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.

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.