With the rapid proliferation of Machine-Learning (ML) and Deep Learning (DL) based decision systems, properly characterizing their often unpredictable performance is a key challenge. In this work we introduce the notion of a Sequential Data-Driven Decision Function (S-D3F), as a data-driven analogue to the Sequential Probability Ratio Test (SPRT). Key performance metrics for sequential analysis are shown suitable for use in analyzing the S-D3F’s performance both in terms of error probabilities and average stopping times. The notion of rate function from large deviations theory is extended to this S-D3F test, and it is shown that with a sequential approach the S-D3F can outperform its Fixed Sample-Size (FSS) counterpart in the D3F as the average number of samples needed to make a decision diverges.

Maritime situational awareness (MSA) refers to the effective understanding of activities related to maritime environment. Central to MSA, particularly concerning non-military vessels, is the automatic identification system (AIS), which provides real-time data on vessel movements. However, anomalies such as intentional AIS transponder disablement pose significant challenges to MSA, potentially indicating illicit activities. This paper introduces the Dark-VADER (dark vessel AIS delay event recognition) algorithm, designed to detect AIS switchoffs by comparing the frequency of message reception from a vessel under examination with that of neighboring vessels. Leveraging a statistical hypothesis testing procedure based on a Bernoulli process, the algorithm distinguishes between normal and anomalous behavior. Validation using real-world AIS data confirms the fitness of the selected distribution model for times between message arrivals, essential for the algorithm’s operation. Overall, this preliminary work provides a foundational framework for improving maritime AIS anomaly detection, with avenues for future development towards more robust and dynamic approaches.

This paper explores filtering methods to protect range-based localization systems from spoofing attacks on vehicles with directional receivers. It focuses on scenarios where multiple spoofers, potentially from unmanned vehicles, disrupt vehicle localization by strategically positioning themselves between the target and the transmitter. The paper introduces an Adaptive Resilience Navigation Filter (ARNF) that detects ongoing attacks, identifies compromised signals, and mitigates their effects using statistical hypothesis testing. Simulations demonstrate the ARNF’s effectiveness under realistic Global Navigation Satellite System conditions, comparing it with the 2-Stage Extended Kalman Fitter and an ideal Clairvoyant Extended Kalman Filter.

Maritime surveillance, characterized by high-volume data streams, necessitates effective methods for the automatic extraction of meaningful information and accurate classification of vessel patterns. We introduce MARITRAC (maritime trajectory classification), an innovative approach that leverages MASK R-CNN, a state-of-the-art computer vision algorithm, to classify maritime trajectories. The key idea behind MARITRAC is to convert trajectory data into images that capture spatiotemporal patterns. These trajectory images are then used as input to a MASK R-CNN model that is trained on synthetically generated data to classify different types of maritime trajectories. By combining computer vision techniques with trajectory data analysis, MARITRAC provides an effective and automated method for characterizing and distinguishing between different maritime behaviors. To overcome the notable lack of labeled trajectory anomaly datasets, the training is performed with a set of synthetically generated trajectories, created using the piecewise Ornstein-Uhlenbeck dynamic model. The effectiveness of MARITRAC is demonstrated through application and evaluation in two main experiments, involving both synthetic and real-world data. The approach showcases promising performance in classifying maritime trajectories, and the results position MARITRAC as a valuable tool for real-time maritime surveillance.

Maneuvering target tracking, where the system undergoes abrupt changes in the underlying motion model, can be challenging. We propose a model-based deep learning approach for prediction of maneuvering targets to exploit partial knowledge of the system physics-based models during training, without requiring an explicit characterization or fine tuning of model parameters. We formulate a supervised training scheme to learn the dynamics of state-space models and capture the jump processes governing model transitions by minimizing the prediction loss of an encoder-decoder network from model-based generated data. The effectiveness of the proposed method is demonstrated in two maneuvering target tracking scenarios using synthetic and real-world test data. The results show that the model-based encoder-decoder network achieves notably improved performance in terms of target prediction compared to conventional multiple-model solutions, especially when facing model inaccuracies, jumps, and dominant nonlinearities during target maneuvers.

Inspired by the fair regularity of the motion of ships, we present a method to derive a representation of the commercial maritime traffic in the form of a graph, whose nodes represent way-point areas, or regions of likely direction changes, and whose edges represent navigational legs with constant cruise velocity. The proposed method is based on the representation of a ship's velocity with an Ornstein-Uhlenbeck process and on the detection of changes of its long-run mean to identify navigational way-points. In order to assess the graph representativeness of the traffic, two performance metrics are introduced, leading to distinct graph construction criteria. Finally, the proposed method is validated against real-world Automatic Identification System data collected in a large area.

