Bearings-only Tracking Research Articles

Application of Sigma Point Particle Filter Method for Passive State Estimation in Underwater

Bearings-only tracking (BOT) plays a vital role in underwater surveillance. In BOT, measurement is tangentially related to state of the system. This measurement is also corrupted with noise due to turbulent underwater environment. Hence state estimation process using BOT becomes nonlinear. This necessitates the use of nonlinear filtering algorithms in place of traditional linear filters like Kalman filter. In general, these nonlinear filters utilize the assumption of measurements being corrupted with Gaussian noise for state estimation. The measurements cannot be always corrupted with Gaussian noise because of the highly unstable sea environment. These problems indicate the necessity for development of nonlinear non-Gaussian filters like particle filter (PF) for underwater tracking. However, PF suffers from severe problems like sample degeneracy and impoverishment and also it is tedious to select an appropriate technique for resampling. To overcome these difficulties in PF implementation, the strategy of combining PF with another filter like unscented Kalman filter is proposed for target’s state estimation. The detailed analysis of the same is presented in comparison with other particle filter combinations using the simulation results obtained in Matlab.

Periodic acoustic source tracking using propagation delayed measurements

There exist a large class of acoustic sources which have an underlying periodic phenomenon. Unlike the well-studied Bearings-Only Tracking (BOT) of an aperiodic acoustic source, this paper considers the problem of tracking a periodic acoustic source. For periodic acoustic tracking, the signal emission time is known. However, the true measurement reception time is unknown because it is corrupted by noise due to propagation delay. We augment the sensor’s signal reception time onto bearing measurements, and the information of the delay constraint is included in the original bearing measurements to compensate for the propagation delay. A Cubature Kalman Filter (CKF) is used for periodic acoustic source tracking, in which measurement prediction cannot be obtained directly because the sensor’s position at the true measurement reception time is unknown. We solve this problem by using the implicit Gauss-Helmert Sensor Model (GHSM) for estimating the sensor’s position, which consists of the sensor’s motion equation and the known measured sensor’s signal reception time equation related to the state. Then a CKF based on the GHSM (CF-GHSM) is developed for periodic acoustic tracking. Illustrative examples demonstrate that the CF-GHSM algorithm is better than other algorithms for periodic acoustic source tracking.

伯努利滤波器在纯角度跟踪场景中的应用

伯努利滤波器在纯角度跟踪场景中的应用

伯努利滤波器在纯角度跟踪场景中的应用

伯努利滤波器在纯角度跟踪场景中的应用

Optimization Algorithm of Bearings Only Tracking based on Cubature Kalman Filter

In view of the shortcomings of low precision and poor performance in the process of bearings only tracking (BOT) in wireless sensor networks(WSNs), an optimization algorithm of BOT based on the cubature Kalman filter(CKF) in WSNs is proposed. The sensors with spatial distribution are divided into several clusters, the number of sensors in each cluster is the same, and each sensor detects data to form a local estimation. Then uploads it to the cluster head (CH) node data fusion, so as to get the accurate information of the target. In order to improve the positioning accuracy, the CKF is used to process the data of each sensor, and then it is uploaded to the CH node to ensure the tracking ability of the filter to the changes of structural parameters. The CH node uses weighted data fusion algorithm to get the final fusion result. The simulation results verify the effectiveness of the method.

Fusion of Angle Measurements from Hull Mounted and Towed Array Sensors

Two sensor arrays, hull-mounted array, and towed array sensors are considered for bearings-only tracking. An algorithm is designed to combine the information obtained as bearing (angle) measurements from both sensor arrays to give a better solution. Using data from two different sensor arrays reduces the problem of observability and the observer need not follow the S-maneuver to attain observability of the process. The performance of the fusion algorithm is comparable to that of theoretical Cramer–Rao lower bound and with that of the algorithm when bearing measurements from a single sensor array are considered. Different filters are used for analyzing both algorithms. Monte Carlo runs need to be done to evaluate the performance of algorithms more accurately. Also, the performance of the fusion algorithm is evaluated in terms of solution convergence time.

