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Sun D, Zhang Y, Teng T, Gao L. Underwater Doppler-bearing maneuvering target motion analysis based on joint estimated adaptive unscented Kalman filter. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2023; 154:2843-2857. [PMID: 37930179 DOI: 10.1121/10.0022323] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2023] [Accepted: 10/16/2023] [Indexed: 11/07/2023]
Abstract
Noncooperative maneuvering target motion analysis is one of the challenging tasks in the field of underwater target localization and tracking for passive sonar. Underwater noncooperative targets often perform various maneuvers, and the targets are commonly modeled as a combination of constant-velocity models and coordinate-turn models with unknown turning rates. Traditional algorithms for Doppler-bearing target motion analysis are incapable of processing noncooperative maneuvering targets because the algorithms rely on a priori information of the turning rate and the center frequency. To address these shortcomings, this paper proposes the joint estimated adaptive unscented Kalman filter (JE-AUKF) algorithm. The JE-AUKF places the center frequency and turning rate into the state vector and constructs a time-varying state model that self-adapts to a maneuvering target. The JE-AUKF also introduces a time-varying fading factor into the process noise covariance matrix to improve the tracking performance. Simulations and sea trials are conducted to compare the performance of the JE-AUKF with the iterative unscented Kalman filter, the interacting multiple model-unscented Kalman filter, the interacting multiple model-iterative unscented Kalman filter, and the interacting multiple model-joint estimated unscented Kalman filter. The result shows that the JE-AUKF achieves better tracking performance for noncooperative maneuvering targets.
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Affiliation(s)
- Dajun Sun
- National Key Laboratory of Underwater Acoustic Technology, Harbin Engineering University, Harbin 150001, China
| | - Yiao Zhang
- National Key Laboratory of Underwater Acoustic Technology, Harbin Engineering University, Harbin 150001, China
| | - Tingting Teng
- National Key Laboratory of Underwater Acoustic Technology, Harbin Engineering University, Harbin 150001, China
| | - Linsen Gao
- National Key Laboratory of Underwater Acoustic Technology, Harbin Engineering University, Harbin 150001, China
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2
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Kim J. Three-Dimensional Tracking of a Target under Angle-Frequency Measurements with Multiple Frequency Lines. SENSORS (BASEL, SWITZERLAND) 2023; 23:5705. [PMID: 37420870 DOI: 10.3390/s23125705] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2023] [Revised: 06/14/2023] [Accepted: 06/16/2023] [Indexed: 07/09/2023]
Abstract
This article considers tracking a constant-velocity underwater target, which emits sound with distinct frequency lines. By analyzing the target's azimuth, elevation and multiple frequency lines, the ownship can estimate the target's position and (constant) velocity. In our paper, this tracking problem is called the 3D Angle-Frequency Target Motion Analysis (AFTMA) problem. We consider the case where some frequency lines disappear and appear occasionally. Instead of tracking every frequency line, this paper proposes to estimate the average emitting frequency by setting the average frequency as the state vector in the filter. As the frequency measurements are averaged, the measurement noise decreases. In the case where we use the average frequency line as our filter state, both the computational load and the root mean square error (RMSE) decrease, compared to the case where we track every frequency line one by one. As far as we know, our manuscript is unique in addressing 3D AFTMA problems, such that an ownship can track an underwater target while measuring the target's sound with multiple frequency lines. The performance of the proposed 3D AFTMA filter is demonstrated utilizing MATLAB simulations.
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Affiliation(s)
- Jonghoek Kim
- System Engineering Department, Sejong University, Seoul 05006, Republic of Korea
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3
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Xue L, Zeng X, Jin A. A Novel Deep-Learning Method with Channel Attention Mechanism for Underwater Target Recognition. SENSORS (BASEL, SWITZERLAND) 2022; 22:5492. [PMID: 35897996 PMCID: PMC9331384 DOI: 10.3390/s22155492] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/06/2022] [Revised: 07/20/2022] [Accepted: 07/21/2022] [Indexed: 06/15/2023]
Abstract
The core of underwater acoustic recognition is to extract the spectral features of targets. The running speed and track of the targets usually result in a Doppler shift, which poses significant challenges for recognizing targets with different Doppler frequencies. This paper proposes deep learning with a channel attention mechanism approach for underwater acoustic recognition. It is based on three crucial designs. Feature structures can obtain high-dimensional underwater acoustic data. The feature extraction model is the most important. First, we develop a ResNet to extract the deep abstraction spectral features of the targets. Then, the channel attention mechanism is introduced in the camResNet to enhance the energy of stable spectral features of residual convolution. This is conducive to subtly represent the inherent characteristics of the targets. Moreover, a feature classification approach based on one-dimensional convolution is applied to recognize targets. We evaluate our approach on challenging data containing four kinds of underwater acoustic targets with different working conditions. Our experiments show that the proposed approach achieves the best recognition accuracy (98.2%) compared with the other approaches. Moreover, the proposed approach is better than the ResNet with a widely used channel attention mechanism for data with different working conditions.