This paper presents a solution to the problem of sequential joint anomaly detection and tracking of a target subject to switching unknown path deviations. Based on a dynamic model described by Ornstein-Uhlenbeck (OU) stochastic processes, the anomaly is represented by a target (e.g., a marine vessel) that deviates from a preset route by changing its nominal mean velocity. The Random Finite Set (RFS) framework is used to represent the switching nature of target's anomalous behavior in the presence of spurious measurements and detection uncertainty. Combining these two ingredients, the problem of jointly detecting target's path deviations and estimating its kinematic state can be formulated within the Bayesian framework, and analytically solved by means of a hybrid Bernoulli filter that sequentially updates the joint posterior density of the unknown OU velocity input (a Bernoulli RFS) and of the target's state random vector. We illustrate the effectiveness of the proposed filter, implemented in Gaussian-mixture form, in a simulated scenario of vessel tracking for maritime traffic monitoring.

A data fusion technique aiming at combining observations from two classes of sensors is proposed. The first class consists of sensors that produce periodic noisy observations of the targets; moreover, they may also miss the targets or generate false alarms. Sensors belonging to the second class, instead, do not generate false alarms, and provide aperiodic noisy observations of the targets that may have an identity. The problem is formalised with specific application to the maritime domain, in which radar sensors and the Automatic Identification System (AIS) are selected as representatives of the two classes, respectively. A Bayesian framework is developed and a detection-estimation problem is formulated, which is then efficiently solved with the use of a Belief Propagation (BP) message passing scheme. The performance and the effectiveness of the proposed algorithm is evaluated in a simulated scenario.

The Bernoulli filter (BF) is a Bayes-optimal method for target tracking when the target can be present or absent in unknown time intervals and the measurements are affected by clutter and missed detections. We propose a distributed particle-based multisensor BF algorithm that approximates the centralized multisensor BF for arbitrary nonlinear and non-Gaussian system models. Our distributed algorithm uses a new extension of the likelihood consensus (LC) scheme that accounts for both target presence and absence and includes an adaptive pruning of the LC expansion coefficients. Simulation results for a heterogeneous sensor network with significant noise and clutter show that the performance of our algorithm is close to that of the centralized multisensor BF.

We propose a Bayesian multisensor-multitarget tracking framework, which adapts to randomly changing conditions by continually estimating unknown model parameters along with the target states. The time-evolution of the model parameters is described by a Markov chain and the parameters are incorporated in a factor graph that represents the statistical structure of the tracking problem. We then use the belief propagation (BP) message passing scheme to calculate the marginal posterior distributions of the targets and the model parameters in an efficient way that exploits conditional statistical independencies. As a concrete example, we develop an adaptive BP-based multisensor-multitarget tracking algorithm for maneuvering targets with multiple dynamic models and sensors with unknown and time-varying detection probabilities. The performance of the proposed algorithm is finally evaluated in a simulated scenario.

In this work, we consider the problem of algorithmically predicting rendezvous among vessels based on their trajectory forecasts in a maritime environment. The problem is treated as hypothesis testing on the expected value of the distance between trajectories. We relate this quantity to the first and second degree Wasserstein distances between trajectory forecast distributions. These distributions are obtained using integrated Ornstein-Uhlenbeck process models with the trajectory measurements collected so far. Building upon these results, we propose an algorithm which traverses the trajectories observed so far for detecting rendezvous over a rolling time horizon. We demonstrate the efficacy of the proposed algorithm using simulations.

A novel anomaly detection procedure is presented, based on the Ornstein-Uhlenbeck (OU) mean-reverting stochastic process. The considered anomaly is a vessel that deviates from a planned route, changing its nominal velocity. In order to hide this behavior, the vessel switches off its Automatic Identification System (AIS) device for a certain time, and then tries to revert to the previous nominal velocity. The decision that has to be taken is either declaring that a deviation happened or not, relying only upon two consecutive AIS contacts. A proper statistical hypothesis testing procedure that builds on the changes in the OU process long-term velocity parameter of the vessel is the core of the proposed approach and enables for the solution of the anomaly detection problem.

Building on a novel methodology based on the Ornstein-Uhlenbeck (OU) process to perform accurate long-term predictions of future positions of ships at sea, we present a statistical approach to the detection of abrupt changes in the process parameter that represents the desired velocity of a ship. Proceeding from well-established change detection techniques, the proposed strategy is also computationally efficient and fit well with big data processing models and paradigms. We report results with a large real-world Automatic Identification System (AIS) data set collected by a network of terrestrial receivers in the Mediterranean Sea from June to August 2016.