In this article, the principles of robust estimation are applied to the standard basic time scale equation to obtain a new method of assigning weights to clocks. Specifically, the Student’s t-distribution is introduced as a new statistical model for an ensemble of clocks that are experiencing phase jumps, frequency jumps or anomalies in their measurement links. The proposed robust time scale is designed to mitigate the effects of these anomalies without necessarily identifying them, but through applying a method of robust estimation for the parameters of a Student’s t-distribution. The proposed time scale algorithm using the Student’s t-distribution (ATST) is shown to achieve comparable robustness to phase jumps, frequency jumps, and anomalies in the measurements with respect to the AT1 oracle time scale. The AT1 oracle is a special realization of the AT1 time scale which corrects all anomalies by having prior knowledge of their occurrences. The similar performance of ATST and AT1 oracle suggests that the ATST algorithm is efficient for obtaining robustness with no prior knowledge or detection of the occurrences of anomalies.

Hyperbolic geometry has recently garnered considerable attention in machine learning due to its ability to embed hierarchical graph structures with low distortions for further downstream processing. This paper introduces a simple framework to detect local outliers for datasets grounded in hyperbolic 2-space, which is referred to as Hyperbolic Local Outlier Probability (HLoOP). Within a Euclidean space, well-known techniques for local outlier detection are based on the Local Outlier Factor (LOF) and its variant, the LoOP (Local Outlier Probability), which incorporates probabilistic concepts to model the outlier level of a data vector. The proposed HLoOP combines the notion of finding nearest neighbors, density-based outlier scoring with a probabilistic, statistically oriented approach. Therefore, the method computes the Riemmanian distance of a data point to its nearest neighbors following a Gaussian probability density function expressed in a hyperbolic space. This is achieved by defining a Gaussian cumulative distribution in this space. The proposed HLoOP algorithm is tested on the WordNet dataset and desmonstrated promising results. The code and data will be made available upon request for reproducibility.

Robust estimation methods are useful in mitigating the impact of anomalies in clock data. Such anomalous clock data is assumed to be well modeled by a Student’s t-distribution. This paper derives a lower bound on the performance of the misspecified Gaussian model using the theory of the Misspecified Cram´er-Rao bound (MCRB). The results of these derivations are verified by analyzing the Mean Square Error (MSE) of the misspecified Gaussian Maximum Likelihood Estimator (MLE) when using data generated by the Student’s t-distribution. The derived MCRB indicates a constraint on the MSE when assuming a Gaussian distribution. The MLE for the mean of the Student’s t-distribution is obtained with an Expectation maximization algorithm and is shown to obtain a lower MSE than the MCRB and hence, the misspecified estimator. This indicates an improvement in performance if anomalous clock data is appropriately accounted for in the statistical model.

State estimation with Kalman Filters (KF) regularly encounters covariance matrices that are unknown or empirically determined, causing sub-optimal performances. Solutions to lift these uncertainties are opening up to estimation techniques based on the hybridization of KF with deep learning methods. In fact, inferring covariance matrices from neural networks gives rise to enforcing symmetric positive definite outputs. In this work, a new Recurrent Neural Network (RNN) model is explored, based on the geometric properties of the Riemannian Symmetric Positive Definite (SPD) manifold. To do so, a neuron function is defined based on the Riemannian exponential map, depending on unknown weights lying on the tangent space of the manifold. In this way, a Riemannian cost function is deduced, enabling to learn the weights as Euclidean parameters with a conventional Gauss-Newton algorithm. It involves the computation of a closedform Jacobian. Through optimization on a simulated covariance dataset, we demonstrate the possibilities of this new approach for RNNs.

