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.

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.

This paper addresses the problem of multitarget tracking using a network of mobile sensors with unknown positions. In contrast to commonly-used approaches which split the sensor localization and target tracking into two different sub-problems, we propose a holistic approach for joint localization and tracking. The theory of graphical models is used to describe the statistical relationship between sensors, targets, and measurements. To jointly infer the states of sensors and targets, we use the statistical processing of belief propagation.

The necessity of long-range underwater surveillance has strongly increased in the last decades, and low-frequency active sonar (LFAS) systems seem to fulfill this need. However, in littoral environments with shallow water LFAS may suffer from an elevate number of false alarms. In this context, the capability to distinguish between object-generated and clutter-generated detections is crucial. This paper describes a multiobject tracking framework based on the sum-product algorithm that exploits the information provided by a convolutional neural network that classifies the LFAS detections. The effectiveness of the proposed approach is demonstrated both in a simulated and in a real underwater scenario.

Multitarget tracking (MTT) is a challenging task that aims at estimating the number of targets and their states from measurements provided by one or multiple sensors. Additional information, such as imperfect estimates of target classes provided by a classifier, can facilitate the target-measurement association and thus improve MTT performance. In this letter, we describe how a recently proposed MTT framework based on the sum-product algorithm can be extended to efficiently exploit class information. The effectiveness of the proposed approach is demonstrated by simulation results.

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.

The sum-product algorithm (SPA) was recently shown to provide a scalable methodology for multitarget tracking (MTT) using multiple sensors. Here, we focus on another advantage of the SPA frame-work, namely, its capacity for Bayesian fusion of heterogeneous data sources and auxiliary information. We develop extensions of the SPA-based multisensor MTT algorithm that integrate data from an auxiliary surveillance system and geographic information about standard target routes. The effectiveness of our approach is demonstrated for a simulated scenario and for a real 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.

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.

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.

Situation-aware technologies enabled by multitarget tracking will lead to new services and applications in fields such as autonomous driving, indoor localization, robotic networks, and crowd counting. In this tutorial paper, we advocate a recently proposed paradigm for scalable multitarget tracking that is based on message passing or, more concretely, the loopy sum-product algorithm. This approach has advantages regarding estimation accuracy, computational complexity, and implementation flexibility. Most importantly, it provides a highly effective, efficient, and scalable solution to the probabilistic data association problem, a major challenge in multitarget tracking. This fact makes it attractive for emerging applications requiring real-time operation on resource-limited devices. In addition, the message passing approach is intuitively appealing and suited to nonlinear and non-Gaussian models. We present message-passing-based multitarget tracking methods for single-sensor and multiple-sensor scenarios, and for a known and unknown number of targets. The presented methods can cope with clutter, missed detections, and an unknown association between targets and measurements. We also discuss the integration of message-passing-based probabilistic data association into existing multitarget tracking methods. The superior performance, low complexity, and attractive scaling properties of the presented methods are verified numerically. In addition to simulated data, we use measured data captured by two radar stations with overlapping fields-of-view observing a large number of targets simultaneously.

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.

In modern heterogeneous sensor networks huge volumes of information rapidly flow across the system, and it is often too difficult or costly to associate data to the sensors that produced them. Then, the set of observations appears to be unlabeled: What comes from whom? We study the classical problem of detecting a known signal embedded in Gaussian noise, but under the peculiar assumption that the signal samples have been scrambled (e.g., in time or space) in an unknown way. Our study sheds light on questions like: How much detection performance is contained in the samples' values and how much in their ordering? Are there nicely-performing detectors with affordable computational complexity?

This letter deals with inverse synthetic aperture radar (ISAR) autofocusing of noncooperative moving targets. The relative motion between the target and the sensor, which provides the angular diversity necessary for ISAR imagery, is also responsible for unwanted range migration and phase changes generating defocusing. In the case of noncooperative targets, the relative motion is unknown: the ISAR needs, hence, to implement an autofocus step [motion compensation (MoCo)] to achieve high resolution imaging. This task is typically carried out via the optimization of functionals based on general image quality parameters. In this letter, we propose the use of a fast and accurate MoCo algorithm based on the estimation of the Doppler parameters, thus fully coping with the nature of the imaging system. The effectiveness of the proposed method is proven on both simulated data and data acquired by operational systems.

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.

