Performance Analysis of Bayesian Filtering and Smoothing Algorithms for Underwater Passive Target Tracking
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Performance Analysis of Bayesian Filtering and Smoothing Algorithms for Underwater Passive Target Tracking Wasiq Ali1
· Yaan Li1 · Nauman Ahmed1 · Jun Su1 · Muhammad Asif Zahoor Raja2
Received: 21 March 2020 / Revised: 21 March 2020 / Accepted: 13 August 2020 © Brazilian Society for Automatics–SBA 2020
Abstract Passive target tracking deals with nonlinear filtering in which dynamics of the system are considered to be linear, while the target state is built on nonlinear measurements. In this paper, a comparative study is conducted for accurate state estimation of an underwater far-field moving target by exploiting the strength of well known nonlinear variant of Bayesian filter, i.e., extended Kalman filter (EKF) with discrete-time Kalman smoother, called Rauch–Tung–Striebel (RTS) smoother. Analysis is performed with two key parameters in target tracking by mean of variation in the number of sensors and different standard deviations of measured noise in the context of underwater bearings-only tracking technology. Exhaustive experiments are performed for finding the least root-mean square error between true and estimated position of target movement in the trajectory at every time instant. Relatively accurate estimation of the target state is observed from noisy measurements of sensors in case of RTS smoother than that of EKF for each scenario. Keywords Nonlinear filtering · Passive tracking · Extended Kalman filter · Rauch–Tung–Striebel smoother · Bearings-only tracking
1 Introduction Accurate state estimation of a moving object in underwater passive target tracking is actually processing the noisy bearing only measurements gained from antennas and keeping an approximation of the present state of the object (Luo et al. 2018). The estimated state primarily holds velocity, displaceThis research is supported in part by the National Natural Science Foundation of China (NSFC) Grant Nos. 11574250 and 11874302.
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Wasiq Ali [email protected] Yaan Li [email protected] Nauman Ahmed [email protected] Jun Su [email protected] Muhammad Asif Zahoor Raja [email protected]
1
School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an, Shaanxi, China
2
Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock, Pakistan
ment, course, and additional real-time motion parameters of the concern target (Kumar et a. 2016). The phenomena of target tracking through passive quantities can be modeled as bearings-only tracking (BOT), which is a knowledge of estimating the current position of a moving object merely over passive observations attained from the complex signals transmitted from the concerned object (Velmurugan and Panakkal 2015). The key issue in BOT is to approximate the real-time trajectory of a moving target from the strong noise depraved signal (Ullah et al. 2018). Target tracking is always considered as a process of uncertainty (Cheung et al. 2010). The cause of uncertainty primarily originates from the ambiguity of
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