Research on Ship Azimuth-only Target Tracking Method Based on Computer Vision

Lian, G., 2020. Research on ship azimuth-only target tracking method based on computer vision. In: Bai, X. and Zhou, H. (eds.), Advances in Water Resources, Environmental Protection, and Sustainable Development. Journal of Coastal Research, Special Issue No. 115, pp. 202-204. Coconut Creek (Florida), ISSN 0749-0208.Due to the influence of external environmental factors, the traditional method has certain deviation in ship bearings-only target tracking. With the development of economic globalization, the number of shipping vessels has increased dramatically. A good video target tracking system must be able to ensure real-time tracking of ship targets. However, the increase in the number of ships not only improves the work efficiency of water transportation, but also causes the problem of higher water traffic density, which has a serious impact on the safe navigation of ships and the ecological environment of waters. The functions of target tracking system include target detection, target feature extraction, target tracking and so on. In this paper, the computer vision technology is introduced into the ship bearings only target tracking, and the computer vision sensor device is installed on the ship to be tracked, and the real-time ship navigation image is collected by the device.

Performance Analysis of Bayesian Filtering and Smoothing Algorithms for Underwater Passive Target Tracking

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.

Observability Metrics for Single-Target Tracking With Bearings-Only Measurements

This work considers the observability problem in bearings-only tracking (BOT). Although the rank criterion has always been used for observability analysis, the evident drawback that it can only give a qualitative result prevents us from exploiting more information from the observability matrix. In reality, we want to know not only if the system is observable but also the degree of the observability. In order to quantitatively describe the system observability, we propose a series of metrics for BOT. Being derived based on the condition number, the novel metrics can reflect the observability degree as well as evaluate the tracking performance. Besides, the metrics can be extended to be used for sensor trajectory optimization and sensor configuration, which are crucial to enhancing the tracking performance.

Performance Analysis of Gaussian Optimal Filtering for Underwater Passive Target Tracking

The problem of passive target tracking in the underwater environment is usually handled with nonlinear filtering algorithms, in which nonlinear measurement model is combined with linear system dynamics. The primary goal in passive target tracking is to extract accurate information about real-time state of the target from noisy nonlinear observations obtained from sensors. In this study, performance analysis of Gaussian optimal filtering is proposed for accurate state prediction of an underwater dynamic object. This paper delicately analyzes the state estimation performances of nonlinear version of Kalman filter like Gauss Hermite Kalman Filter (GHKF) and discrete-time Kalman smoother, called Gauss Hermite Rauch-Tung-Striebel (GHRTS) smoother. This analysis is done through variation in standard deviation of white Gaussian measurement noise which is a key feature in the target tracking framework. This performance-based study is conducted in the context of Bearings Only Tracking (BOT) phenomena by using two and three acoustics sensors installed on observer base station. All the experiments are performed for finding the Root Mean Square Error (RMSE) among true and predicted state of the object. Independent Monte Carlo simulations based numerical results demonstrate that GHRTS smoother provides better performance from GHKF for given circumstances.

Generalized pseudo Bayesian algorithms for tracking of multiple model underwater maneuvering target

