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.
Highlights
In the last two decades, a lot of nonlinear estimation approaches have been proposed from the research community for solving nonlinear state estimation problems [1]
Simulation results in the form of state estimates and position errors of Spherical Radial Cubature Kalman Filter (SRCKF), Spherical Radial Cubature Rauch–Tung–Striebel (SRCRTS), Unscented Kalman Filter (UKF), and Unscented Rauch–Tung–Striebel (URTS) are discussed briefly
Strength of nonlinear Bayesian filtering through SRCKF, UKF algorithms, and smoothing based on SRCRTS and URTS algorithms is efficiently and effectively exploited for bearings only passive target tracking problem arises in ocean environment studies
Summary
In the last two decades, a lot of nonlinear estimation approaches have been proposed from the research community for solving nonlinear state estimation problems [1]. Some researchers have done comparative analysis of different nonlinear filters for especially passive bearings only target tracking applications for analyzing their worth in ocean environment [33,34,35]. These all discussed tracking methods are mainly applied for a single motion model of a target. Due to the complications and randomness of object dynamics, it is not suitable to precisely explain different maneuvering phases in a single model, which leads to a divergence between true dynamics of the target and state model [37] To address this complex issue, researchers proposed an interactive multiple model (IMM) filter that can solve this problem efficiently. The final section of this paper reports significant contributions of the proposed methodology
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