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.

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.

Seabed-to-space situational awareness (S3A) aims to organize, fuse, and synthesize the massive volume of information collected from heterogeneous sensors, i.e., underwater, terrestrial, and space-based sensors, and therefrom extract knowledge thence available to defence operators, enabling informed decision-making. Heterogeneous sensors provide observations of targets in different domains (e.g., air, water surface, undersea), and with different modalities, perspectives, latencies, and update rates. They complement each other, and an effective approach is needed to combine the data they generate. This paper introduces a comprehensive framework for multi-target tracking based on the sum-product algorithm (SPA) that models the different characteristics of the sensors and handles the appearance of targets in a complex multi-domain environment both through spontaneous births and through spawning from existing targets. The efficacy of this approach is demonstrated through a simulated maritime scenario informed by real-world observation streams.

We investigate the performance of machine learning (ML) binary classification models in terms of error probabilities to detect targets (specifically, ships) from optical satellite imagery. The ML approach uses a Data-Driven Decision Function (D3F), learned during training, as a decision statistic. Inspired by the Large Deviations Analysis (LDA), we observe that, under suitable conditions, the detection error probabilities decrease as the number of pixels occupied by the target(s) in the image increases. Coherent with the LDA, the D3F follows a Gaussian distribution, conditioned to parameters like the background. We propose a methodology to set a desired false alarm rate and estimate the correct decision probability, beneficial for various remote sensing applications, including 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.

Today, the maritime domain is at the cusp of a new era, driven by technological advances in automation, robotics, multisensor perception, and artificial intelligence (AI), together with digitalization and connectivity. Smart ship infrastructure and technology, remotely controlled and autonomous ship operation to improve safety, security, cost efficiency, and sustainability are the future of maritime transportation[1], representing now the engine of 90% of global trade[2]. Ships will soon benefit from recent developments in sensors, telecommunications, and computing technologies to turn the smart shipping revolution into reality[3]and[4], as it has already happened for autonomous vehicles such as driverless cars, aerial drones, unmanned (or remotely piloted) aircraft, and underwater vehicles.

In this paper we present how automatic maritime anomaly detection tools can be successfully applied in real-world situations such as the major event of the container vesselEver Given, which grounded in the Suez Canal on March 23rd 2021. The anomaly detector is designed to process the available sequence of Automatic Identification System (AIS) reports, information from ground-based or satellite radar systems if available, and contextual information defining the expected nominal behavior of navigation. A statistical hypothesis testing procedure is sequentially run to decide whether or not a deviation from the nominal behavior happened within a specific time period, for instance two consecutive data points. We show, based on the recorded AIS data from theEver Given, that the proposed detector could have been triggered and alerted to anomalous behavior fully 19 minutes before the grounding.

This paper develops an easily-implementable version of Page's CUSUM quickest-detection test, designed to work in certain composite hypothesis scenarios with time-varying data statistics. The decision statistic can be cast in a recursive form and is particularly suited for on-line analysis. By back-testing our approach on publicly-available COVID-19 data we find reliable early warning of infection flare-ups, in fact sufficiently early that the tool may be of use to decision-makers on the timing of restrictive measures that may in the future need to be taken.

In this paper, we address the problem of predicting vessel trajectories based on Automatic Identification System (AIS) data. The goal is to learn the predictive distribution of maritime traffic patterns using historical data during the training phase, in order to be able to forecast future target trajectory samples online on the basis of both the extracted knowledge and the available observation sequence. We explore neural sequence-to-sequence models based on the Long Short-Term Memory (LSTM) encoder-decoder architecture to effectively capture long-term temporal dependencies of sequential AIS data and increase the overall predictive power. The experimental evaluation on a real-world AIS dataset demonstrates the effectiveness of sequence-to-sequence recurrent neural networks (RNNs) for vessel trajectory prediction and shows their potential benefits compared to model-based methods.

In this article, we present a fully analytical model for the evaluation of the electromagnetic (EM) field scattered from a composite target in a generic bistatic configuration. The scenario comprises a rectangular parallelepiped target with smooth dielectric faces lying over a rough background surface, modeled as a stochastic process. The single- and multiple-bounce scattering contributions arising from the target, the rough background, and their interactions have been derived under the Kirchhoff approximation (KA)-geometrical optics (GO) solution. This framework enables the evaluation of the bistatic radar cross section (RCS) of the considered composite target via closed-form expressions. The proposed model exhibits good agreement with the literature results based on accurate and well-established numerical methods. Our analytical model is therefore proposed as a valid alternative to numerical techniques, being able to provide reliable results at a negligible computational burden. Finally, the role of the main scene parameters, i.e., target orientation, surface roughness, and polarization in the bistatic RCS of the target, have been analyzed and discussed.

Piecewise mean-reverting stochastic processes have been recently proposed and validated as an effective model for long-term object prediction. In this paper, we exploit the Ornstein-Uhlenbeck (OU) dynamic model to represent an anomaly as any deviation of the long-run mean velocity from the nominal condition. This amounts to modeling the anomaly as an unknown switching control input that can affect the dynamics of the object. Under this model, the problem of joint anomaly detection and tracking can be addressed within the Bayesian random set framework by means of a hybrid Bernoulli filter (HBF) that sequentially estimates a Bernoulli random set (empty under nominal behavior) for the unknown long-run mean velocity, and a random vector for the kinematic state of the object. An additional challenge is represented by the fact that two extra parameters, i.e. the reversion rate and the noise covariance of the underlying OU process, need to be specified for Bayes-optimal prediction. We propose a multiple-model adaptive filter (MMA-HBF) for anomaly detection, tracking and simultaneous estimation of the OU unknown parameters. The effectiveness of these tools is demonstrated on a simulated maritime scenario.

