**1. Introduction**

High-frequency surface wave radar (HFSWR) has become the primary technical means for maritime-state monitoring [1,2]. However, track breakages frequently occur in large-scale marine surveillance due to highly maneuverable targets, dense channels, target occlusion, strong clutter/ interference, long sampling intervals, and low detection probabilities, which substantially degrade the overall tracking performance and adversely affect situation assessment [3,4]. Hence, continuous tracking of vessels is one of the key problems to be solved in the field of target tracking in marine surveillance.

At present, algorithm research studies for long-term vessel tracking mainly center on segment association, which can be divided into two categories: one is based on statistics [5–9]; the other is based on fuzzy mathematics [10–13]. The former takes the difference of the state estimation as the statistic, establishes the hypothesis, and then uses the given probability to accept or reject the hypothesis to determine whether the track is associated or not. The latter selects the membership degree of association, and calculates the membership value of two tracks to determine whether the track is associated or not. Bar-Shalom et al. [5] applied the fixed distance metric in the weighted statistical method. Yeom et al. [6] presented a track segment association algorithm on the basis of discrete optimization. Zhang et al. [7] stitched broken tracks by using an interacting multiple model (IMM) estimator. Aybars et al. [8] calculated an association cost in order to associate tracks on the basis of Mahalanobis distance. Zhu et al. [9] proposed a mixed integer nonlinear programming (MINLP) model in the maximum likelihood rule. Ashraf et al. [10] presented a fuzzy correlation approach on the basis of the fuzzy clustering means algorithm. Stubberud et al. [11] proposed a straightforward fuzzy-logic-based association method based on the chi 2 metric. Shao et al. [12] used fuzzy k-nearest neighbors and fuzzy C-means clustering to achieve track segment association. Hong et al. [13] presented a track segment association algorithm by calculating the fuzzy membership matrix and clustering methodology. All of these methods compare the distances of track segments point by point without considering the relevance of the track segments' features, which can cause invalid track association when a vessel is in a complex situation, such as in a dense channel or strong clutter interference region.

These track segment association (TSA) algorithms are feasible in theory, however, the backward prediction error of the present track is often large due to the noise of the system and measurement, which results in poor accuracy of association. Even worse, the performance of TSA algorithms drops suddenly due to track crossing and bifurcation when affected by surrounding large vessels or strong clutters. In order to solve the track breakage problem effectively and track targets steadily and continuously, we consider combining the conventional tracking algorithm with the machine learning method, which can achieve track segment association through studying the training dataset. The back propagation (BP) network has a strong nonlinear mapping ability, although it easily becomes trapped in local minimums during its training, which limits the stability and accuracy of classification [14,15]. Although the support vector machine (SVM) is able to avoid a local optimal solution, it has some shortcomings, such as training slowly and having a low efficiency [16,17]. The extreme learning machine (ELM) is a single hidden layer neural network with low computational complexity and good general performance [18]. Compared with the traditional neural network, ELM can randomly initialize the input weight and offset without adjusting during the training process, which make it simple and fast with the guarantee of accuracy [19]. Moreover, the ELM is more suited to handle small sample classification problems than deep learning [20,21].

We propose a long-term continuous tracking method based on an interacting multiple model extended Kalman filter (IMMEKF) combined with an extreme learning machine (ELM). When using the IMMEKF tracking method alone, we can determine only the intermittent track segments. Long-term continuous tracking is achieved when the ELM is combined with this method. In order to sufficiently reflect the track segment features, we associate the tracks on the basis of features extracted from track segments rather than comparing the distances of track segments point by point. Moreover, we present a new scheme to solve the problem of track segment association using an ELM network. The method decides whether the present track segment is associated with the former tracks through the ELM network, whose feature vectors in the training set are extracted from the track segments obtained by the IMMEKF. Hence, the long-term continuous tracking of multiple targets can be achieved via the cooperation between the IMMEKF and the ELM. Both the simulation and the field experiment results show that the proposed method has better tracking performance than conventional algorithms.

This paper is organized as follows. In Section 2, we briefly introduce the stereoscopic HFSWR station and the system model of the vessel target. In Section 3, we propose the long-term continuous tracking method with stereoscopic HFSWR based on IMMEKF combined with ELM. Furthermore, the simulation and the field data experiment results are presented to show the effectiveness of the proposed method in Section 4. In Section 5, the results are discussed, and areas for future potential research are considered. Finally, conclusions are drawn in Section 6.
