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This paper presents a strategy called the alternating iterative minimization method (AIMM), aimed at enhancing the precision of direction of arrival (DOA) estimation when utilizing an acoustic vector sensor array (AVSA) with unknown swing deviation elements (SDEs). The AVSA model with unknown SDEs is formulated by incorporating the swing deviation parameter. Later, to estimate the swing deviation matrix (SDM) and the sparse signal power by using the alternating iteration method, the auxiliary cost functions with respect to SDM and the sparse signal power are formulated based on the regularized weighted least squares (RWLS) and regularized covariance matrix fitting (RCMF) criteria. Furthermore, their analytical expressions have also been quantified. In order to mitigate the effect of unknown SDEs on the accuracy of DOA estimation, any sub-time segment (STS) in the dataset is selected as the reference to convert the received data of different STS into the reference STS using the estimated SDM. The simulation and experimental outcomes conclusively represent the effectiveness of the suggested TSIM approach using AVSA in handling unknown SDEs. [ABSTRACT FROM AUTHOR]

In underwater environments, the accurate estimation of state features for passive object is a critical aspect of various applications, including underwater robotics, surveillance, and environmental monitoring. This study presents an innovative neuro computing approach for instantaneous state features reckoning of passive marine object following dynamic Markov chains. This paper introduces the potential of intelligent Bayesian regularization backpropagation neuro computing (IBRBNC) for the precise estimation of state features of underwater passive object. The proposed paradigm combines the power of artificial neural network with Bayesian regularization technique to address the challenges associated with noisy and limited underwater sensor data. The IBRBNC paradigm leverages deep neural networks with a focus on backpropagation to model complex relationships in the underwater environment. Furthermore, Bayesian regularization is introduced to incorporate prior knowledge and mitigate overfitting, enhancing the model's robustness and generalization capabilities. This dual approach results in a highly adaptive and intelligent system capable of accurately estimating the state features of passive object in real-time. To evaluate the efficacy of this intelligent computing approach, a controlled supervised maneuvering trajectory for underwater passive object is constructed. Real-time estimations of location, velocity, and turn rate for dynamic target are scrutinized across five distinct scenarios by varying the Gaussian observed noise's standard deviation, aiming to minimize mean square errors (MSEs) between real and estimated values. The effectiveness of the proposed IBRBNC paradigm is demonstrated through extensive simulations and experimental trials. Results showcase its superiority over traditional nonlinear filtering methods like interacting multiple model extended Kalman filter (IMMEKF) and interacting multiple model unscented Kalman filter (IMMUKF), especially in the presence of noise, incomplete measurements and sparse data. [ABSTRACT FROM AUTHOR]

This study proposes a novel application of neural computing based on deep learning for the real-time prediction of motion parameters for underwater maneuvering object. The intelligent strategy utilizes the capabilities of Scaled Conjugate Gradient Neural Intelligence (SCGNI) to estimate the dynamics of underwater target that adhere to discrete-time Markov chain. Following a state-space methodology in which target dynamics are combined with noisy passive bearings, nonlinear probabilistic computational algorithms are frequently used for motion parameters prediction applications in underwater acoustics. The precision and robustness of SCGNI are examined here for effective motion parameter prediction of a highly dynamic Markov chain underwater passive vehicle. For investigating the effectiveness of the soft computing strategy, a steady supervised maneuvering route of undersea passive object is designed. In the framework of bearings-only tracking technology, system modeling for parameters prediction is built, and the effectiveness of the SCGNI is examined in ideal and cluttered marine atmospheres simultaneously. The real-time location, velocity, and turn rate of dynamic target are analyzed for five distinct scenarios by varying the standard deviation of white Gaussian observed noise in the context of mean square error (MSE) between real and estimated values. For the given motion parameters prediction problem, sufficient Monte Carlo simulation results support SCGNI's superiority over typical generalized pseudo-Bayesian filtering strategies such as Interacting Multiple Model Extended Kalman Filter (IMMEKF) and Interacting Multiple Model Unscented Kalman Filter (IMMUKF). [ABSTRACT FROM AUTHOR]