The strength of Generalized Pseudo Bayesian (GPB) algorithms is exploited in the presented study to enhance the target tracking precision, effective model approximation and rapid convergence of multimodel maneuvering object tracking. The GPB methods are considered to be suitable for approximating systems whose dynamics follow discrete-time and fixed state Markov process. Underwater maneuvering target tracking problems are usually solved with nonlinear Bayesian algorithms, in which kinetics of object are associated with passive bearings using state-space modeling. Here accuracy and convergence of GPB methods based on Interacting Multiple Model Extended Kalman Filter (IMMEKF), Interacting Multiple Model Extended Kalman Smoother (IMMEKS), Interacting Multiple Model Unscented Kalman Filter (IMMUKF) and Interacting Multiple Model Unscented Kalman Smoother (IMMUKS) are efficiently analyzed for tracking of multimodel maneuvering target in complex ocean environment. Application of these algorithms is systematically presented for estimating the real-time state of a maneuvering object that follows a coordinated turn trajectory. Performance analysis of IMM Kalman filters and smoothers is done with variations in the standard deviation of white Gaussian measurement noise by following Bearings Only Tracking (BOT) phenomena. Least Mean Square Error (MSE) between approximated and the real position of maneuvering target in rectangular coordinates is calculated for analyzing the performance of filtering and smoothing techniques. Simulation results of the Monte Carlo runs validate the effectiveness of IMMEKS and IMMUKS over IMMEKF and IMMUKF for scenario of given framework.

Underwater Bearing-Only Multitarget Tracking in Dense Clutter Environment Based on PMHT

Underwater bearing-only multitarget tracking in clutter environment is challenging because of the measurement nonlinearity, range unobservability, and data association uncertainty. In terms of the principle of expectation maximization, combining the extended Kalman filter (EKF) and unscented Kalman filter algorithm(UKF), a new bearing-only multi-sensor multitarget tracking via probabilistic multiple hypothesis tracking(PMHT) algorithm is proposed. The PMHT algorithm introduces an association variable to deal with the data association uncertainty problem between the measurements and the targets. Furthermore, the EKF-based PMHT for multi-sensor multitarget system is simplified, which obviate the need to "stack" the synthetic measurements and can reduce the computation cost. The estimation accuracy of the EKF based on PMHT approach and UKF based on PMHT approach in simulation experiments for underwater bearing-only cross-moving targets and closely spaced targets for the case of stationary multiple observations and maneuvering single observation under dense clutter environment is analyzed. The experimental results demonstrate that the present algorithm is very well in a highly clutter environment and its computational load is low, which confirms the effectiveness of the algorithm to the bearing-only multitarget tracking in dense clutter.

Trajectory optimization for rendezvous with bearing-only tracking

In this paper the observability of bearing-only tracking is analyzed and the trajectory optimization algorithms to enhance the observability during the rendezvous are presented. Firstly, the relative dynamic model and measurement model are established, and the necessary and sufficient condition for observability when maneuvering is determined using the pseudo linear method. Then, the observability indices, such as the filter covariance matrix trace and the Fisher information matrix (FIM) determinant, are combined with the fuel consumption index to optimize the approaching trajectory. In order to keep the line-of-sight (LOS) aligned with the target and to ensure continuous observation, the attitude of the observer is adjusted synchronously during the rendezvous. Finally, the coordinated control of attitude and orbit for the observer is achieved by optimizing the thrust distribution of the onboard propulsion system. Numerical results demonstrate that the combined optimization of the observability and fuel consumption can generate an optimal control trajectory with high tracking accuracy. The simulation also presents how to choose the optimal relative weight of the two optimization terms, optimal rendezvous time and optimal docking point according to the practical requirements to get the best comprehensive performance of observability and fuel consumption.

Gaussian sum pseudolinear Kalman filter for bearings‐only tracking

The efficacy of a bearings-only tracking algorithm, to a great extent, depends on the target-sensor geometry and motion. Although the pseudolinear Kalman filter and its variants have demonstrated comparable performance with the elite non-linear filters, they still suffer from bias problems and the tracking performance is inevitably affected by the relative geometry and motion relationships. In this study, an observability metric based on classical control theory is first presented to characterise the relative relationships between the target and the sensor. Then an efficient bearings-only tracking algorithm called Gaussian sum pseudolinear Kalman filter is developed. It is based on the bias-compensated pseudolinear Kalman filter and is built within a Gaussian sum framework. In the novel algorithm, a splitting and merging procedure will be triggered when a low degree of observability is detected. Simulation results show the significant performance improvement of the proposed algorithm.

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

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.

