Search Results (50)

Accurate direction-of-arrival (DOA) estimation with high resolution is fundamental to many array sensing applications. In practice, however, sparse arrays with missing sensors and snapshot-limited observations often lead to incomplete and noisy second-order statistics, which substantially degrades the performance of conventional eigendecomposition-based estimators. In this paper, we propose a two-stage Transformer framework for sparse-array DOA estimation that explicitly separates correlation recovery from angle inference. The first stage operates in the correlation domain and learns to reconstruct a clean and complete correlation vector from partially observed measurements using masking-aware tokenization and global-context modeling. The recovered representation can be further converted into a structured covariance matrix, providing an interpretable interface to classical signal processing back-ends. Based on the recovered features, the second stage adopts a Transformer regressor to directly predict multi-source DOAs. Extensive simulations on a large-scale dataset with SNRs from −5 to 10 dB and various snapshot numbers demonstrate that the proposed method delivers robust accuracy and improved stability in low-SNR and snapshot-limited regimes, while maintaining competitive performance at higher SNRs. Additional evaluations with an ESPRIT back-end further confirm that the recovery-based covariance yields more reliable DOA estimation than conventional difference–coarray processing, with particularly evident gains under challenging noise conditions. Full article

Nonlinear state estimation plays an important role in aerospace sensing applications, where estimation accuracy must be balanced against computational efficiency. In this paper, a sparse-grid Gaussian kernel quadrature Kalman filter (SGKQKF) is proposed for discrete-time nonlinear state estimation by combining Gaussian kernel quadrature (GKQ) weighting with a Smolyak sparse-grid construction. The univariate GKQ rule is constructed on scaled Gauss–Hermite nodes through a truncated Mercer eigendecomposition of the Gaussian kernel and is then extended to multivariate cases via the Smolyak construction to alleviate the curse of dimensionality associated with tensor-product rules. The proposed method is positioned within the established sparse-grid filtering framework, with the specific contribution of integrating kernel-adapted quadrature weights into sparse-grid structures for discrete-time nonlinear Gaussian filtering. For fixed nodes, the exact kernel-quadrature weights minimize the worst-case integration error in the reproducing kernel Hilbert space (RKHS) induced by the Gaussian kernel, whereas the closed-form weights used in the implementation are interpreted as a Mercer-based practical approximation to this exact rule, with the approximation error characterized through the Mercer spectral-tail expression of the Gaussian kernel. For sparse grids, where a closed-form RKHS optimality result is not available, numerical maximum mean discrepancy (MMD) evaluations are presented as empirical diagnostics in the tested configurations. Numerical experiments demonstrate that the proposed filter achieves a favorable accuracy–efficiency trade-off compared with conventional deterministic Gaussian filters. Full article

In this paper, the two-dimensional DOA estimation problem of coherent signals in an electromagnetic vector sensor (EMVS) array is studied. A new decorrelation method is proposed by extending the multiple-Toeplitz matrices reconstruction (MTOEP) method to a polarization sensitive array. After that, a closed-form solution is derived based on the ESPRIT algorithm for DOA and polarization parameter estimation. Pairing matching is based on the correspondence between eigenvectors obtained by independent eigen-decomposition. Simulation results verify the effectiveness of the proposed work and show the proposed algorithm has better performance than the traditional spatial smoothing (SS) method, especially in scenarios with low signal-to-noise ratios (SNRs) and small angular separations. Full article

Binding affinity prediction in computational drug discovery is confounded by trivial correlations between molecular size and measured potency. We introduce cellular sheaf Laplacians as descriptors of ligand molecular geometry that quantify geometric frustration independent of system size. Sheaves are constructed over molecular graphs by assigning three-dimensional coordinate spaces to atoms and projection operators encoding ideal bonding geometry to edges; eigendecomposition of the resulting Laplacian yields spectral features measuring inconsistencies between local geometric constraints and global topology. Applied to 14,050 protein-ligand complexes from the PDBbind v2020 refined set, MW-residualized Sheaf features capture a statistically significant geometric signal ($r_{\mathrm{partial}} = 0.171$, $p<{10}^{-70}$) that is orthogonal to the Wiener index ($r=0.013$) and persists after controlling for both molecular weight and classical graph-theoretic descriptors ($r_{\mathrm{partial}} = 0.390$, $p<{10}^{-9}$). Sheaf spectral features alone achieve predictive performance ($R^2=0.403$) approaching that of fourteen classical cheminformatics descriptors ($R^2=0.446$), and their combination yields consistent improvements across the binding affinity spectrum (RMSE $=1.43$$p{K}_d$). Permutation importance analysis confirms the Sheaf Frobenius norm as the second most influential descriptor after molecular weight. We introduce Topological Binding Efficiency as a size-normalized quality metric identifying ligands that achieve potent binding through geometric complementarity rather than molecular bulk. Gaussian mixture analysis of the maximum eigenvalue distribution among strong binders reveals two distinct spectral modes corresponding to planar aromatic and three-dimensional sp3-rich scaffolds, confirmed by significant differences in fraction of sp3 carbons and aromatic ring counts ($p<{10}^{-8}$). As an intentionally ligand-centric framework, our approach complements rather than replaces protein-aware co-modelling architectures. This work establishes cellular sheaf theory as a principled framework for encoding molecular topology with statistically significant associations with binding affinity, providing interpretable geometric insights that are inaccessible to conventional molecular descriptors. Full article