Recently, many direction-of-arrival (DOA) estimation techniques based on sparse representation have been proposed. However, these techniques often suffer from performance degradation issues in the presence of impulsive noise. This paper aims to overcome this challenge in conventional sparse-based techniques on an acoustic vector sensor array (AVSA). Firstly, to remove high outliers from the array output data, the output information of the AVSA is weighted by using the infinite norm. To further suppress outliers, a p-order cost function is formulated by extending the Frobenius norm to lower order, and then the expression of the signal power is quantified. Lastly, the DOA is approximated on the signal power by a spectral peak search mechanism. DOA estimation results based on Monte Carlo simulations validate the accuracy and robustness of the proposed techniques herein compared to the current, available methods in the context of intense impulsive noise, low generalized signal–to–noise ratio (GSNR), and a smaller number of snapshots. [ABSTRACT FROM AUTHOR]

To minimize the major decline in direction of arrival (DOA) estimation performance for an acoustic vector sensor array (AVSA) with the coexistence of axial deviation and non-uniform noise, a two-step iterative minimization (TSIM) method is proposed in this paper. Initially, the axial deviation measurement model of an AVSA is formulated by incorporating the disturbance parameter into the signal model, and then a novel AVSA manifold matrix is defined to estimate the sparse signal power and noise power mutually. After that, to mitigate a joint optimization problem to achieve the sparse signal power, the noise power and the axial deviation matrix, two auxiliary cost functions, are presented based on the covariance matrix fitting (CMF) criterion and the weighted least squares (WLS), respectively. Furthermore, their analytical expressions are also derived. In addition, to further enhance their prediction accuracy, the estimated axial deviation matrix is modified based on its specific structural properties. The simulation results demonstrate the superiority and robustness of the proposed technique over several conventional algorithms. [ABSTRACT FROM AUTHOR]

Compared with the traditional tracking problem, the underwater 3‐D passive manoeuvring target tracking faces the following challenging problems: (1) Since the signal propagation delay is varying and unknown, the relationship between the two adjacent target states is hard to describe; (2) limited by the underwater environment, it is more difficult to establish a target manoeuvring motion model; (3) the propagation speed of the underwater acoustic signal varies with the depth, and the propagation path will be curved instead of straight. Various parameters including signal propagation delay, target pitch angle and receiving frequency measured by the observer cannot be calculated as usual. In this paper, we improved a 3‐D constant turn (3D‐CT) model to match the underwater target motion. For the problems (1) and (3), this paper proposes a novel interacting multiple model underwater Gauss‐Helmert unscented Kalman filter (IMM‐UGHUKF) with isogradient sound velocity profile, which analytically describes the relationship between the state to be estimated and the passive measurement. This method augments the unknown signal emission time into the state with implicit equations, and transits the state by the Gauss–Helmert model. Simulation tests have been carried out, and the results show that IMM‐UGHUKF can significantly reduce the estimation error compared with other approaches. [ABSTRACT FROM AUTHOR]

Developing the parameter estimation, particularly direction of arrival (DOA), utilizing the swarming intelligence-based flower pollination algorithm (FPA) is considered an optimistic solution. Therefore, in this paper, the features of FPA are applied for viable DOA in the case of several robust underwater scenarios. Moreover, acoustic waves impinging from the far-field multitarget are evaluated using the different number of hydrophones of uniform linear array (ULA). The measuring parameters like robustness against noise and element quantity, estimation accuracy, computation complexity, various numbers of hydrophones, variability analysis, frequency distribution and cumulative distribution function of root mean square error (RMSE), and resolution ability are applied for analyzing the performance of the proposed model with additive white Gaussian noise (AWGN). For this purpose, particle swarm optimization (PSO), minimum variance distortion-less response (MVDR), multiple signal classification (MUSIC), and estimation of signal parameter via rotational invariance technique (ESPRIT) standard counterparts are employed along with Crammer–Rao bound (CRB) to improve the worth of the proposed setup further. The proposed scheme for estimating the DOA generates efficient outcomes compared to the state-of-the-art algorithms over the Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

