Optimal planning for autonomous vehicles over long time horizons, where sensor information and multiple objectives form part of the decision-making process, is still in its infancy. The challenges of uncertainty, inherent in sensor information, and the computational complexity of their implementation typically render direct approaches infeasible. We present a practical, close to optimal, approach to the problem of long horizon path planning and goal-seeking for an autonomous mobile platform with sensing capability. Optimal autonomous vehicle planning is notoriously difficult, presenting several significant challenges: handling the uncertainty inherent in the sensor data and in a potentially unknown environment; coping with the ostensibly large data storage requirements; and the computational complexity of looking many epochs ahead. To overcome these problems, our model-based solution leverages a stochastic search methodology to obtain long-term, continuous, trajectories. We demonstrate its capability in handling both uncertainty in sensor measurements as well as multiple, possibly conflicting, objectives.
Phase retrieval is a fundamental problem in optics, particularly in ptychography, where reconstructing an unknown wavefield from intensity-only measurements poses significant computational challenges. In this work, we introduce a novel phase retrieval method using the bilinear Hessian and Hessian operator to improve optimization efficiency. By formulating the problem in a differential calculus framework over linear spaces, we derive gradient and Hessian expressions without explicitly differentiating, enabling efficient second-order based solvers. This enables to implement and analyze conjugate gradient, quasi-Newton, and gradient descent methods with Newton step size, demonstrating a one-order-of-magnitude improvement in convergence speed compared to traditional approaches. Numerical experiments on near-field ptychography data validate the method’s robustness and computational efficiency. Our approach significantly reduces reconstruction time, making it highly relevant for real-time imaging applications, such as in-situ experiments.
The integrated sensing and communication (ISAC) paradigm focuses on the interaction between communication parameters and their optimization to improve the sensing performance in sixth-generation cellular systems. Beamsteering is particularly beneficial in communication systems, where highly directional beams provide fine-grained spatial information which are essential for accurate localization and tracking in ISAC systems. This paper investigates passive object localization based on beam pattern searching and selection in 60 GHz frequency band. We design a passive localization algorithm that uses beam information as the main feature, along with machine learning tools for localization. The approach is tested through experimental activities conducted in the considered frequency band, forming multiple extremely narrow beams. These beams can be selectively oriented towards moving subjects or objects in the area or directed to illuminate different regions of the same environment. Initial results presented in the paper are very promising, confirming that high accuracy (up to 99 %) is achievable under controlled monitoring conditions.
A hybrid filterbanks is a convolutional neural network (convnet) whose learnable filters operate over the subbands of a non-learnable filterbank, which is designed from domain knowledge. While hybrid filterbanks have found successful applications in speech enhancement, our paper shows that they remain susceptible to large deviations of the energy response due to randomness of convnet weights at initialization. Against this issue, we propose a variant of hybrid filterbanks, by inspiration from residual neural networks (ResNets). The key idea is to introduce a shortcut connection at the output of each non-learnable filter, bypassing the convnet. We prove that the shortcut connection in a residual hybrid filterbank lowers the relative standard deviation of the energy response while the pairwise cosine distances between non-learnable filters contributes to preventing duplicate features.
This paper deals with robust system identification in the presence of impulsive noise. To this end, we present a new robust variant of the recursive-least-squares (RLS) estimator, called measure-transformed (MT)-RLS. The MT-RLS is an exact recursive counterpart to the recently developed MT least-squares estimator (MT-LSE), which operates by applying a transform to the probability measure of the data. This stands in contrast to other robust RLS variants that only approximate robust batch estimators. The considered measure transform is generated by a non-negative data-weighting function, called the MT-function. We have previously shown that a properly chosen MT-function can significantly mitigate the influence of outliers arising from impulsive noise, thereby substantially enhancing the estimation accuracy of the MT-LSE. Consequently, as an exact recursive extension, the MT-RLS fully inherits the robustness of MT-LSE. The MT-RLS is illustrated in simulations, underscoring its advantage over RLS and other robust extensions in both stationary and non-stationary environments.
In this paper, we present a bespoke Variational Autoencoder (VAE) architecture focused on identifying critical parameters of hazardous material releases, including source location, release start time, and wind speeds affecting dispersion, from a temporal series of color images. Our VAE architecture is unique in its incorporation of dual latent spaces. The primary latent space is dedicated to the probabilistic inference of source term attributes, along with their associated uncertainties. Concurrently, a secondary latent space is designed to capture salient features of the release that are complementary to the source parameters inferred in the primary space. We benchmark our methodology against a recent deterministic deep learning model using simulated data, demonstrating superior performance across different temporal resolutions. Real-world validation on the Jack Rabbit II Trial 7 experiment confirms the VAE’s ability to estimate key release parameters with reliable uncertainty quantification.
