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Journal Article•DOI•

Acceptance Criteria of Bearings-only Passive Target Tracking Solution

05 Apr 2021-Iete Journal of Research (Informa UK Limited)-pp 1-12
TL;DR: In passive target tracking, target motion parameters (TMP) i.e. range, course, and speed are estimated using bearing measurements as mentioned in this paper, and the accuracy of the estimated solution can be estimated in simulation mode.
Abstract: In passive target tracking, target motion parameters (TMP) i.e. range, course, and speed are estimated using bearing measurements. In the simulation mode, the accuracy of the estimated solution can...
Citations
More filters
DOI•
21 Feb 2022
TL;DR: In this paper , the performance of the neural-based extended/unscented Kalman (EKF/UKF) filter was investigated for undersea target tracking using passive bearings only.
Abstract: In order to apply undersea target tracking using passive bearings only, this work aims to investigate the performance capabilities of the neural-based extended/unscented Kalman (EKF/UKF) filter. In this paper, the assumption is that a submarine is tracking in underwater another submarine or ship. Application of UKF for target tracking utilizing passive bearings-only measurements is a standard and well-known technique and published in the literature. Here a case study is taken up with the objective of improving results further adding neural network (NN) to EKF/UKF. This technique uses NN nonlinear state-space model approximation and NN's weights are trained on-line by the EKF/UKF. The Monte-Carlo simulations is utilized, and the outcomes are compared to the EKF/UKF procedure, since it is stochastic. It is discovered that the results with EKF/UKF are better than that of the corresponding EKF/UKF with NN. It is understood that NN is to be used when the process uncertainties cannot be modeled exactly or where there is unobservability. In passive target tracking, unobservability exists and this problem is solved by observer maneuver. However, when NEKF/NUKF is used, the observer maneuver is not able to solve the problem. Hence, NN need not be utilized when the analytical solution is feasible, and the solution is tractable.
DOI•
21 Feb 2022
TL;DR: In this paper , an unscented Kalman filter (UKF) with neural network (NN) is applied to estimate the motion parameters of target, and the model is approximated by the nonlinear state space NN, and its weights are then trained online through the UKF.
Abstract: The motive of the work is to investigate the use of active sonar measurements by submarines to track a ship's trajectory underwater. An unscented Kalman filter (UKF) with neural network (NN) is applied to estimate the motion parameters of target. The model is approximated by the nonlinear state space NN, and its weights are then trained online through the UKF. As the process is stochastic, Monte-Carlo simulation is used and the outcomes are compared with that of UKF algorithm. As expected, the results with UKF are better than that of UKF with NN. The purpose of NN is to be used when the process uncertainties cannot be modeled exactly. NN need not be used when the analytical solution is possible, and solution is tractable.
Journal Article•DOI•
TL;DR: In this article , an algorithm has been developed to detect multiple targets and fuse state vectors when a single target is detected, considering the state vectors from two different sensor arrays with various noise variances.
Abstract: The issue of real-time state estimation in passive target tracking using only bearing measurements is addressed in this research. An algorithm has been developed to detect multiple targets and fuse state vectors when a single target is detected. Target detection is carried out considering the state vectors from two different sensor arrays with various noise variances. The algorithm is evaluated against targets having unique and identical parameters such as range, speed and course. The state vectors are determined using three different filtering techniques, namely, extended Kalman filter (EKF), modified gain bearings-only EKF and unscented Kalman filter. Using the MATLAB software environment, Monte-Carlo simulations are conducted to more precisely assess algorithm performance.
References
More filters
Proceedings Article•DOI•
28 Jul 1997
TL;DR: It is argued that the ease of implementation and more accurate estimation features of the new filter recommend its use over the EKF in virtually all applications.
Abstract: The Kalman Filter (KF) is one of the most widely used methods for tracking and estimation due to its simplicity, optimality, tractability and robustness. However, the application of the KF to nonlinear systems can be difficult. The most common approach is to use the Extended Kalman Filter (EKF) which simply linearizes all nonlinear models so that the traditional linear Kalman filter can be applied. Although the EKF (in its many forms) is a widely used filtering strategy, over thirty years of experience with it has led to a general consensus within the tracking and control community that it is difficult to implement, difficult to tune, and only reliable for systems which are almost linear on the time scale of the update intervals. In this paper a new linear estimator is developed and demonstrated. Using the principle that a set of discretely sampled points can be used to parameterize mean and covariance, the estimator yields performance equivalent to the KF for linear systems yet generalizes elegantly to nonlinear systems without the linearization steps required by the EKF. We show analytically that the expected performance of the new approach is superior to that of the EKF and, in fact, is directly comparable to that of the second order Gauss filter. The method is not restricted to assuming that the distributions of noise sources are Gaussian. We argue that the ease of implementation and more accurate estimation features of the new filter recommend its use over the EKF in virtually all applications.