The major advantage of the passive multiple-target tracking is that the sonars do not emit signals and thus they can remain covert, which will reduce the risk of being attacked. However, the nonlinearity of the passive Doppler and bearing measurements, the range unobservability problem, and the measurement to target data association uncertainty make the passive multiple-target tracking problem challenging. To deal with the target to measurement data association uncertainty problem from multiple sensors, this paper proposed a batch recursive extended Rauch-Tung-Striebel smoother- (RTSS-) based probabilistic multiple hypothesis tracker (PMHT) algorithm, which can effectively handle a large number of passive measurements including clutters. The recursive extended RTSS which consists of a forward filter and a backward smoothing is used to deal with the nonlinear Doppler and bearing measurements. The target range unobservability problem is avoided due to using multiple passive sensors. The simulation results show that the proposed algorithm works well in a passive multiple-target tracking system under dense clutter environment, and its computing cost is low. [ABSTRACT FROM AUTHOR]

In this study, an application of deep learning-based neural computing is proposed for efficient real-time state estimation of the Markov chain underwater maneuvering object. The designed intelligent strategy is exploiting the strength of nonlinear autoregressive with an exogenous input (NARX) network model, which has the capability for estimating the dynamics of the systems that follow the discrete-time Markov chain. Nonlinear Bayesian filtering techniques are often applied for underwater maneuvering state estimation applications by following state-space methodology. The robustness and precision of NARX neural network are efficiently investigated for accurate state prediction of the passive Markov chain highly maneuvering underwater target. A continuous coordinated turning trajectory of an underwater maneuvering object is modeled for analyzing the performance of the neural computing paradigm. State estimation modeling is developed in the context of bearings only tracking technology in which the efficiency of the NARX neural network is investigated for ideal and complex ocean environments. Real-time position and velocity of maneuvering object are computed for five different cases by varying standard deviations of white Gaussian measured noise. Sufficient Monte Carlo simulation results validate the competence of NARX neural computing over conventional generalized pseudo-Bayesian filtering algorithms like an interacting multiple model extended Kalman filter and an interacting multiple model unscented Kalman filter. [ABSTRACT FROM AUTHOR]

A major advantage of the use of passive sonar in the tracking multiple underwater targets is that they can be kept covert, which reduces the risk of being attacked. However, the nonlinearity of the passive Doppler and bearing measurements, the range unobservability problem, and the complexity of data association between measurements and targets make the problem of underwater passive multiple target tracking challenging. To deal with these problems, the cardinalized probability hypothesis density (CPHD) recursion, which is based on Bayesian information theory, is developed to handle the data association uncertainty, and to acquire existing targets' numbers and states (e.g., position and velocity). The key idea of the CPHD recursion is to simultaneously estimate the targets' intensity and the probability distribution of the number of targets. The CPHD recursion is the first moment approximation of the Bayesian multiple targets filter, which avoids the data association procedure between the targets and measurements including clutter. The Bayesian-filter-based extended Kalman filter (EKF) is applied to deal with the nonlinear bearing and Doppler measurements. The experimental results show that the EKF-based CPHD recursion works well in the underwater passive multiple target tracking system in cluttered and noisy environments. [ABSTRACT FROM AUTHOR]

In this study, an intelligent computing paradigm built on a nonlinear autoregressive exogenous (NARX) feedback neural network model with the strength of deep learning is presented for accurate state estimation of an underwater passive target. In underwater scenarios, real-time motion parameters of passive objects are usually extracted with nonlinear filtering techniques. In filtering algorithms, nonlinear passive measurements are associated with linear kinetics of the target, governing by state space methodology. To improve tracking accuracy, effective feature estimation and minimizing position error of dynamic passive objects, the strength of NARX based supervised learning is exploited. Dynamic artificial neural networks, which contain tapped delay lines, are suitable for predicting the future state of the underwater passive object. Neural networks-based intelligence computing is effectively applied for estimating the real-time actual state of a passive moving object, which follows a semi-curved path. Performance analysis of NARX based neural networks is evaluated for six different scenarios of standard deviation of white Gaussian measurement noise by following bearings only tracking phenomena. Root mean square error between estimated and real position of the passive target in rectangular coordinates is computed for evaluating the worth of the proposed NARX feedback neural network scheme. The Monte Carlo simulations are conducted and the results certify the capability of the intelligence computing over conventional nonlinear filtering algorithms such as spherical radial cubature Kalman filter and unscented Kalman filter for given state estimation model. [ABSTRACT FROM AUTHOR]

