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Open AccessArticle

Application of Spherical-Radial Cubature Bayesian Filtering and Smoothing in Bearings Only Passive Target Tracking

1
School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, China
2
Department of Electrical and Computer Engineering COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan
3
School of Electronic Information and Artificial Intelligence, ShaanXi University of Science & Technology, Xi’an 710021, ShaanXi, China
*
Authors to whom correspondence should be addressed.
Entropy 2019, 21(11), 1088; https://doi.org/10.3390/e21111088
Received: 4 October 2019 / Revised: 30 October 2019 / Accepted: 4 November 2019 / Published: 7 November 2019
(This article belongs to the Special Issue Entropy and Information Theory in Acoustics)
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. View Full-Text
Keywords: Bayesian filtering; passive target tracking; spherical radial cubature Kalman filter; Gaussian measurement noise; Rauch–Tung–Striebel smoother Bayesian filtering; passive target tracking; spherical radial cubature Kalman filter; Gaussian measurement noise; Rauch–Tung–Striebel smoother
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MDPI and ACS Style

Ali, W.; Li, Y.; Chen, Z.; Raja, M.A.Z.; Ahmed, N.; Chen, X. Application of Spherical-Radial Cubature Bayesian Filtering and Smoothing in Bearings Only Passive Target Tracking. Entropy 2019, 21, 1088.

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