The large spread of sensors and smart devices in urban infrastructures are motivating research in the area of the Internet of Things (IoT) to develop new services and improve citizens’ quality of life. Sensors and smart devices generate large amounts of measurement data from sensing the environment, which is used to enable services such as control of power consumption or traffic density. To deal with such a large amount of information and provide accurate measurements, service providers can adopt information fusion, which given the decentralized nature of urban deployments can be performed by means of consensus algorithms. These algorithms allow distributed agents to (iteratively) compute linear functions on the exchanged data, and take decisions based on the outcome, without the need for the support of a central entity. However, the use of consensus algorithms raises several security concerns, especially when private or security critical information is involved in the computation. In this article we propose ODIN, a novel algorithm allowing information fusion over encrypted data. ODIN is a privacy-preserving extension of the popular consensus gossip algorithm, which prevents distributed agents from having direct access to the data while they iteratively reach consensus; agents cannot access even the final consensus value but can only retrieve partial information (e.g., a binary decision). ODIN uses efficient additive obfuscation and proxy re-encryption during the update steps and garbled circuits to make final decisions on the obfuscated consensus. We discuss the security of our proposal and show its practicability and efficiency on real-world resource-constrained devices, developing a prototype implementation for Raspberry Pi devices.

Radar imaging is typically based on linear models of the electromagnetic scattering phenomenon. These models are robust and computationally efficient, but do not account for mutual interactions among targets in the scene and between the targets and the surrounding environment. As a result, the radar images are characterized by spurious targets, i.e., multipath ghosts, which appear at positions where no physical targets exist. In this letter, we compare two key approaches for clutter suppression. The first approach applies multiplicative fusion of the images corresponding to subapertures of the deployed array, whereas the second approach is based on coherence factor filtering, which enhances the image quality by suppressing low-coherence features. We assess the performance of these two methods in terms of imaging and detection capabilities. Numerical results based on synthetic data are reported to support the comparative analysis.

We examine the interplay between learning and privacy over multiagent consensus networks. The learning objective of each individual agent consists of computing some global network statistic, and is accomplished by means of a consensus protocol. The privacy objective consists of preventing inference of the individual agents' data from the information exchanged during the consensus stages, and is accomplished by adding some artificial noise to the observations (obfuscation). An analytical characterization of the learning and privacy performance is provided, with reference to a consensus perturbing and to a consensus-preserving obfuscation strategy.

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.

This paper examines the close interplay between cooperation and adaptation for distributed detection schemes over fully decentralized networks. The combined attributes of cooperation and adaptation are necessary to enable networks of detectors to continually learn from streaming data and to continually track drifts in the state of nature when deciding in favor of one hypothesis or another. The results in this paper establish a fundamental scaling law for the steady-state probabilities of miss detection and false alarm in the slow adaptation regime, when the agents interact with each other according to distributed strategies that employ small constant step-sizes. The latter are critical to enable continuous adaptation and learning. This paper establishes three key results. First, it is shown that the output of the collaborative process at each agent has a steady-state distribution. Second, it is shown that this distribution is asymptotically Gaussian in the slow adaptation regime of small step-sizes. Third, by carrying out a detailed large deviations analysis, closed-form expressions are derived for the decaying rates of the false-alarm and miss-detection probabilities. Interesting insights are gained from these expressions. In particular, it is verified that as the step-size μ decreases, the error probabilities are driven to zero exponentially fast as functions of 1μ, and that the exponents governing the decay increase linearly in the number of agents. It is also verified that the scaling laws governing the errors of detection and the errors of estimation over the network behave very differently, with the former having exponential decay proportional to 1μ, while the latter scales linearly with decay proportional to μ. Moreover, and interestingly, it is shown that the cooperative strategy allows each agent to reach the same detection performance, in terms of detection error exponents, of a centralized stochastic-gradient solution. The results of this paper are illustrated by applying them to canonical distributed detection problems.

In [1], an important step toward the characterization of distributed detection over adaptive networks has been made by establishing the fundamental scaling law of the error probabilities. However, empirical evidence reported in [1] revealed that a refined asymptotic analysis is necessary in order to capture the exact impact of network connectivity on the detection performance of each individual agent. Here we address this open issue by exploiting the framework of exact asymptotics.

In practical target tracking problems, the target detection performance of the sensors may be unknown and may change rapidly with time. In this work we develop a target tracking procedure able to adapt and react to time-varying changes of the detection capability for a network of sensors. The proposed tracking strategy is based on a Bayesian framework, in which the dynamic target state is augmented to include the sensor detection probabilities. The method is validated using computer simulations and real-world experiments conducted by the NATO Science and Technology Organization (STO) - Centre for Maritime Research and Experimentation (CMRE).