The traditional target tracking is a process of estimating the state of a moving target using measurement information obtained by sensors. However, underwater passive acoustic target tracking will confront further challenges, among which the system incomplete observability and time delay caused by the signal propagation create a great impact on tracking performance. Passive acoustic sensors cannot accurately obtain the target range information. The introduction of Doppler frequency measurement can improve the system observability performance; signal time delay cannot be ignored in underwater environments. It varies with time, which has a continuous negative impact on the tracking accuracy. In this paper, the Gauss–Helmert model is introduced to solve this problem by expanding the unknown signal emission time as an unknown variable to the state. This model allows the existence of the previous state and current state at the same time, while handling the implicit equations. To improve the algorithm accuracy, this paper further takes advantage of the estimated state and covariance for the second stage iteration and propose the Gauss–Helmert iterated Unscented Kalman filter under a three-dimensional environment. The simulation shows that the proposed method in this paper shows superior estimation accuracy and more stable performance compared with other filtering algorithms in underwater environments. [ABSTRACT FROM AUTHOR]

In this paper, an application of spherical radial cubature Bayesian filtering and smoothing algorithms is presented to solve a typical underwater bearings only passive target tracking problem effectively. Generally, passive target tracking problems in the ocean environment are represented with the state-space model having linear system dynamics merged with nonlinear passive measurements, and the system is analyzed with nonlinear filtering algorithms. In the present scheme, an application of spherical radial cubature Bayesian filtering and smoothing is efficiently investigated for accurate state estimation of a far-field moving target in complex ocean environments. The nonlinear model of a Kalman filter based on a Spherical Radial Cubature Kalman Filter (SRCKF) and discrete-time Kalman smoother known as a Spherical Radial Cubature Rauch–Tung–Striebel (SRCRTS) smoother are applied for tracking the semi-curved and curved trajectory of a moving object. The worth of spherical radial cubature Bayesian filtering and smoothing algorithms is validated by comparing with a conventional Unscented Kalman Filter (UKF) and an Unscented Rauch–Tung–Striebel (URTS) smoother. Performance analysis of these techniques is performed for white Gaussian measured noise variations, which is a significant factor in passive target tracking, while the Bearings Only Tracking (BOT) technology is used for modeling of a passive target tracking framework. Simulations based experiments are executed for obtaining least Root Mean Square Error (RMSE) among a true and estimated position of a moving target at every time instant in Cartesian coordinates. Numerical results endorsed the validation of SRCKF and SRCRTS smoothers with better convergence and accuracy rates than that of UKF and URTS for each scenario of passive target tracking problem. [ABSTRACT FROM AUTHOR]

Extracting useful features from ship-radiated noise can improve the performance of passive sonar. The entropy feature is an important supplement to existing technologies for ship classification. However, the existing entropy feature extraction methods for ship-radiated noise are less reliable under noisy conditions because they lack noise reduction procedures or are single-scale based. In order to simultaneously solve these problems, a new feature extraction method is proposed based on improved complementary ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), normalized mutual information (norMI), and multiscale improved permutation entropy (MIPE). Firstly, the ICEEMDAN is utilized to obtain a group of intrinsic mode functions (IMFs) from ship-radiated noise. The noise reduction process is then conducted by identifying and eliminating the noise IMFs. Next, the norMI and MIPE of the signal-dominant IMFs are calculated, respectively; and the norMI is used to weigh the corresponding MIPE result. The multi-scale entropy feature is finally defined as the sum of the weighted MIPE results. Experimental results show that the recognition rate of the proposed method achieves 90.67% and 83%, respectively, under noise free and 5 dB conditions, which is much higher than existing entropy feature extraction algorithms. Hence, the proposed method is more reliable and suitable for feature extraction of ship-radiated noise in practice. [ABSTRACT FROM AUTHOR]