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

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.

Design of Nonlinear Autoregressive Exogenous Model Based Intelligence Computing for Efficient State Estimation of Underwater Passive Target

“…State estimation framework consists of various parameters that need to be properly tuned for obtaining better performance from state prediction algorithms. The parameters and their relevent setting is selected on a similar manner as in reported studies [ 3 , 19 , 21 , 22 ]. Appropriate values of these parameters are listed in Table 1 .…”

“…In the dynamic model, target state vector consist on position and velocity at time step in the two-dimensional rectangular coordinate system [ 21 ]. These motion variables are illustrated in state vector of the target as: where is representing transpose of matrix in the above equation.…”

“…UKF algorithm has the advantage of less computational cost than PF and high filtering precision than EKF in nonlinear systems [ 20 ]. Along with these filtering techniques, researchers also proposed many nonlinear filters like cubature Kalman filter [ 21 ], Gaussian filters [ 22 ], Gauss-Hermite quadrature filter [ 23 ], the sparse grid quadrature filter [ 24 ], shifted Rayleigh filter [ 25 ] and ensemble Kalman filter [ 26 ]. Some scholars integrate information entropy theory with parameter extraction techniques to investigate characteristics of underwater object.…”

“…This proposed work establishes a novel state estimation application of neural networks to analyze different underwater scenarios for semi-curved trajectory of the target. The simulation results are compared with our recent reported study [ 21 ], in which spherical radial cubature Kalman filter (SRCKF) and UKF are used for the same state estimation model.…”

Underwater 3D Doppler-Angle Target Tracking with Signal Time Delay

“…In some special applications, a passive system has the advantage of keeping covert and hardly being detected [ 7 ]. The angle-only tracking and Doppler-angle tracking problems relied on acoustic sensors and belonged to the passive target tracking [ 8 , 9 ]. The main problem is estimating the unknown target state through the noisy measurements acquired by acoustic sensors [ 10 , 11 ].…”