In the last years significant effort has been dedicated to prove that increased information and/or better performance can be retrieved in radar and radar imaging using a network of cooperating sensors. In this paper, data acquired by two Inverse Synthetic Aperture Radar sensors observing a target from different points of view in the long range surveillance operative case is exploited to estimate both radial and cross-radial components of a target's translational motion. Simulated objective functions prove the feasibility of the proposed techniques, confirmed by the analysis of the results of their application against real data acquired by the Radar Sensor Network installed at the NATO Centre for Maritime Research and Experimentation.

Recent developments in high resolution sensors have encouraged the use of Extended Target Tracking (ETT) algorithms specifically designed to deal with targets that generate more than one detection per frame. At the same time, the availability of more powerful computational resources enable the use of soft computing techniques that yield a target probability, instead of a hard decision. This paper proposes a realistic target model feasible for an Extended Target - Track before Detect framework. Physical phenomena related to the acquisition of high resolution X-band marine radar data are considered. Real radar data is used to assess the superior performance of the featured model with respect to previous approaches. Results show that the realistic model provides better estimations of the target velocity and size.

The work addresses the problem of compensating the distortion effects induced by the translational motion of moving targets in Inverse Synthetic Aperture Radar (ISAR) imaging systems. The ISAR motion compensation is the most crucial step in the Autofocusing ISAR technique; this task is typically solved by implementing exhaustive search algorithms by adopting proper functionals based f.i. on image entropy or image contrast. In this work, we discuss an innovative and fast motion compensation procedure that is based on the estimation of two Doppler key Parameters: the Doppler Centroid and the Doppler Rate, which are related to the target motion parameters. The effectiveness of the proposed method is tested on real data acquired by a static Frequency Modulated Continuous Wave radar with an azimuth wide beamwidth; the radar is installed near the inner harbor of La Spezia (Italy) and it owned to the Centre for Maritime Research and Experimentation of the North Atlantic Treaty Organization (CMRE-NATO).

X-band Marine radar systems are low-cost tools for monitoring multiple targets in a surveillance area. Although they may suffer from several sources of interference, high resolution measurements in both space and time can be provided. Such features offer the opportunity to get accurate information not only about the targets' kinematics, as other conventional sensors, but also about the targets' extent. In this paper, a signal processing chain composed by a detector and a joint probabilistic data association tracker is proposed to address the problem of tracking using X-band Marine radar data. Estimations of both the targets' kinematics, i.e. positions and velocities, and length and width, are provided. The performance assessment, conducted on real data acquired by an X-band Marine radar located in the Gulf of La Spezia, Italy, demonstrates the ability of the processing chain to obtain high tracking performance with a limited computational burden.

In recent years, low-power high-frequency surface-wave radars have received significant attention thanks to their over-the-horizon coverage capability and the continuous-time operation mode. These radars have become effective long-range early-warning tools for maritime situational awareness applications. In this paper a knowledge-based multi-target tracking algorithm is described. The advantages in using a prior information on ship traffic are assessed exploiting real data acquired by two high-frequency surface-wave radars. The outcomes confirm the ability of the proposed approach to better follow targets with a time-on-target increment up to 30% with respect to existing methods. A reduction of the track fragmentation up to 20% is also observed.

Tracking moving targets hidden behind visually opaque structures as building walls is a crucial issue in many surveillance, rescue, and security applications. The electromagnetic waves at the low microwave frequency range penetrate into common building materials and thereby enable the radar to expose behind the wall scene. However, due to complexity of the scattering scenario, the radar signal undergoes multipath propagation phenomena. These typically manifest themselves as environmental clutter which may impair detection and tracking of true targets. In this paper, a signal processing strategy is proposed to track multiple extended targets in a scene by means of a wide-band monostatic through-wall radar. The system collects data sets at regular time steps which are first processed by a microwave tomographic technique. Then, a detection/tracking stage is implemented in order to track the position and dynamics of targets in real time. An extended target-tracking approach is applied to properly exploit at the tracking stage the information related to extended nature of targets. The effectiveness of the proposed signal processing chain is assessed by numerical tests based on full-wave data pertaining to an indoor scenario.