In this work, we propose a data driven trajectory forecasting algorithm that utilizes both recorded historical and streaming trajectory observations. The algorithm performs Bayesian inference on a directed graph the walks on which represent stochastic change point models of trajectory classes. Parameter distributions of these models are learnt from recorded trajectories. Forecasting is then made by calculating the class - or, walk- probabilities and corresponding predictive distributions for a given stream of location and velocity observations. This approach is tailored for the maritime domain and automatic identification system (AIS) data exploitation through the use of an Ornstein-Uhlenbeck process driven stochastic process model that captures vessel motion characteristics. We demonstrate the efficacy of this approach on a real data set.

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.

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.

Global Navigation Satellite System-Reflectometry (GNSS-R), is succesfully employed for ocean altimetric and scatterometric applications. Recently, it has been suggested that GNSS-R can also be used for ship detection applications. To this purpose, an accurate electromagnetic modeling of the bistatic radar cross section of a ship lying over the sea surface would be very helpful. However, existing models are typically limited to monostatic configurations, thus restricting their applicability in multistatic scenarios, such as GNSS-R systems. In this work, we show a procedure to determine the bistatic radar cross section of a ship target, under the geometrical optics approximation. Numerical results show the impact of the geometry of acquisition and polarization on the bistatic radar cross section.

In this paper, a comparative study of spaceborne Global Navigation Satellite System (GNSS)-Reflectometry for ship detection applications is provided. The analysis is conducted by evaluating the impact of 1) the acquisition geometry and 2) the received signal polarization on ship detectability in GNSS-R data. In particular, the backscattering acquisition geometry is demonstrated to be more suitable for ship detection applications, thus allowing for the detection of 20 m-length ships. Even very large ships are hardly detectable in the conventional forward-scattering geometry. Moreover, receiving right-hand circular polarization is demonstrated to provide significant improvements of the signal-to-noise-plus-clutter with respect to the conventional left-hand circular polarization channel, conventionally exploited in GNSS-R remote sensing. The study is based on a numerical tool for the bistatic radar cross section of the ship, which is presented in a companion paper.

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.

Ship traffic monitoring is a foundation for many maritime security domains, and monitoring system specifications underscore the necessity to track vessels beyond territorial waters. However, vessels in open seas are seldom continuously observed. Thus, the problem of long-term vessel prediction becomes crucial. This paper focuses attention on the performance assessment of the Ornstein-Uhlenbeck (OU) model for long-term vessel prediction, compared with usual and well-established nearly constant velocity (NCV) model. Heterogeneous data, such as automatic identification system (AIS) data, high-frequency surface wave radar data, and synthetic aperture radar data, are exploited to this aim. Two different association procedures are also presented to cue dwells in case of gaps in the transmission of AIS messages. Suitable metrics have been introduced for the assessment. Considerable advantages of the OU model are pointed out with respect to the NCV model.

We describe how we leveraged best practices in big data processing pipeline design and visual analytics to prototype the Maritime Patterns-of-Life Information Service (MPoLIS), an information product currently under development at the NATO Centre for Maritime Research and Experimentation (CMRE). MPoLIS supports the maritime industry, governments, and international organizations with visual analytics on vessel traffic in seaports. It addresses three main requirements: a) storing and processing large amounts of data; b) on-demand availability of statistical summaries of vessel traffic in ports; c) intuitive and interactive interface for subject matter experts (SMEs) in the maritime domain. MPoLIS has contributed to building a data-driven, self-service analytics culture within NATO and has been sanctioned for use in support of maritime situational awareness (MSA) in ongoing NATO operations.

Seaports play a vital role in the global economy, as they operate as the connection corridors to all other modes of transport and as engines of growth for the wider region. But ports today are faced with numerous unique challenges and for them to remain competitive, significant investments are required. In support of greater transparency in policy making, decisions regarding investment need to be supported by data-driven intelligence. It is often an overlooked fact that seaports do not remain static over time; such spatial units often evolve according to environmental patterns both in size but also connectivity and operational capacity. As such any valid decision making regarding port investment and policy making, essentially needs to take into account port evolution over time and space. In this work, we leverage the huge amounts of vessel data that are progressively becoming available through the Automatic Identification System (AIS) and distributed machine learning to define a seaport's extended area of operation. Specifically, we present our adaptation of the well-known KDE algorithm to the map-reduce paradigm, and report results on the port of Shanghai.

In this letter, we study the problem of estimating the long-run mean of the Ornstein-Uhlenbeck (OU) stochastic process and its effect on the long-term prediction of future vessel states, which is a crucial problem for Maritime Situational Awareness (MSA). We employ a sample mean estimator (SME) to estimate the key OU parameter from the observations, computing the closedform SME covariance error in both the random and constant sampling time regimes, providing a fundamental building block of the overall long-term state prediction covariance. We show also that the SME is: √n-consistent when the sampling time is random; asymptotically efficient when the sampling time is constant; and very close to the Cramer-Rao lower bound in the cases of practical interest for MSA.

Computational Maritime Situational Awareness (MSA) supports the maritime industry, governments, and international organizations with machine learning and big data techniques for analyzing vessel traffic data available through the Automatic Identification System (AIS). A critical challenge of scaling computational MSA to big data regimes is integrating the core learning algorithms with big data storage modes and data models. To address this challenge, we report results from our experimentation with MongoDB, a NoSQL document-based database which we test as a supporting platform for computational MSA. We experiment with a document model that avoids database joins when linking position and voyage AIS vessel information and allows tuning the database index and document sizes in response to the AIS data rate. We report results for the AIS data ingested and analyzed daily at the NATO Centre for Maritime Research and Experimentation (CMRE).