5,314 citations

Proceedings Article•DOI•
01 Oct 2000
TL;DR: The unscented Kalman filter (UKF) as discussed by the authors was proposed by Julier and Uhlman (1997) for nonlinear control problems, including nonlinear system identification, training of neural networks, and dual estimation.
Abstract: This paper points out the flaws in using the extended Kalman filter (EKE) and introduces an improvement, the unscented Kalman filter (UKF), proposed by Julier and Uhlman (1997). A central and vital operation performed in the Kalman filter is the propagation of a Gaussian random variable (GRV) through the system dynamics. In the EKF the state distribution is approximated by a GRV, which is then propagated analytically through the first-order linearization of the nonlinear system. This can introduce large errors in the true posterior mean and covariance of the transformed GRV, which may lead to sub-optimal performance and sometimes divergence of the filter. The UKF addresses this problem by using a deterministic sampling approach. The state distribution is again approximated by a GRV, but is now represented using a minimal set of carefully chosen sample points. These sample points completely capture the true mean and covariance of the GRV, and when propagated through the true nonlinear system, captures the posterior mean and covariance accurately to the 3rd order (Taylor series expansion) for any nonlinearity. The EKF in contrast, only achieves first-order accuracy. Remarkably, the computational complexity of the UKF is the same order as that of the EKF. Julier and Uhlman demonstrated the substantial performance gains of the UKF in the context of state-estimation for nonlinear control. Machine learning problems were not considered. We extend the use of the UKF to a broader class of nonlinear estimation problems, including nonlinear system identification, training of neural networks, and dual estimation problems. In this paper, the algorithms are further developed and illustrated with a number of additional examples.

3,903 citations

Proceedings Article•
01 Jan 2001

3,169 citations

Journal Article•DOI•
TL;DR: In this paper, the authors derived exact state equations for the MP filter without imposing any restrictions on own-ship motion; thus, prediction accuracy inherent in the traditional Cartesian formulation is completely preserved.
Abstract: Previous studies have shown that the Cartesian coordinate extended Kalman filter exhibits unstable behavior characteristics when utilized for bearings-only target motion analysis (TMA). In contrast, formulating the TMA estimation problem in modified polar (MP) coordinates leads to an extended Kalman filter which is both stable and asymptotically unbiased. Exact state equations for the MP filter are derived without imposing any restrictions on own-ship motion; thus, prediction accuracy inherent in the traditional Cartesian formulation is completely preserved. In addition, these equations reveal that MP coordinates are well-suited for bearings-only TMA because they automatically decouple observable and unobservable components of the estimated state vector. Such decoupling is shown to prevent covariance matrix ill-conditioning, which is the primary cause of filter instability. Further investigation also confirms that the MP state estimates are asymptotically unbiased. Realistic simulation data are presented to support these findings and to compare algorithm performance with respect to the Cramer-Rao lower bound (ideal) as well as the Cartesian and pseudolinear filters.

477 citations

Journal Article•DOI•
TL;DR: In this article, a modified gain extended Kalman observer (MGEKO) was developed for a special class of systems and a sufficient condition for the estimation errors of the MGEKF to be exponentially bounded in the mean square was obtained.
Abstract: A new globally convergent nonlinear observer, called the modified gain extended Kalman observer (MGEKO), is developed for a special class of systems. This observer structure forms the basis of a new stochastic filter mechanization called the modified gain extended Kalman filter (MGEKF). A sufficient condition for the estimation errors of the MGEKF to be exponentially bounded in the mean square is obtained. Finally, the MGEKO and the MGEKF are applied to the three-dimensional bearings-only measurement problem where the extended Kalman filter often shows erratic behavior.

287 citations