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Kumar K, Bhaumik S, Arulampalam S. Tracking an Underwater Object with Unknown Sensor Noise Covariance Using Orthogonal Polynomial Filters. SENSORS 2022; 22:s22134970. [PMID: 35808465 PMCID: PMC9269813 DOI: 10.3390/s22134970] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/10/2022] [Revised: 06/19/2022] [Accepted: 06/28/2022] [Indexed: 11/16/2022]
Abstract
In this manuscript, an underwater target tracking problem with passive sensors is considered. The measurements used to track the target trajectories are (i) only bearing angles, and (ii) Doppler-shifted frequencies and bearing angles. Measurement noise is assumed to follow a zero mean Gaussian probability density function with unknown noise covariance. A method is developed which can estimate the position and velocity of the target along with the unknown measurement noise covariance at each time step. The proposed estimator linearises the nonlinear measurement using an orthogonal polynomial of first order, and the coefficients of the polynomial are evaluated using numerical integration. The unknown sensor noise covariance is estimated online from residual measurements. Compared to available adaptive sigma point filters, it is free from the Cholesky decomposition error. The developed method is applied to two underwater tracking scenarios which consider a nearly constant velocity target. The filter’s efficacy is evaluated using (i) root mean square error (RMSE), (ii) percentage of track loss, (iii) normalised (state) estimation error squared (NEES), (iv) bias norm, and (v) floating point operations (flops) count. From the simulation results, it is observed that the proposed method tracks the target in both scenarios, even for the unknown and time-varying measurement noise covariance case. Furthermore, the tracking accuracy increases with the incorporation of Doppler frequency measurements. The performance of the proposed method is comparable to the adaptive deterministic support point filters, with the advantage of a considerably reduced flops requirement.
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Affiliation(s)
- Kundan Kumar
- Department of Electrical Engineering, Indian Institute of Technology Patna, Patna 801103, India; (K.K.); (S.B.)
| | - Shovan Bhaumik
- Department of Electrical Engineering, Indian Institute of Technology Patna, Patna 801103, India; (K.K.); (S.B.)
| | - Sanjeev Arulampalam
- Maritime Division, Defence Science and Technology (DST) Group, Edinburgh, SA 5111, Australia
- Faculty of Engineering, Computer & Mathematical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia
- Correspondence:
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5
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Kim J. Locating an Underwater Target Using Angle-Only Measurements of Heterogeneous Sonobuoys Sensors with Low Accuracy. SENSORS 2022; 22:s22103914. [PMID: 35632325 PMCID: PMC9146392 DOI: 10.3390/s22103914] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/19/2022] [Revised: 05/11/2022] [Accepted: 05/20/2022] [Indexed: 12/04/2022]
Abstract
This paper considers locating an underwater target, where many sonobuoys are positioned to measure the bearing of the target’s sound. A sonobuoy has very low bearing accuracy, such as 10 degrees. In practice, we can use multiple heterogeneous sonobuoys, such that the variance of a sensor noise may be different from that of another sensor. In addition, the maximum sensing range of a sensor may be different from that of another sensor. The true target must exist within the sensing range of a sensor if the sensor detects the bearing of the target. In order to estimate the target position based on bearings-only measurements with low accuracy, this paper introduces a novel target localization approach based on multiple Virtual Measurement Sets (VMS). Here, each VMS is derived considering the bearing measurement noise of each sonar sensor. As far as we know, this paper is novel in locating a target’s 2D position based on heterogeneous sonobuoy sensors with low accuracy, considering the maximum sensing range of a sensor. The superiority (considering both time efficiency and location accuracy) of the proposed localization is verified by comparing it with other state-of-the-art localization methods using computer simulations.