Comparison of MGBEKF and UKF Algorithms for Bearings-Only Tracking

Comparison of MGBEKF and UKF Algorithms for Bearings-Only Tracking

Robust adaptive unscented Kalman filter for bearings-only tracking in three dimensional case

This paper proposes an improved version of Unscented Kalman Filter (UKF), namely Robust Adaptive UKF (RAUKF), with a special focus on Bearings-Only Target Tracking for three-dimensional case (3DBOT). The automatic tuning of the noise covariance matrices and the robust estimation of the target states form a critical point for the performance of the Kalman-type filtering algorithms, especially in the variable environmental conditions exposed in underwater. The key idea of the proposed filter is to combine robust aspects of UKF and adaption of the process and measurement noise covariance matrices with low computational complexity. The main contribution of this paper is to adjust these matrices by means of the steepest descent algorithm, and the H∞ technique is embedded to achieve superior performance in terms of accuracy and robustness against initial conditions and model uncertainties. Different experiments are performed to evaluate the performance of the proposed algorithm in the 3DBOT problem with a single moving observer. Simulations demonstrate that the proposed filter produce more accurate results with satisfactory computational burden in comparison with other methods.

Gaussian Sum Shifted Rayleigh Filter for Underwater Bearings-Only Target Tracking Problems

In this paper, a new Gaussian sum (GS) filter with shifted Rayleigh filter (SRF) as proposal has been developed for the bearings-only tracking (BOT) problem. The proposed filter estimates the prior and posterior probability density functions as weighted sum of several Gaussian densities, where the individual Gaussian densities are generated from the SRF. Performance of the proposed filter on the BOT problem is compared with the SRF, the GS sparse-grid Gauss-Hermite filter, and other available GS and quadrature-based filters. Performance of filters is compared in terms of a root-mean-square error (RMSE), track divergence, and computational time. The effect of initial uncertainty, measurement noise covariance, and sampling time on filtering accuracy are also studied. Finally, RMSEs of all the filters are evaluated in comparison with the Cramer-Rao lower bound. From simulation results, it is observed that the performance of the proposed GS-SRF is superior to all other nonlinear filters considered.

A Method of Target Tracking Based on Monocular Vision for Mobile Robot in Unknown Environment

In order to solve the problem of target tracking based on monocular vision for mobile robot in unknown environment, a robot simultaneous localization, map building and target tracking method is proposed. This method can realize the simultaneous online estimation of robot, environment features and target states by using the bearings only observations from monocular sensors. In the process of estimation, the monocular vision based Simultaneous localization and mapping (MVSLAM) runs independent of the Object Tracking(OT), as the basis of the OT, MVSLAM provides the state information of the robot platform for the OT, and OT uses the bearing measurements of target and robot state to estimates the state of target. MVSLAM is based on inverse depth parameterization and running under framework of full probability Extended Kalman Filter (EKF), and another EKF is also used for target tracking independently. The simulation experiments show the performance of the design method, and analyze the problem of observability of Bearing-only tracking. To solve the observability problem, a robot motion control method is presented, under the control of this method, the robot will make satellite surround motion around the target. Finally, the feasibility and accuracy of the method are verified by simulation experiments.

Variational Bayesian Based Adaptive Shifted Rayleigh Filter for Bearings-Only Tracking in Clutters.

This paper considers bearings-only target tracking in clutters with uncertain clutter probability. The traditional shifted Rayleigh filter (SRF), which assumes known clutter probability, may have degraded performance in challenging scenarios. To improve the tracking performance, a variational Bayesian-based adaptive shifted Rayleigh filter (VB-SRF) is proposed in this paper. The target state and the clutter probability are jointly estimated to account for the uncertainty in clutter probability. Performance of the proposed filter is evaluated by comparing with SRF and the probability data association (PDA)-based filters in two scenarios. Simulation results show that the proposed VB-SRF algorithm outperforms the traditional SRF and PDA-based filters especially in complex adverse scenarios in terms of track continuity, track accuracy and robustness with a little higher computation complexity.