Stochastic differential equations (SDEs) are widely used to model complex stochastic dynamical systems. For observational data that follows stochastic dynamical systems driven by random perturbations, modeling the data using SDEs to capture these dynamics is essential for understanding the underlying probabilistic behaviors. Recently, Neural SDEs have emerged as a powerful tool for modeling continuous-time stochastic dynamics. By naturally accommodating irregular observation intervals and leveraging the adjoint method for memory-efficient computations, Neural SDE provides a flexible framework for continuous-time modeling. This paper proposes a flexible and scalable framework for flexibly learning Neural SDE expressions with Brownian motions as functions of both observed values and time, ensuring that the correct formulations for both the drift and diffusion terms are obtained. Our data-driven Neural SDE identification framework (NSDE-ID) leverages the path signature, which is a collection of all the iterated integrals and efficiently extracts features from time-series data, and incorporates path-dependent distributions, enabling SDE estimation that extends beyond point-in-time predictions. Building upon recent advancements in Neural SDE, our approach is designed to enforce statistical consistency in the learning process, thereby enabling robust modeling of complex dynamics. We demonstrate the efficacy of NSDE-ID on three benchmark SDE parameter estimation problems and analyze its numerical performance and robustness. Overall, NSDE-ID offers a promising new direction for systematically unraveling the continuous stochastic dynamics within observational data through a flexible SDE representation.
In this work, we develop an end-to-end differentiable multi-view visual tracking architecture and explore fine-tuning model parameters via gradient-based optimization and automatic differentiation. We consider a setting with multiple camera nodes distributed in the tracking environment that collaboratively track objects. The architecture that we construct includes within-image-plane deep learning-based detection models, probabilistic camera models, object dynamics models, and an $N$-object Kalman filter-based tracking model. We demonstrate fully differentiable choices for each of these components, enabling learning and fine-tuning of the parameters of all system components based on different forms of supervision. Our results show performance gains for $N$-object tracking when fine-tuning the parameters of the system for end-to-end tracking performance.
Autonomous path planning for radar and sonar sensing faces significant challenges arising from dynamic targets, obstacle occlusions, and low signal-to-noise (SNR) conditions. We propose a hierarchical sensor scheduling framework that combines a long-horizon strategic planner, based on the Rapidly-exploring Random Tree star (RRT*) algorithm, with a fast-adapting tactical planner. Efficient coordination of the two planners is achieved via a novel message passing mechanism, enabling guidance of the sensor out of complex environments while maintaining effective target tracking. Additionally, we introduce an RRT* rerooting strategy that significantly reduces computation time and so expedites the update of the strategic plan. Extensive simulation results demonstrate that our proposed fusion approach outperforms conventional stand-alone short-term and long-term planners in challenging scenarios and low-SNR regimes,
Bayesian filtering problem is considered in linear Gaussian systems with unknown inverse Wishart distributed process noise covariance. A Bayesian filter is formulated to approximate the joint posterior for the state and the process noise covariance. This involves utilizing moment matching and a scale Gaussian mixture approximation of the t-distribution. The proposed filter distinguishes itself by being non-iterative, setting it apart from existing Bayesian solutions given in the literature. The algorithm's performance is demonstrated through its application to a scenario where a target is tracked in two dimensions. Simulation results indicate that the proposed filter achieves similar or better performance compared to state-of-the-art solutions while demanding a reduced computational load.
Space situational awareness requires estimation of satellite tracks with sparse observations. The sparsity of novel information makes critical tasks such as maneuvering target tracking and track initialization challenging. Bayesian inference via Markov-Chain Monte Carlo (MCMC) can improve robustness when compared to recursive estimation, but high-fidelity orbit propagation yields objectionable runtimes in such solvers. This challenge may be mitigated via multi-fidelity methods, i.e., the use of varying fidelity propagators that trade some accuracy for reduced runtime. In this paper, multi-fidelity methods are combined with a delayed acceptance approach in Metropolis-Hastings-based MCMC to reduce runtime for satellites in low-Earth orbits. The delayed acceptance approach is a two-step process. The first considers a sample propagated via a rapid, multifidelity model. In the second step, any preliminarily accepted samples are propagated via the full-fidelity model. This reduces the number of high-fidelity propagations. The multi-fidelity approach also includes proposal density adaptation and produces mixing ratios consistent with optimal rates. This MCMC method is demonstrated for sparse orbit determination in a low-Earth orbit scenario. Accuracy of the multi-fidelity approach is consistent with full-fidelity inference while reducing the runtime by almost a factor of two in the cases considered.