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Affiliation(s)
- Jonghoek Kim
- Electronic and Electrical Department, Sungkyunkwan University, Suwon 16419, Korea
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6
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Kita KR, Randeni S, DiBiaso D, Schmidt H. Passive acoustic tracking of an unmanned underwater vehicle using bearing-Doppler-speed measurements. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2022; 151:1311. [PMID: 35232098 DOI: 10.1121/10.0009568] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2021] [Accepted: 01/24/2022] [Indexed: 06/14/2023]
Abstract
Tracking unmanned underwater vehicles (UUVs) in the presence of shipping traffic is a critical task for passive acoustic harbor security systems. In general, the vessels can be tracked by their unique acoustic signature caused by machinery vibration and cavitation noise. However, cavitation noise of UUVs is quiet relative to that of ships. Furthermore, tracking a target with bearing-only measurements requires the observing platform to maneuver. In this work, it is demonstrated that it is possible to passively track an UUV from its high-frequency motor noise using a stationary array in a shallow-water experiment with passing boats. The motor noise provides high signal-to-noise ratio measurements of the bearing, range rate, and speed, which we combined in an unscented Kalman filter to track the target. First, beamforming is applied to estimate the bearing. Next, the range rate is calculated from the Doppler effect on the motor noise. The propeller rotation rate can be estimated from the motor signature and converted to the speed using a pre-identified model of the robot. The bearing-Doppler-speed measurements outperformed the traditional bearing-Doppler target motion analysis: the bearing, bearing rate, range, and range rate accuracy improved by a factor of 2×, 16×, 3×, and 6×, respectively. Finally, the robustness of the tracking solution to an unknown vehicle model is evaluated.
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Affiliation(s)
- Kristen Railey Kita
- Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue 5-204, Cambridge, Massachusetts 02139, USA
| | - Supun Randeni
- Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue 5-204, Cambridge, Massachusetts 02139, USA
| | - Dino DiBiaso
- Systems Engineering, Draper, 555 Technology Square, Cambridge, Massachusetts 02139, USA
| | - Henrik Schmidt
- Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue 5-204, Cambridge, Massachusetts 02139, USA
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7
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Passive Tracking of Multiple Underwater Targets in Incomplete Detection and Clutter Environment. ENTROPY 2021; 23:e23081082. [PMID: 34441221 PMCID: PMC8391381 DOI: 10.3390/e23081082] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Revised: 07/22/2021] [Accepted: 08/17/2021] [Indexed: 11/16/2022]
Abstract
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.
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Adaptive Two-Step Bearing-Only Underwater Uncooperative Target Tracking with Uncertain Underwater Disturbances. ENTROPY 2021; 23:e23070907. [PMID: 34356448 PMCID: PMC8305256 DOI: 10.3390/e23070907] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/03/2021] [Revised: 06/30/2021] [Accepted: 07/14/2021] [Indexed: 11/17/2022]
Abstract
The bearing-only tracking of an underwater uncooperative target can protect maritime territories and allows for the utilization of sea resources. Considering the influences of an unknown underwater environment, this work aimed to estimate 2-D locations and velocities of an underwater target with uncertain underwater disturbances. In this paper, an adaptive two-step bearing-only underwater uncooperative target tracking filter (ATSF) for uncertain underwater disturbances is proposed. Considering the nonlinearities of the target’s kinematics and the bearing-only measurements, in addition to the uncertain noise caused by an unknown underwater environment, the proposed ATSF consists of two major components, namely, an online noise estimator and a robust extended two-step filter. First, using a modified Sage-Husa online noise estimator, the uncertain process and measurement noise are estimated at each tracking step. Then, by adopting an extended state and by using a robust negative matrix-correcting method in conjunction with a regularized Newton-Gauss iteration scheme, the current state of the underwater uncooperative target is estimated. Finally, the proposed ATSF was tested via simulations of a 2-D underwater uncooperative target tracking scenario. The Monte Carlo simulation results demonstrated the reliability and accuracy of the proposed ATSF in bearing-only underwater uncooperative tracking missions.
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Ali W, Khan WU, Raja MAZ, He Y, Li Y. Design of Nonlinear Autoregressive Exogenous Model Based Intelligence Computing for Efficient State Estimation of Underwater Passive Target. ENTROPY 2021; 23:e23050550. [PMID: 33947058 PMCID: PMC8146196 DOI: 10.3390/e23050550] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/01/2021] [Revised: 04/24/2021] [Accepted: 04/27/2021] [Indexed: 12/01/2022]
Abstract
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.
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Affiliation(s)
- Wasiq Ali
- School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China; (W.A.); (Y.L.)
- Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan
| | - Wasim Ullah Khan
- School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China
- Correspondence: (W.U.K.); (Y.H.)
| | - Muhammad Asif Zahoor Raja
- Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan;
| | - Yigang He
- School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China
- Correspondence: (W.U.K.); (Y.H.)
| | - Yaan Li
- School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China; (W.A.); (Y.L.)
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10
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Su J, Li Y, Ali W, Li X, Yu J. Underwater 3D Doppler-Angle Target Tracking with Signal Time Delay. SENSORS (BASEL, SWITZERLAND) 2020; 20:E3869. [PMID: 32664431 PMCID: PMC7412531 DOI: 10.3390/s20143869] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/28/2020] [Revised: 07/06/2020] [Accepted: 07/06/2020] [Indexed: 11/22/2022]
Abstract
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.
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Affiliation(s)
- Jun Su
- School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China; (J.S.); (W.A.); (J.Y.)
| | - Yaan Li
- School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China; (J.S.); (W.A.); (J.Y.)
| | - Wasiq Ali
- School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China; (J.S.); (W.A.); (J.Y.)
| | - Xiaohua Li
- Shaanxi Key Laboratory for Network Computing and Security Technology, School of Computer Science and Engineering, Xi’an University of Technology, Xi’an 710048, China;
| | - Jing Yu
- School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China; (J.S.); (W.A.); (J.Y.)
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11
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Shi J, Zhang Q, Tan W, Mao L, Huang L, Shi W. Underdetermined DOA Estimation for Wideband Signals via Focused Atomic Norm Minimization. ENTROPY 2020; 22:e22030359. [PMID: 33286133 PMCID: PMC7516832 DOI: 10.3390/e22030359] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/21/2020] [Revised: 03/17/2020] [Accepted: 03/17/2020] [Indexed: 11/16/2022]
Abstract
In underwater acoustic signal processing, direction of arrival (DOA) estimation can provide important information for target tracking and localization. To address underdetermined wideband signal processing in underwater passive detection system, this paper proposes a novel underdetermined wideband DOA estimation method equipped with the nested array (NA) using focused atomic norm minimization (ANM), where the signal source number detection is accomplished by information theory criteria. In the proposed DOA estimation method, especially, after vectoring the covariance matrix of each frequency bin, each corresponding obtained vector is focused into the predefined frequency bin by focused matrix. Then, the collected averaged vector is considered as virtual array model, whose steering vector exhibits the Vandermonde structure in terms of the obtained virtual array geometries. Further, the new covariance matrix is recovered based on ANM by semi-definite programming (SDP), which utilizes the information of the Toeplitz structure. Finally, the Root-MUSIC algorithm is applied to estimate the DOAs. Simulation results show that the proposed method outperforms other underdetermined DOA estimation methods based on information theory in term of higher estimation accuracy.
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Affiliation(s)
- Juan Shi
- School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China; (J.S.); (Q.Z.); (L.H.)
| | - Qunfei Zhang
- School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China; (J.S.); (Q.Z.); (L.H.)
| | - Weijie Tan
- State Key Laboratory of Public Big Data, Guizhou University, Guiyang 550025, China;
| | - Linlin Mao
- Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China;
| | - Lihuan Huang
- School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China; (J.S.); (Q.Z.); (L.H.)
| | - Wentao Shi
- School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China; (J.S.); (Q.Z.); (L.H.)
- Correspondence: ; Tel.: +86-1399-137-3645
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12
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Ali W, Li Y, Chen Z, Raja MAZ, Ahmed N, Chen X. Application of Spherical-Radial Cubature Bayesian Filtering and Smoothing in Bearings Only Passive Target Tracking. ENTROPY 2019. [PMCID: PMC7514433 DOI: 10.3390/e21111088] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
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.
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Affiliation(s)
- Wasiq Ali
- School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, China; (Z.C.); (N.A.)
- Correspondence: (W.A.); (Y.L.); Tel.: +86-183-9213-6464 (W.A.)
| | - Yaan Li
- School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, China; (Z.C.); (N.A.)
- Correspondence: (W.A.); (Y.L.); Tel.: +86-183-9213-6464 (W.A.)
| | - Zhe Chen
- School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, China; (Z.C.); (N.A.)
| | - Muhammad Asif Zahoor Raja
- Department of Electrical and Computer Engineering COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan;
| | - Nauman Ahmed
- School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, China; (Z.C.); (N.A.)
| | - Xiao Chen
- School of Electronic Information and Artificial Intelligence, ShaanXi University of Science & Technology, Xi’an 710021, ShaanXi, China;
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