X-band marine radar systems represent a flexible and low-cost tool for the tracking of multiple targets in a given region of interest. Although suffering several sources of interference, e.g., the sea clutter, these systems can provide high-resolution measurements, both in space and time. Such features offer the opportunity to get accurate information not only about the target position/motion but also about the targets size. Accordingly, in this paper, we exploit emergent extended target tracking (ETT) methodologies in which the target state, typically position/velocity/acceleration, is augmented with the target length and width. In this paper, we propose an ETT procedure based on the popular probability hypothesis density filter, and in particular, we describe the extended target state through the gamma Gaussian inverse Wishart model. The comparative simplicity of the used models allows us to meet the real-time processing constraint required for the practical surveillance purposes. Real-world data from an experimental and operational campaign, collected during the recovery operations of the Costa Concordia wreckage in October 2013, are used to assess the performance of the proposed target tracking methodology. The full signal processing chain is implemented, and considerations of the experimental results are provided. Important nonideal effects, common to every marine radar, are observed and discussed in relation to the assumptions made for the tracking procedure.

These last decades spawned a great interest toward low-power high-frequency (HF) surface-wave (SW) radars for ocean remote sensing. By virtue of their over-the-horizon coverage capability and continuous-time mode of operation, these sensors are also effective long-range early warning tools in maritime situational awareness applications providing an additional source of information for target detection and tracking. Unfortunately, they also exhibit many shortcomings that need to be taken into account, and proper algorithms need to be exploited to overcome their limitations. In this paper, we develop a knowledge-based (KB) multitarget tracking methodology that takes advantage of a priori information on the ship traffic. This a priori information is given by the ship sea lanes and by their related motion models, which together constitute the basic building blocks of a variable structure interactive multiple model procedure. False alarms and missed detections are dealt with using a joint probabilistic data association rule and nonlinearities are handled by means of the unscented Kalman filter. The KB-tracking procedure is validated using real data acquired during an HF-radar experiment in the Ligurian Sea (Mediterranean Sea). Two HFSW radar systems were operated to develop and test target detection and tracking algorithms. The overall performance is defined in terms of time-on-target, false-alarm rate (FAR), track fragmentation (TF), and accuracy. A full statistical characterization is provided using one month of data. A significant improvement of the KB-tracking procedure, in terms of system performance, is demonstrated in comparison with a standard joint probabilistic data association tracker recently proposed in the literature to track HFSW radar data. The main improvement of our approach is the better capability of following targets without increasing the FAR. This increment is much more evident in the region of low FAR, where it can be over the 30% for both the HFSW radar systems. The KB-tracking exhibits on average a reduction of the TF of about the 20% and the 13% of the utilized HFSW-radar systems.

In distributed inference, local cooperation among network nodes can be exploited to enhance the performance of each individual agent, but a challenging requirement for networks operating in dynamic real-world environments is that of adaptation. The interplay between these two fundamental aspects of cooperation and adaptation has been investigated in recent years in the context of estimation problems. Less explored in the literature is the case of detection, which is our focus. Capitalizing on the powerful tool of large deviations analysis, we show how to design and characterize the performance of diffusion strategies that reconcile both needs of adaptation and detection in decentralized systems.

This paper presents a Bayesian multi-sensor tracking strategy for a network of autonomous underwater vehicles (AUVs) for the purpose of anti-submarine warfare (ASW). A bistatic configuration and the corresponding acoustic model for the bistatic signal-to-noise ratio (SNR) is used. The Bayesian posterior distribution of the target state based on all available information from sensors and on the acoustic model is reconstructed via particle filtering methods, taking into account the port-starboard ambiguity typical of horizontal line arrays. The posterior distribution is the optimal estimation procedure, the only approximation derives from the particle representation. The effectiveness of the proposed algorithm is demonstrated on a real data set collected by the NATO Centre for Maritime Research and Experimentation (CMRE) during the NATO Proud Manta 2012 exercise (ExPOMA12).

Information fusion is the keystone of many surveillance systems, in which the security of the information is a crucial aspect. This paper proposes a method to fuse information exchanging only encrypted data, through a secure extension of the popular consensus gossip algorithm using secure multi-party computation methodology. Sensor entities exchange only encrypted information and never have direct access to the data while iteratively reaching consensus. The agents do not have access to the final value and can just retrieve partial information, for instance a binary decision. An innovative implementation of the consensus algorithm in the encrypted domain is proposed and analyzed.

