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Syed, M.A.B.; Ahmed, I. Sequential Tracking Models, Physics-Based Models and Hybrid Models. Encyclopedia. Available online: (accessed on 15 June 2024).
Syed MAB, Ahmed I. Sequential Tracking Models, Physics-Based Models and Hybrid Models. Encyclopedia. Available at: Accessed June 15, 2024.
Syed, Md Asif Bin, Imtiaz Ahmed. "Sequential Tracking Models, Physics-Based Models and Hybrid Models" Encyclopedia, (accessed June 15, 2024).
Syed, M.A.B., & Ahmed, I. (2023, August 05). Sequential Tracking Models, Physics-Based Models and Hybrid Models. In Encyclopedia.
Syed, Md Asif Bin and Imtiaz Ahmed. "Sequential Tracking Models, Physics-Based Models and Hybrid Models." Encyclopedia. Web. 05 August, 2023.
Sequential Tracking Models, Physics-Based Models and Hybrid Models
Spatio-temporal, geo-referenced datasets are rapidly expanding and will continue to do so in the near future due to technological advancements as well as social and commercial factors. The introduction of the automatic identification system (AIS), which allows neighboring ships to communicate frequently with their location and navigation status via a radio signal, has enabled researchers to get their hands on datasets rich in spatio-temporal information. AIS data are collected from satellites and ground stations located all over the world. AIS data facilitates the mapping and characterization of maritime human and vessel activities, thus allowing for the real-time geo-tracking and identification of vessels equipped with AIS. Hence, in addition to its initial application in collision avoidance, AIS is now also a massive data source of unparalleled quality for diverse tracking tasks. The AIS dataset contains the location and motion features of the vessels. Each data point or row in the AIS data file is represented by a time-sequenced node that contains the vessel’s coordinates, speed, and traveling direction. Each node also has an associated time stamp indicating the data collection time. AIS dataset is suitable for  the track association problem solving approach for its spatio-temporal characteristics.
neural networks deep learning automatic identification system (AIS) multi-object tracking

1. Sequential Tracking Models

Sequential tracking algorithms, such as global nearest neighbor (GNN) [1] and joint probabilistic data association (JPDA), [2], are commonly employed to update tracks based on the contribution of several objects. These algorithms utilize a cost assignment matrix to minimize costs and employ soft assignment, also known as track association probability, to achieve this goal. While global nearest neighbor (GNN) [1] and joint probabilistic data association (JPDA) [2] focus on a single hypothesis for tracking objects, there are other techniques available. For example, multiple hypotheses tracking (MHT) [3] constructs a tree of hypotheses for each item and computes the likelihood of each track to determine the most probable combination of tracks. The random finite set (RFS)-based approaches were also been utilized for tracking objects, as they are capable of handling the inherent uncertainty involved in the tracking process [4]. The majority of sequential tracking-based algorithms are based on the Kalman filtering (KF) approach [5] or its variations, which are frequently employed to track moving objects and provide information regarding their velocity and acceleration based on their position. However, the accuracy of KF is predicated on the assumption of linear motion, and it struggles to accommodate nonlinear motion patterns. Furthermore, the KF framework has limited capacity for handling the distinct characteristics of vessel movements.

2. Physics-Based Models

The physics-based approaches rely on mathematical equations to describe the motion of ships, taking into account factors such as mass, force, and inertia. These equations utilize physical laws to calculate the future motion characteristics of the ship [6][7][8][9]. Such motion models can be useful for developing simulation systems to study ideal ship kinematic characteristics or even to train navigation systems. However, applying these models to track the trajectory patterns of multiple ships can be challenging. While these models can incorporate the spatio-temporal patterns of vessel movements [10] in the learning process, they are still limited in nature, only considering the last known position to track vessels.

3. Machine Learning and Hybrid Models

These methods rely solely on historical data and employ machine learning techniques to learn from past information, enabling them to predict future positions when provided with a new feature vector. These prominent machine learning methods used in trajectory prediction studies include the Gaussian process, support vector machine, principal component analysis (PCA), etc. While these methods [11][12][13][14][15] typically perform well in predicting immediate future positions, their prediction accuracy tends to decrease as the prediction time span increases. Furthermore, the performance of these models is highly dependent on the proper tuning of hyperparameters, which can be difficult to achieve. Additionally, they are not capable of processing long sequences and unraveling the spatial and temporal dependencies present in sequential observations. Hybrid approaches, on the other hand, combine physics-based models and machine learning models or different machine learning models to enhance the quality of the trajectory tracking process [16][17][18][19][20][21]. These approaches, however, are not free from the limitations imposed by the physics-based and machine learning models.

