Multipath Data Association Research Articles

Measurement based dimension descent association algorithm for OTHR multi-detection multi-target tracking

The problem of multi-detection multi-target tracking (MDMTT) using over-the-horizon radar in dense clutter environment is studied in this paper. The biggest challenge of MDMTT is the 3-dimensional multipath data association among measurements, detection models and targets. In particular, a lot of clutter measurements are generated in dense clutter environment, which increase the computational burden of 3-dimensional multipath data association greatly. A measurement based dimension descent association (DDA) algorithm is proposed to solve the 3-dimensional multipath data association, which decomposes the 3-dimensional multipath data association into two 2-dimensional data associations. The proposed algorithm can reduce the computational burden compared with the optimal 3-dimensional multipath data association and the computational complexity is analyzed. Besides, a time extension method is designed to detect the new-born targets that appear in the tracking scene, which is based on the sequential measurements. The convergence of the proposed measurement based DDA algorithm is analyzed. The estimation error can convergence to 0 as the number of Gaussian mixtures tends to infinity. The effectiveness and rapidity of the measurement based DDA algorithm are demonstrated by the comparative simulation with the previously proposed algorithms.

A doppler modified multipath data association algorithm for shipborne high frequency hybrid sky-surface wave radar

Shipborne HF hybrid sky-surface wave radar (HFHSSWR) system contains skywave transmit channel and surface channel. The ionosphere is delaminated and highly uncertain, which causes the sky wave channel to be uncertain, results in multiple measurements for one target and leads to track loss. In addition, due to the size of shipborne receiving platform, the measurement accuracy is low, which leads to the decrease of track filtering accuracy and more serious tack loss. In this paper, we establish a measurement model of Shipborne HF hybrid sky-surface wave radar. Based on this model we model the ionospheric height as a Gaussian distribution and introduce this error into the multi-detection model, and then use the fusion Doppler to modify the feasible joint probability of the multi-detection model JPDA. In the end, simulation experiments are conducted. The results show that the algorithm proposed in this paper effectively improves the filtering accuracy and reduces the loss rate of the trajectory.

Measurement-Level Target Tracking Fusion for Over-the-Horizon Radar Network Using Message Passing

Tracking an unknown number of targets based on multipath measurements provided by an over-the-horizon radar (OTHR) network with a statistical ionospheric model is complicated, which requires solving four subproblems: Target detection, target tracking, multipath data association, and ionospheric heights identification. A joint solution is desired since the four subproblems are highly correlated, but suffering from the intractable inference problem of high-dimensional latent variables. In this article, a unified message passing (MP) approach, combining belief propagation (BP) and mean-field (MF) approximation, is developed for simplifying the intractable inference. Based upon the factor graph corresponding to a factorization of the joint probability density function (PDF) of the latent variables and a choice for a separation of this factorization into BP region and MF region, the posterior PDFs of target kinematic state and ionospheric heights, are approximated by MF due to its simple MP update rules for conjugate-exponential models. The posterior PDFs of target visibility state and multipath data association which contains one-to-one frame (hard) constraints (i.e., at each time, a measurement is either originated from one target via a particular path or it is clutter, and each target generates at most one measurement under a particular path) are approximated by BP. Finally, the approximated posterior PDFs are updated iteratively in a closed-loop manner, which is effective for dealing with the coupling issue among latent variables. Meanwhile, the proposed approach has the measurement-level fusion architecture due to the direct processing of the raw multipath measurements from an OTHR network, which is beneficial to improving tracking fusion performance. Its performance is demonstrated on a simulated OTHR network multitarget tracking scenario.

OTHR multitarget tracking with a GMRF model of ionospheric parameters

The ionosphere is the propagation medium for radio waves transmitted by an over-the-horizon radar (OTHR). Ionospheric parameters, typically, virtual ionospheric heights (VIHs), are required to perform coordinate registration for OTHR multitarget tracking and localization. The inaccuracy of ionospheric parameters has a significant deleterious effect on the target localization of OTHR. Therefore, to improve the localization accuracy of OTHR, it is important to develop accurate models and estimation methods of ionospheric parameters and the corresponding target tracking algorithms. In this paper, we consider the variation of the ionosphere with location and the spatial correlation of the ionosphere. We use a Gaussian Markov random field (GMRF) to model the VIHs, providing a more accurate representation of the VIHs for OTHR target tracking. Based on expectation-conditional maximization and GMRF modeling of the VIHs, we propose a novel joint optimization solution, namely ECM-GMRF, to perform target state estimation, multipath data association and VIHs estimation simultaneously. In ECM-GMRF, the measurements from both ionosondes and OTHR are exploited to estimate the VIHs, leading to a better estimation of the VIHs which improves the accuracy of data association and target state estimation, and vice versa. The simulation indicates the effectiveness of the proposed algorithm.