Non-convex stochastic optimization presents fundamental mathematical challenges across machine learning, wireless networks, data center resource allocation, and optical wireless communication systems, where complex loss landscapes with multiple local minima and saddle points impede classical variational inference methods. This paper introduces the Quantum-Inspired Variational Inference (QIVI) framework, which systematically integrates quantum mechanical principles (superposition, entanglement, and measurement operators) into classical variational inference through rigorous mathematical formulations grounded in Hilbert space theory and operator algebras. We develop a unified optimization framework that encodes classical parameters as quantum-inspired states within finite-dimensional complex Hilbert spaces, employing unitary evolution operators and adaptive basis selection governed by gradient covariance eigendecomposition. The core mathematical contribution establishes that QIVI achieves a convergence rate of $\mathit{O}({log}^{2}T/T^{1/2})$ for $\sigma$-strongly non-convex functions, provably improving upon the classical $\mathit{O}\left(T^{-1/4}\right)$ rate, yielding a theoretical speedup factor of $1.85$–$1.96\times$. Comprehensive experiments across synthetic benchmarks, Bayesian neural networks, and real-world applications in network optimization and financial portfolio management demonstrate 23–$47\%$ faster convergence, 15–$35\%$ superior objective values, and 28–$46\%$ improved uncertainty calibration. The principal contributions include: (i) a rigorous Hilbert space-based mathematical framework for quantum-inspired variational inference grounded in operator algebras, (ii) a novel hybrid quantum–classical algorithm (QIVI) with adaptive basis selection via gradient covariance eigendecomposition, (iii) formal convergence proofs establishing provable improvement over classical methods, (iv) comprehensive empirical validation across diverse problem domains relevant to machine learning and network optimization, and (v) demonstration of the framework’s applicability to optimization problems arising in wireless networks, data center resource allocation, and network system design. Statistical validation using the Friedman test (${\chi }^2=847.3$, $p<0.001$) and post hoc Wilcoxon signed-rank tests with Holm–Bonferroni correction confirm that QIVI’s improvements over all baseline methods are statistically significant at the $\alpha =0.05$ level across all benchmark categories. The framework discovers $18.1$ out of 20 true modes in multimodal distributions versus $9.1$ for classical methods, demonstrating the potential of quantum-inspired optimization approaches for challenging stochastic problems arising in machine learning, wireless communication, and network optimization. Full article

Model-based polarimetric SAR (PolSAR) algorithms for bio- and geophysical parameter estimation rely on the effective separation of the combined scattering response of vegetation canopies and the soil surface through physically based models. However, the interpretation of polarimetric features derived from physical models is still subject to some ambiguity. Another strategy for complementing the model-based approaches for scattering mechanisms characterisation deals with the separation of the polarised and depolarised contributions of the PolSAR data according to their degree of polarisation. In this paper, we propose a two-component decomposition for estimating the depolarised and polarised components within the target and their corresponding coherency matrices. The method requires the previous calculation of the backscattering powers given by the model-free three-component (MF3C) decomposition, which in turn relies on the 3-D Barakat degree of polarisation. This quantitative information allows us to construct an inversion algorithm to retrieve the proportion of the polarised and depolarised contributions for all the elements of the observed coherency matrix under the reflection symmetry assumption. In essence, the proposed decomposition can be regarded as an extension of the MF3C method and, as a consequence, it enables the exploitation of both model-free and model-based approaches by using a physical rationale driven by the capability of the 3-D Barakat degree of polarisation. Therefore, practical applications can benefit from this approach as the retrieval of target parameters could presumably be done in a more accurate way by directly applying existing scattering models to both components. Indoor multi-frequency datasets acquired over three vegetation samples from the European Microwave Signature Laboratory (EMSL) and P-, L-, and C-band AIRSAR images over a boreal forest in Germany have been employed for testing the proposed decomposition. Performance analysis was performed using different polarimetric tools applied to the outcomes of the two-component decomposition, namely, the eigendecomposition and the copolar cross-correlation analysis of polarised and depolarised components, as well as histograms and a correlation analysis among backscattering powers. Overall, it has been observed that the method outputs are consistent with the theoretical expectations for the depolarised and polarised scattering components for a wide range of scenarios and sensor frequencies. Full article