This paper studies a new fusion method designed for magnetic resonance (MR) and ultrasound (US) images, with a specific focus on endometriosis diagnosis. The proposed method is based on guided filtering, leveraging the advantages of this technique to enhance the quality of fused images. The fused image is a weighted average of base and detail images from the MR and US images. The weights assigned to the US image account for the presence of speckle noise, a common challenge in US imaging whereas the weights assigned to the MR image allow the contrast of the fused image to be enhanced. The effectiveness of the method is evaluated using synthetic and phantom data, showing promising results. The image provided by the proposed fusion method holds potential for enhancing visualization and aiding decision-making in endometriosis surgery, offering a valuable contribution to the field of medical image fusion.

High resolution spectrometers, such as the CNES/UKSA MicroCarb instrument, are widely used in remote sensing applications to retrieve atmospheric trace gas concentrations. Potential radiometric errors or errors in the approximation of the Instrument Spectral Response Function (ISRF) can induce significant errors in the determination of these gas concentrations. This paper presents a new strategy for the joint estimation of a spectrometer ISRF and the potential radiometric errors affecting the spectrometer measurements. These radiometric errors are modeled as polynomial functions of the error-free spectrum. An iterative algorithm is then proposed to estimate the coefficients of these polynomials and the spectrometer ISRFs. This algorithm alternates between ISRF estimation steps using the orthogonal matching pursuit algorithm and a radiometric error estimation step using the least squares method.

This paper studies an algorithm allowing the isolation forest method to be adapted to time series associated with ship trajectories. This algorithm builds decision trees using different similarity measures between the ship trajectories of interest and the atoms of a dictionary constructed by the user. The similarity measure used to compare trajectories with potentially different lengths is based on dynamic time warping. Results obtained on synthetic data with an available ground truth yield promising results, when compared to the state-of-the-art.

Multiple sensors, such as AIS and radar, are used to monitor nearby ships during maritime surveillance operations. The data from these sensors must be associated so as to accurately locate the targets and identify their behavior, while taking into account the presence of potential sensor biases. Several algorithms exist in the state-of-the-art to solve this association problem. However, few of them allow the sensor biases to be corrected. This paper adapts the coherent point drift method to the association of AIS and radar tracks while taking into account the radar uncertainty. The proposed adaptation is based on an expectation-maximization algorithm that jointly estimates the bias of the radar sensor with respect to the AIS sensor (in polar coordinates), the radar and AIS uncertainties and solves the association problem. The performance of this algorithm is evaluated using AIS and radar tracks obtained from numerous scenarios yielding promising results.

This paper analyzes multidimensional time series through the lens of their integrals of various moment orders, constituting their signatures, a novel tool for detecting anomalies in time series. The proposed anomaly detection (AD) method is compared using classical distance-based methods such as Local Outlier Factor (LOF) and One-Class Support Vector Machine (OCSVM). These methods are investigated using different similarity measures: distance on signature features, Euclidean distance and Dynamic TimeWarping (DTW). The combination of signature features with a specific segmentation of time series leads to a multi-scale analysis tool that is competitive with respect to the state-of-the-art results, while maintaining low computational costs thanks to a property of the signature features.

The monitoring of abnormal ship behavior is an important task for maritime surveillance for which the automatic identification system (AIS) has been widely exploited. Several works have proposed graph-based anomaly detection (AD) methods on spatial AIS points to provide further information regarding the interactions between the observed data through graph structures. This paper studies a new AD framework on graphs constructed from AIS trajectories. This framework considers a diffusion kernel at multiple scales of the graph Laplacian matrix, referred to as multiscale AD for AIS trajectories (MADAIS). MAD-AIS builds an attributed graph from a set of AIS trajectories, where nodes encode spatio-temporal trajectories and edges connect them via a similarity measure. In a second stage, AD is performed by computing scaled versions of the graph Laplacian matrix that are used to assess the graph connectivity. Simulation results are first conducted on synthetic data with controlled ground truth showing that the proposed MAD-AIS can effectively detect the abnormal behavior of ships in terms of spatio-temporal irregularities. Simulations conducted on real AIS subtrajectories (i.e., segments of AIS trajectories) show that abnormal features/attributes can be localized along AIS paths.