (4) to compensate for the existing shortcomings, review papers are only centered on target tracking based on WSNs.Multiple target tracking. Few of the algorithms previously mentioned in Enhancing measurement accuracy of passive tracking. In ASW applications, the target of interest is usually far from the tracker; the tracker can only passively listen to the signal radiated from the target for concealment. Furthermore, the development of silent technologies makes it hard to receive signals from target for passive tracking. Even if the signal is detected successfully, if the passive tracker has a low accuracy when measuring bearing information about the target, the tracking performance will degenerate significantly. (3) Data fusion. The tracking system will tend to the multi-state system. Therefore, how to make an effective fusion of homogeneous or heterogeneous measurements information to achieve more robust and accurate tracking will be a research hot issue. (4) Motion strategies for mobile sensors. Underwater target tracking is usually realized in large scale areas. Sensors with mobility outperform static sensors. Considering the influence of topology, how to design effective coordinate motion strategies for sensor is a hot issue. On this basis, the adaptive motion strategies based on local information can be developed. (5) Quantized methods. As mentioned in The future work in this area can focus on several aspects: (1)