In the context of maritime surveillance, low-power HF surface-wave (HFSW) radars have demonstrated to be a cost-effective long-range early-warning sensor for ship detection and tracking. In this work, multi-target tracking and data fusion techniques are applied to live-recorded data from a network of oceanographic HFSW radars installed in the German Bight (North Sea). This experimentation closely follows the one conducted in the Ligurian Sea (Mediterranean Sea) by NATO Science and Technology Organization (STO) Centre for Maritime Research and Experimentation (CMRE) during the Battlespace Preparation 2009 (BP09) campaign. Ship reports from the Automatic Identification System (AIS), recorded from both coastal and satellite-based stations, are exploited as ground truth information and a methodology is applied to classify the fused tracks and to estimate system performances. Preliminary results are presented and discussed, together with an outline for future works.

In the last decades, great interest has been directed toward low-power high-frequency (HF) surface-wave radars as long-range early warning tools in maritime-situational-awareness applications. These sensors, developed for ocean remote sensing, provide an additional source of information for ship detection and tracking, by virtue of their over-the-horizon coverage capability and continuous-time mode of operation. Unfortunately, they exhibit many shortcomings that need to be taken into account, such as poor range and azimuth resolution, high nonlinearity, and significant presence of clutter. In this paper, radar detection, multitarget tracking, and data fusion (DF) techniques are applied to experimental data collected during an HF-radar experiment, which took place between May and December 2009 on the Ligurian coast of the Mediterranean Sea. The system performance is defined in terms of time on target (ToT), false alarm rate (FAR), track fragmentation, and accuracy. A full statistical characterization is provided using one month of data. The effectiveness of the tracking and DF procedures is shown in comparison to the radar detection algorithm. In particular, the detector's FAR is reduced by one order of magnitude. Improvements, using the DF of the two radars, are also reported in terms of ToT as well as accuracy.

Recently it has been shown that the Multi-Sensor Probability Hypothesis Density (MS-PHD) has some optimality properties in the regime of large number of sensors [1, 2], achieving the same performance of the Bayes multi-sensor/multi-target posterior in the Random Finite Set (RFS) framework [3]. However, when the number of sensors N is relatively large, the traditional PHD filter loses its computational efficiency, the complexity being exponential in N. On the other hand, the complexity of the full Bayes posterior is only linear in N, and this paper suggests an idea for its computation using Sequential Monte Carlo (SMC) methods. The MS-PHD is then evaluated, and numerical examples show that it is possible to deal with a scenario where the number of sensors is very large while targets, appearing and disappearing, evolve in time.

Low-power HF surface-wave radars fit well the role of long-range early-warning tools in maritime situational awareness applications, by virtue of their over-the-horizon coverage capability and continuous-time mode of operation. In fact, these sensors, developed for ocean remote sensing, can represent also a further low-cost source of information for ship detection and tracking. Unfortunately, many shortcomings, like poor range and azimuth resolution, high non-linearity and significant presence of clutter, may degrade their performance. In this paper, multi-target tracking and data fusion techniques are applied to experimental data collected during the NATO Battlespace Preparation 2009 HF-radar campaign, which took place between May and December 2009 in the Mediterranean Sea. The system performance is defined in terms of time-on-target, false alarm rate and accuracy. Experimental results are presented and discussed.

High-frequency surface wave radar (HFSWR) is used in oceanography to monitor surface wind waves and currents and, more recently, to detect ships in maritime surveillance. The radar accuracy is affected by range-Doppler coupling, which yields a displacement in the measured range proportional to the target radial velocity, i.e., the Doppler shift in the returned pulse. Although in oceanography this effect is usually not accounted for, its relevance grows in ship detection. In this letter, we present the results of two experimental data sets showing displacements in the HFSWR range measurements of up to 300 m and confirming the theoretical analysis. Furthermore, we show that the correction based on theoretical arguments, achieved by the statistical correlation between the range and Doppler measurements, provides remarkable improvement in the radar accuracy.

Low-power High-Frequency Surface-Wave (HFSW) radars, designed for oceanic applications, are promising tools also for long-range surveillance in open-water Multi-Target Tracking (MTT) applications. This paper focuses on the fusion of multiple aspects over single-perspective systems. The single-sensor tracking steps, made up by the Joint Probabilistic Data Association (JPDA) rule and the Unscented Kalman Filter (UKF), are followed by a Track-to-Track association and Fusion (T2TF) strategy. Tracking performance improvements are investigated using real data collected by two simultaneously operated HFSW-radars.