Joint Target Detection and Tracking in Multipath Environment: A Variational Bayesian Approach

We consider multitarget detection and tracking problem for a class of multipath detection system where one target may generate multiple measurements via multiple propagation paths, and the association relationship among targets, measurements, and propagation paths is unknown. In order to effectively utilize multipath measurements from one target to improve detection and tracking performance, a tracker has to handle high-dimensional estimation of latent variables including target existence state, target kinematic state, and multipath data association. Based on variational Bayesian inference, we propose a novel joint detection and tracking algorithm that incorporates multipath data association, target detection, and target state estimation in a unified Bayesian framework. The posterior probabilities of these latent variables are derived in a closed-form iterative manner, which is effective for reducing the performance deterioration caused by the coupling between estimation errors and identification errors. Loopy belief propagation is exploited to approximately calculate the probability of multipath data association, saving the computational cost significantly. Simulation results of over-the-horizon radar multitarget tracking show that the proposed algorithm outperforms multihypothesis multipath track fusion and multidetection (hypothesis-oriented) multiple hypothesis tracker, especially under low signal-to-noise ratio circumstance.

Distributed ECM Algorithm for OTHR Multipath Target Tracking With Unknown Ionospheric Heights

Over-the-horizon radar (OTHR) target tracking in the presence of complicated ionospheric environment mainly faces three challenges, i.e., discrete uncertainty of multipath data association, continuous uncertainty of ionospheric heights, and coupling of target state estimation and ionospheric parameters identification. The existing OTHR target tracking algorithms demanded that the ionospheric heights should be exactly known or statistical properties known. However, the ionospheric heights is inaccurate due to the inherent variability of ionosphere, especially when the deployment of ionosondes is unavailable in the sea area or hostile zone. This paper introduces a joint optimization scheme called distributed expectation-conditional maximization (DECM), which solves the target state estimation, multipath data association, and ionospheric heights identification simultaneously. The proposed DECM algorithm consists of a local estimation level and a global fusion level, whereas information is exchanged within these two levels until iteration terminates. This dual-level processing framework transforms the high-dimensional estimation problems into several low-dimensional parallel path-dependent estimation problems, which improves the computational efficiency of expectation maximization under high-dimensional latent variables case. In addition, the closed-loop structure is beneficial to the coupling problem. The simulation indicates the effectiveness of the proposed scheme.

An EM Algorithm for Multipath State Estimation in OTHR Target Tracking

Multi-path tracks of a single target exist in skywave over-the-horizon radar (OTHR) surveillance, due to the availability of multiple signal propagation paths through the ionosphere. Different from the traditional multipath data association and estimation methods for OTHR target tracking, a novel scheme for joint multipath data association and state estimation (JMAE) is developed based on the expectation-maximization (EM) framework. The proposed scheme has the iterative optimization of identification (including data association and ionospheric mode identification) and estimation (including path-conditional state estimation and multipath track fusion). Due to the mechanism of iterative optimization, the closed loop between identification and estimation is established, which is desirable to deal with the coupling issue of identification risk and estimation errors. The simulation shows that JMAE is superior to the well-known multipath probabilistic data association (MPDA).

Authors' reply to 'comments on "multipath data association tracker for over-the-horizon radar"

For original paper see Pulford and Evans (IEEE Transactions on Aerospace and Electronic Systems, vol.34, no.4, p.1165-83, 1998). The present paper replies to a comment by Liu et al. (IEEE Transactions on Aerospace and Electronic Systems, vol.41, no.3, p.1147-8, 2005). The corrections to the Jacobian matrix elements of the transformation from the ground to radar coordinates are discussed.

Comments on "Multipath data association tracker for over-the-horizon radar"

Two mistakes in the Jacobian matrix of the transformation from the ground to radar coordinates in Pulford and Evans (IEEE Transactions on Aerospace and Electronic Systems, vol. 34, no.4, p.1165-83, 1998) are corrected. Besides this, a missing equation in is also given.

A multipath data association tracker for over-the-horizon radar

A new algorithm, multipath probabilistic data association (MPDA), for initiation and tracking in over-the-horizon radar (OTHR) is described. MPDA is capable of exploiting multipath target signatures arising from discrete propagation modes that are resolvable by the radar. Nonlinear measurement models exhibiting multipath target signatures in azimuth, slant range, and Doppler are used. Tracking is performed in ground coordinates and therefore depends on the provision of estimates of virtual ionospheric heights to achieve coordinate registration. Although the propagation mode characteristics are assumed to be known, their correspondence with the detections is not required to be known. A target existence model is included for automatic track maintenance. Numerical simulations for four resolvable propagation modes are presented that demonstrate the ability of the technique to initiate and maintain track at probabilities of detection of 0.4 per mode in clutter densities for which conventional probabilistic data association (PDA) has a high probability of track loss, and suffers from track bias. A nearest neighbor version of MPDA is also presented.