Multiple Signal Classification (MUSIC) is a high-resolution Direction-Of-Arrival (DoA) estimator that uses the eigendecomposition of the Sample Covariance Matrix (SCM). Random matrix theory (RMT) describes the sample eigenvalues and eigenvectors that determine MUSIC's performance, particularly predicting the phase transition when sample eigenvectors align with the true signal subspace. The phase transition depends on the number of sensors and snapshots used to estimate the SCM, and signal-to-noise ratio. For Uniform Linear Arrays (ULAs) in stationary environments, the ensemble covariance is Toeplitz, but the SCM is not. Enforcing a Toeplitz structure can improve MUSIC's performance for low-SNR sources, especially in snapshot-limited scenarios. Prior work shows that in the presence of loud sources, Toeplitz-Rectified (TR) MUSIC misses weaker sources due to a subspace swap. This paper applies perturbation theory to derive the phase transition for TR-SCM and predict when Toeplitz rectification outperforms conventional MUSIC. Results are validated using Monte Carlo simulations.
Recently, it has been validated that the arithmetic average (AA) fusion exhibits robust theoretical properties and demonstrates significant practical efficacy in multi-sensor multi-target tracking contexts. The fusion density in question may pertain to either the single-target probability density function (PDF) or the multi-target probability hypothesis density (PHD) function. In this study, we extend the applicability of AA fusion from the conventional PDF/PHD fusion to the domain of trajectory fusion. In this context, the spatiotemporal trajectory is modeled as stochastic processes (SPs) with mean function represented as a curve function of time (FoT). Specifically, we explore the Gaussian process and the Student’s t process within this letter. This extension substantially broadens the scope of the existing AA fusion methodology. Nonetheless, it introduces novel challenges, particularly in preserving fusion closure and addressing practical implementation requirements. This letter analyzes these challenges and proposes preliminary solutions. Simulation studies are also provided.
Determining an accurate rank is essential for parameter estimation in low-rank distributed networks. To address this challenge, this paper proposes a rank-adaptive learning algorithm that ensures the estimated local matrices match the true rank. Given a strongly convex cost function at each node in the network, matrix factorization is firstly employed to formulate the optimization problem, decomposing a matrix into the product of two low-rank matrices to maintain a potentially low-rank structure. To promote row sparsity, a weighted sparse norm is imposed on one of the factorized matrices as a regularization term. Since the choice of weights critically affects rank estimation, an adaptive strategy is introduced to set weights. The local optimization problem is then solved using the half-quadratic splitting (HQS) algorithm. Finally, simulation results demonstrate the effectiveness of the proposed algorithm.
Covariance intersection (CI) is a widely studied method to combine posterior state probability densities in sensor fusion. CI combines two input densities by first considering their exponential mixture density (EMD), or weighted geometric mean density, followed by selecting the mixture weights. In this work, we first introduce Kullback-Leibler divergence centroid (KLDC) and minimum Entropy (ME) generalisations of CI to an arbitrary number of state densities. Then, we compare these two generalisations and the equally-weighted geometric average (EWGA) fusion, which is widely used in the literature, in scenarios with correlated measurements and clutter, or false alarms. Our experiments indicate that ME fusion performs the best in the case of highly correlated measurement errors or false alarms, whilst EWGA shows better performance in no to medium correlation with no false alarms.
Covariance estimation is a core part of adaptive target detection. Most of the works focus on the Mean Squared Error (MSE) metric because it is easy to work with. However, MSE does not always capture the statistical information needed for detection. We advocate for switching to the Kullback-Leibler (KL) divergence. To support this, we analyze the Normalized Signal to Noise Ratio (NSNR) associated with the worst-case target. We show that the KL metric has a structure similar to NSNR and bounds it. To further clarify our point, we derive a simple variant of a classic MSE-based estimator by incorporating KL in a leave-one-out cross-validation (LOOCV) framework. Numerical experiments with various estimators on both synthetic and real data also demonstrate that KL and NSNR behave similarly and are different than MSE. Simply changing the metric in the LOOCV estimator improves KL and NSNR performance while reducing MSE performance.
Passive sonar signals can be classified according to the objects present in the data. This paper presents a dataset containing examples of background noise and a commercial vessel. Two feature sets based on either the mean spectrum or lofargram over short time segments are described. Support vector machine (SVM) and convolutional neural net (CNN) classifiers are applied to the data. Results are presented according to a number of different processing parameters. For small datasets the SVM is best, but the CNN is the better classifier when more data are available.
Robust tensor decomposition has been applied in a variety of domains including hyperspectral image restoration, anomaly detection in spatiotemporal traffic data, and event detection in video monitoring. In many of these applications, noise or outliers are commonly modeled as sparse noise. However, in a lot of cases the noise has some inherent structure. In these cases, ℓ1-norm sparsity is not sufficient to capture the structure of grouped anomalies or non-instantaneous events. In this paper, we introduce a robust tensor decomposition method where the normal part of the tensor is modeled as low-rank and the anomalous part is modeled using latent overlapping group norm. A general notion of grouping is introduced through node- and edge-based grouping using the graph structure corresponding to the underlying spatio-temporal data. The resulting optimization problem is solved using ADMM. The proposed method is evaluated on both simulated and real data for anomaly detection1.