The exponential growth of the Internet of Things (IoT) has introduced unprecedented challenges in data processing, privacy preservation, and energy efficiency. Traditional centralized approaches are often unsuitable for IoT environments due to bandwidth limitations, data heterogeneity, and privacy concerns. This study proposes a novel framework combining federated learning (FL) and autoencoders to address these issues in IoT-based image classification tasks. By lever-aging Unmanned Aerial Vehicles (UAVs) as intermediaries for model aggregation and distribution, the framework minimizes communication overhead while maintaining data privacy. Autoencoders are employed for unsupervised feature extraction, enabling effective data representation even in the absence of labeled data. Results demonstrate that, while autoencoders achieve lower classification accuracy compared to supervised approaches, they provide significant advantages in bandwidth efficiency, scalability, and privacy preservation. The integration of UAVs further enhances the system by optimizing communication and enabling model improvement in real-time. This framework offers a flexible and resource-efficient solution for IoT applications, particularly in scenarios where data labeling is impractical or privacy is paramount.
Accurate uncertainty quantification is critical for robust and trustworthy predictions in many real-world applications. Bayesian Neural Networks (BNNs) provide a principled approach for modeling uncertainty but are often limited by the computational complexity of Bayesian inference. In this paper, we introduce a statistical linearization approach for multilayer feedforward BNNs. We demonstrate that this statistical linearization is equivalent to the Kalman Bayesian Neural Networks (KBNN) framework. This equivalence unifies these methodologies, providing a theoretical foundation for understanding the relationship between different BNN training approaches.
Player tracking systems in soccer provide valuable insights for broadcasters, coaches and teams. Action recognition enhances these systems by providing player statistics in addition to player tracking data. This study investigates which features are suitable for soccer player action recognition when fusing radar and camera data. The created dataset consists of four movement classes: walk, jog, dribble walk, and dribble jog. The data was obtained using mm-Wave industrial radar and a smartphone camera. PCA, t-SNE and random forest feature importance analysis is performed and it is concluded that the fusion of radar and camera data better separates the classes than only using any sensor in isolation for the soccer player action recognition scenario. The histogram of oriented gradients of both the full frame and the region of interest are determined to be the best camera features, whereas the mel-spectrogram and mel-coefficients are the best radar features according to the random forest feature importance analysis. For the radar-camera fusion the HOG for the full frame along with mel-spectrograms and some simple radar features were determined to be the best features and using them achieved a high classification accuracy.
Evaluating uncertainty in large language model (LLM) reasoning is challenging due to their vast parameter space, abstract knowledge representation, and limited transparency regarding training data. While normative formalisms, such as deductive logic, clearly define sound reasoning in the absence of uncertainty, reasoning under uncertainty admits multiple approaches, including probabilistic reasoning (e.g. Bayesian), belief function reasoning (e.g. Dempster-Shafer), or fuzzy logic, to name a few. This paper examines how LLMs handle uncertainty by analyzing outcomes based on an atomic fusion and reasoning problem. We establish a point of reference using the simplest of fusion topologies to facilitate transparency and understanding of how LLMs align with established theories. The reasoning approaches of different LLMs with varying complexities are compared to established normative frameworks, providing insights into which formalism best aligns with LLM reasoning and assessing its soundness and consistency. A deviation function for assessment is developed, and the results indicate that the tested LLMs' reasoning under uncertainty does not consistently align with established theories, even for the simplest information fusion topologies. These preliminary results form the basis for further investigations and LLM refinements.