4. Deep Learning-Based Models

Deep learning, which is a subclass of machine learning models, stands out from the rest due to its superior learning capabilities. In the context of marine vessel trajectories, neural networks have been widely used for their ability to process large datasets and discover long-term patterns hidden in vessel trajectories.Because of the robust adaptability, the earliest form of neural network, including the multi-layer perceptron (MLP) [22] and artificial neural network (ANN) [23][24] played a significant role in traffic and marine vessel trajectory prediction. Nevertheless, despite their wide applications, these neural networks exhibit low interpretability. Additionally, they present substantial challenges in terms of spatial and temporal information processing capability [25] since these networks are not equipped to handle such characteristics.
The exploration of incorporating sequential temporal patterns into marine ship trajectory prediction has motivated researchers to investigate the potential application of recurrent neural networks (RNNs) [5]. However, RNNs encounter challenges in capturing long-term dependencies within a sequence due to the issue of vanishing gradients during backpropagation [26]. As a result, the limited long-term memory of these networks can hinder their performance when the data contain significant long-term dependencies [27][28][29]. Two prominent variations of recurrent neural networks (RNNs), specifically long short-term memory (LSTM) [30][31] and gated recurrent unit (GRU) [32], have garnered substantial attention for their remarkable ability to uncover underlying patterns within extended input sequences, proving particularly advantageous for trajectory prediction.
Further advancements in research have led to the utilization of more efficient variants of LSTM and GRU, such as bidirectional LSTM (Bi-LSTM) [33][34], bidirectional GRU (Bi-GRU) [35], context-aware LSTM (C-LSTM) model [36], and multi-step prediction LSTM (MP-LSTM) [37]. Distinct from traditional LSTM, Bi-LSTM has the ability to process data from both past and future contexts. This bidirectional information processing, encompassing both forward and backward information, empowers Bi-LSTM to capture a comprehensive understanding of the sequence. Consequently, numerous innovative models based on Bi-LSTM have been proposed for ship trajectory prediction. However, these models often exhibit significant computational complexity and limited generalization capabilities. The design parameters of these neural network-based frameworks are adjusted in real-time as the vessel progresses, enabling them to identify all potential trajectories a vessel may follow and reconstruct (predict) its trajectories for future time points [24]. Additionally, LSTM networks have demonstrated remarkable multitasking performance [38].
Another neural network, the convolutional neural network (CNN), originally devised to address computer vision problems, has also been explored for the trajectory prediction and classification of the tracks [38] as it can help capture the spatial patterns exist in the trajectory data. Instead of using the original features, several methods advocate the use of latent features derived from the neural network architecture. These methods leverage latent space representation using variational recurrent autoencoder (VRAE) [39] or LSTM [40]. These latent features can capture the spatial patterns present in the data. Temporal ordering and attention maps are also proven to be effective for object tracking [41].
Instead of using the original features, several methods advocate the use of latent features derived from the neural network architecture. These methods leverage latent space representation using variational recurrent autoencoder (VRAE) [39] or LSTM [40]. These latent features can capture the spatial patterns present in the data. Temporal ordering and attention maps are also proven to be effective for object tracking [41].
In addition to conventional deep learning approaches, the research field has expanded to include the application of hybrid deep learning architectures directly to raw datasets. This advancement goes beyond transforming data into a latent space and aims to reveal both temporal and spatial relationships among features. It has proven to be particularly effective in extracting spatio-temporal relationships within the AIS dataset. Hybrid deep learning-based models for ship trajectory prediction, such as the integration of bidirectional LSTM and RNN (BLSTM-RNN) [42] and CNN-LSTM-SE [43], have emerged as notable techniques due to their rapid learning and adaptability capabilities. These approaches excel in producing highly accurate results when dealing with complex and dynamic trajectory data.
However, it is important to note that these methods primarily focus on predicting the next points by considering the sequence of vessel nodes. This differs from track association, which aims to link vessels to their respective tracks. Furthermore, following the prediction route would require a separate prediction model for each vessel, which can complicate the tracking process when dealing with more than ten vessels. The proposed 1D CNN-LSTM model can overcome all these issues and classify multiple vessels by capturing the spatial and temporal patterns hidden in the data.


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