In this paper, we propose a scalable broadband angle-of-arrival (AoA) estimation approach based on an estimated uniform planar array (UPA) polynomial matrix. The proposed method employs least-squares (LS) Khatri-Rao factorization in discrete Fourier transform (DFT) frequency bins to compute samples of the space-time covariance matrix in both azimuth and elevation directions. This approach eliminates the need for computing a polynomial singular value decomposition (PSVD), thereby enhancing scalability with respect to the number of sources and array elements. The proposed method’s performance is showcased in a simulation where a polynomial steering matrix for three sources is deliberately perturbed with varying degrees of estimation error to simulate different signal to noise ratio (SNR) scenarios. With azimuth and elevation angles determined independently, these are paired using an economical angle pairing strategy specifically designed for broadband scenarios.
Plug-and-play (PnP) approaches currently achieve state-of-the-art quality in image restoration. These methods rely on a Gaussian denoiser, often parametrized by an artificial neural network (ANN) that learns the image key features. This work adapts the PnP approach to bivariate time series, with an emphasis on preserving the polarization, that is, the geometrical dependence between the two components of the signal. It designs an ANN denoiser in the time-frequency domain, using exclusively a synthetic dataset and data-augmentation operations. The interest of the approach is demonstrated with a non-trivial application to gravitational wave astronomy. Up to our knowledge, this work is one of the first applications of a PnP approach to inverse problems involving (multivariate) time series.
Acoustic Anomaly Detection (AAD) has gained significant attention as a method for identifying faults or malicious activities. Previous state-of-the-art (SOTA) unsupervised AAD algorithms, particularly contrastive learning-based approaches, have advanced significantly beyond traditional models. However, their performance often deteriorates in real-world applications due to reliance on clean, noise-free training data. To address the challenge of noisy data, this paper proposes ConUAD, a selective contrastive learning framework for unsupervised AAD. The core idea of ConUAD is to mitigate the influence of noisy data by generating pseudo-labels to identify and select trustworthy pairs, thereby improving the robustness of representation learning within the contrastive learning framework. Experimental results on the real-world industrial MIMII dataset demonstrate the effectiveness of ConUAD, achieving a 3.22% improvement in AUC compared to previous state-of-the-art unsupervised methods.
Magnetic anomaly detection involves exploiting the earth field local anomaly created by the presence of ferromagnetic objects to detect them. In this work, we revisit the classical detection scheme, taking better account of the physics that creates the anomaly. It is well known that the signal measured by the sensor of a moving object along a rectilinear trajectory decomposes on a basis, where the coefficients depend on the unknown magnetic moment of the object. In the case where the measured signal is the squared induction modulus, we show that by constraining the basis coefficients to live in the semi-algebraic subspace which stems from their relationships to the moment components (i.e., the physics of the problem), we significantly improve detection performance. Even more, the performance is very close to the optimal detector one, based on the full knowledge of the parameters.
We consider sensors deployed in diverse locations measuring a common parameter through noisy observations. These observations are quantized to be sent to a fusion center doing the estimation of the common parameter. We design these quantizers to minimize the worst-case mean square error for common parameter estimation. Relying on an asymptotic regime in terms of sensors’ number and on random multi-bit quantizer per sensor, we provide a relevant continuous distribution for the thresholds of these quantizers via signomial programming. Through numerical simulations, we show that the proposed quantizers outperform the uniformly-distributed one and some deterministic ones even when the number of sensors is limited.
We show that analytic singular values of randomly perturbed matrices loose intersections and zero crossings compared to the unperturbed ground truth with probability one. As a result, the extracted singular values can significantly vary from the ground truth ones and may require a much high approximation order. To recover a solution closer to the ground truth, we extend a recent approach to extract ground truth analytic eigenvalues from a parahermitian matrix to the specific properties of analytic singular values. This method identifies segments where singular values are well separated, aligns them via partial reconstructions, and then performs an extraction based on the aligned segments. We demonstrate the approach in examples and ensemble simulations, thus highlighting its impact for applications that rely on solutions with low approximation order, and hence low implementation cost and latency.
Modeling electroencephalography signals using graphs has recently gained a significant attention for different data analysis tasks in neuroscience. A key challenge is identifying the most effective representation that incorporates both the structural positioning of the electrodes and the signal’s statistical features to distinguish between brain states. Most graph based classification frameworks through the engineering of graph structural features, under-explore the positions of the electrodes. This study introduces a novel EEG classification approach that leverages the spatial arrangement of electrodes and a learned graph structure to define interaction forces between them. The latter are then used as node features for a brain activity classification using classical classifiers such as Support-Vector Machines. The resulting original method achieves a promising performance level in mental workload classification compared to conventional approaches.