Particle filters are an important class of algorithms for Bayesian estimation. One of their drawbacks is the socalled particle degeneration where only very few particles with a meaningful weight remain after the filter step. This effect is typically remedied by regularly resampling the particles, yielding a set of equally weighted particles. This paper investigates an approach to deterministically sample particles from the proposal distribution in such a way to automatically have equally weighted particles at the end of the filter step. The proposed method is first motivated and presented for the one-dimensional case. Using the Radon transform and projected cumulative distributions, the one-dimensional algorithm is extended to multivariate problems. Some examples of the usefulness of the proposed algorithm are also shown.
Point cloud registration is crucial for applications in computer vision and robotics. The Iterative Closest Point (ICP) algorithm has been a key, but limited, solution for this problem, with subsequent methods having been devised to address occlusions and variable point overlap. To cope with detection errors, the Particle Swarm Optimization (PSO)-Cardinalized Optimal Linear Assignment (COLA) algorithm was introduced, providing robustness against point data missed detections and false alarms showing significant performance improvements in data sets with limited overlap. However, since PSO is based on particle swarm optimization, it can be affected by local minima problems. To mitigate these issues, the Artificial Rabbit Optimization (ARO)-COLA algorithm is used in this article, incorporating the ARO approach together with the COLA metric. In this paper, the ARO-COLA and PSO-COLA algorithms will be applied to the challenging outdoor “Wood Summer” dataset, comparing their performances with other state-of-the-art methods. The results will show that with such unstructured data sets, the ARO-COLA registration algorithm outperforms most state-of-the-art registration methods, achieving similar accuracy to its PSO-COLA registration predecessor, but with improvements in runtime.
This paper proposes a novel type of random finite set (RFS), namely augmented RFS, to address the problem of resolvable group target tracking, which integrates the information of both the group attributes and the dynamic state of group targets into random finite sets. Specifically, we initially introduce an augmented random finite set framework, incorporating group labels and group cardinality to estimate both the trajectories and states of group targets. Then, a new multi-target filter based on the augmented RFS is proposed to achieve the process of group target tracking. Finally, simulation experiments are conducted to demonstrate the effectiveness of the proposed filter in group target tracking scenarios.
The Automatic Identification System (AIS) is crucial for maritime navigation and monitoring, but it is vulnerable to data manipulation caused by equipment malfunctions, deliberate tampering, or external attacks. This study focuses on detecting vessels that change their identifiers to evade monitoring systems, with a proposed solution with two steps. The first step is to predict vessel trajectories and the second step is to classify de predicted trajectories. We employ the TrAISformer neural network architecture, adapting it to predict future and past trajectories using multiple AIS datasets with varying sampling intervals and regional characteristics. For the classification step, we use Random Forest and SVM algorithm. The datasets include AIS data collected from the regions near Denmark, the Port of Santos, and the Gulf of Mexico, with 2 to 10 minutes of sampling intervals. In this work, compared to the previous work, an in-depth study was carried out on the results obtained in the trajectory prediction stage, showing that higher sampling frequency improves prediction accuracy, while regional characteristics influence model performance over extended prediction periods. These findings laid the foundation for the subsequent classification step, performed in this work, to match pairs of trajectories and identify continuous vessel paths despite altered identifiers. The classification step was directly affected by the prediction trajectory accuracy result in the first step. This twostage approach offers a promising solution for detecting AIS spoofing and can be applied to address a critical challenge in maritime traffic monitoring.
The ubiquitous and widespread implementation of Global Satellite Navigation System (GNSS) in development, operation, and usage of the GNSS-based applications requires a robust risk model providing the probability that the GNSS positioning accuracy would not meet the requirements of a particular GNSS application. Our group has already proposed the Probability-of-Occurrence (PoO) model, a Complementary Cumulative Distribution Function (CCDF) -based model as the solution of the problem. Here the PoO model is validated in terms of the potential seasonality using the experimental GNSS observations in the scenario of usage in the economically attractive Arctic region. It is shown that the seasonal PoO models/curves does not differ significantly from the annual PoO model/curve. Additionally, solar and space weather disturbances are identified as a dominant source of the GNSS utilisation risk, overcoming the systemic seasonality effects of the Earth's atmosphere. The PoO is confirmed as a seasonality agnostic risk model, which enables the GNSS application developers, operators, and users to establish the QoS of their applications, and to assess the risk of their failure due to GNSS PNT performance degradation caused by the ionospheric effects.
Extended object tracking is essential yet challenging in Advanced Driver Assistance Systems (ADAS) development. This paper introduces a novel hybrid filtering framework designed to integrate low-, mid-, and high-level features into a unified box representation of tracked objects. The framework provides a structured approach to multi-level fusion, ensuring consistent and accurate state estimation across different sensor inputs. To achieve this, we incorporate Probabilistic Multi-Hypothesis Tracking (PMHT) for low-level data and a Box-to-Box update model for mid- and high-level features. Comprehensive validation using high-fidelity simulated scenarios demonstrates the framework's ability to enhance tracking accuracy and robustness by leveraging structured sensor representations, closely reflecting real-world conditions.
In this work, we present our augmented approach to fuse optical detections with a varying number of identifiable features into robust tracks. After laying out the motivation of enabling automated intermittent optical following of ground targets from a moving airborne observer equipped with a steerable optical sensor, we describe the implementation in detail. In consideration of the performance requirements of edge computing, the system is designed to run in real-time on actual flight hardware deployable on medium and small unmanned aerial vehicles (UAVs), Raycasting based on standardized video metadata and the Unscented Transform (UT) is used to generate position measurements and their associated covariance from the image position of each detected target. We additionally describe how these measurements are used to update the ground targets' state estimation building on the Stone Soup framework using a cascading approach for measurement-to-track association. Using representative hardware, we verify and test the integrated system in flight.
This paper presents an exact quality of service (QoS)-based radar resource management (RRM) method that manages multiple radar sensors, while also taking task dependencies into account. This contrasts with other approaches that mostly do not consider dependencies and assume independence among the tasks. However, this simplification is generally incorrect. Our method optimizes the tasks' assignment to the radar sensors as well as the selection of the radar control parameters jointly, while also exploiting dependencies between tasks. The problem is formulated and solved as mixed-integer linear programming (MILP) optimization problem. A simulated tracking scenario shows that by exploiting task dependencies in combination with coordinating the task assignments among the sensors, our RRM method can improve the operational performance significantly in comparison to the benchmark algorithms.
This paper investigates the benefit of using game theoretic sensor control for the tracking of a reactive intelligent target. Game theory is adopted as a robust strategy which facilitates the study of interactions between intelligent players, in contrast to the alternative control strategies which only consider non-reactive targets. A general multi-step ahead optimisation strategy is designed and studied in the context of a passive tracking operation. Numerical results demonstrate the advantages of employing game-theoretic control for optimal tracking of evasive targets.
Maritime transport and vessel monitoring rely on multiple systems for positioning, such as the Automatic Identification System, electro-optical systems, and shore-based radar systems, to improve safety and efficiency in vessel tracking. However, each system has inherent limitations, including coverage gaps, reliance on vessel compliance, and limited real-time monitoring capabilities. As a complementary approach to existing methods and systems, this paper presents the SeaSentry system, a passive sensor network designed to detect, position, and track vessels in real time, thus eliminating the need for onboard installations. The sensors detect radar pulses emitted by the vessels' rotating radar antennas and compute time stamps as the radar beams pass over them. Geometric constraints can be derived from time differences of arrival to localize the vessels, with time error and synchronization demands in the millisecond range. Along with some initial results, this paper discusses the SeaSentry setup and data processing pipeline.
Maritime Situational Awareness (MSA) is crucial for identifying suspicious vessel activities, such as dark-ship operations and prolonged loitering activities. However, the development of robust detection systems requires high-quality datasets that capture vessel encounters, particularly encounters that occur beyond 20 nautical miles (NM) from the coast. This paper presents the creation and analysis of a comprehensive data set that contains vessel trajectories associated with offshore encounters. The dataset, constructed using 12 months of data from the Marine Cadastre Automatic Identification System (AIS), leverages the H3 geohash system for spatial proximity detection and MovingPandas for trajectory extraction. The dataset analysis demonstrates that the dataset is a powerful tool for enhancing Maritime Domain Awareness (MDA), contributing to monitoring and security in the maritime environment. The analysis of encounter patterns highlights both the importance of reliable data and the need for a robust detection system to address uncertainties and information gaps.