Reliable state estimation in railway environments presents significant challenges due to geometric degeneracy resulting from repetitive structural layouts and point cloud sparsity caused by high-speed motion. Conventional LiDAR-based SLAM systems frequently suffer from longitudinal drift and mapping artifacts when operating in such feature-scarce and dynamically complex scenarios. To address these limitations, this paper proposes SERail-SLAM, a robust semantic-enhanced multi-sensor fusion framework that tightly couples LiDAR odometry, inertial pre-integration, and GNSS constraints. Unlike traditional approaches that rely on rigid voxel grids or binary semantic masking, we introduce a Semantic-Enhanced Adaptive Voxel Map. By leveraging eigen-decomposition of local point distributions, this mapping strategy dynamically preserves fine-grained stable structures while compressing redundant planar surfaces, thereby enhancing spatial descriptiveness. Furthermore, to mitigate the impact of environmental noise and segmentation uncertainty, a confidence-aware filtering mechanism is developed. This method utilizes raw segmentation probabilities to adaptively weight input measurements, effectively distinguishing reliable landmarks from clutter. Finally, a category-weighted joint optimization scheme is implemented, where feature associations are constrained by semantic stability priors, ensuring globally consistent localization. Extensive experiments in real-world railway datasets demonstrate that the proposed system achieves superior accuracy and robustness compared to state-of-the-art geometric and semantic SLAM methods. Full article

Hierarchical Bayesian models based on Gaussian processes are considered useful for describing complex nonlinear statistical dependencies among variables in real-world data. However, effective Monte Carlo algorithms for inference with these models have not yet been established, except for several simple cases. In this study, we show that, compared with the slow inference achieved with existing program libraries, the performance of Riemannian manifold Hamiltonian Monte Carlo (RMHMC) can be drastically improved by applying the chain rule for the differentiation of the Hamiltonian in the optimal order determined by the model structure, and by dynamically programming the eigendecomposition of the Riemannian metric with the recursive update of the eigenvectors at the previous move. This improvement cannot be achieved when using a naive automatic differentiator included in commonly used libraries. We numerically demonstrate that RMHMC effectively samples from the posterior, allowing the calculation of model evidence, in a Bayesian logistic regression on simulated data and in the estimation of propensity functions for the American national medical expenditure data using several Bayesian multiple-kernel models. These results lay a foundation for implementing effective Monte Carlo algorithms for analysing real-world data with Gaussian processes, and highlight the need to develop a customisable library set that allows users to incorporate dynamically programmed objects and to finely optimise the mode of automatic differentiation depending on the model structure. Full article

In this paper, we present rigorous asymptotic componentwise perturbation bounds for regular Hermitian indefinite matrix eigendecompositions, obtained via the method of splitting operators. The asymptotic bounds are derived from exact nonlinear expressions for the perturbations and allow each entry of every matrix eigenvector to be bounded in the case of distinct eigenvalues. In contrast to the perturbation analysis of the Schur form of a nonsymmetric matrix, the bounds obtained here do not rely on the Kronecker product, which significantly reduces both memory requirements and computational cost. This enables efficient sensitivity analysis of high-order problems. The eigenvector perturbation bounds are further applied to estimate the angles between perturbed and unperturbed one-dimensional invariant subspaces spanned by the corresponding eigenvectors. To reduce conservatism in the case of high-order problems, we propose the use of probabilistic perturbation bounds based on the Markov inequality. The analysis is illustrated by two numerical experiments of order 5000. Full article

This study evaluated ten drought indices focusing on their ability to monitor drought events in Marathwada, a semi-arid region of India. High-resolution gridded monthly total precipitation data for 75 years (1950–2024) from the European Centre for Medium-Range Weather Forecasts (ECMWF) were used to evaluate the drought indices. These indices were computed across six timescales: 1, 3, 4, 6, 9, and 12 months. A Generalized Autoregressive Conditional Heteroscedastic (GARCH) model was employed to detect temporal volatility in precipitation, followed by a second-order geospatial autocorrelation eigenfunction eigendecomposition using Global Moran’s Index statistics to geolocate both aggregated and non-aggregated precipitation locations. The performance of drought indices was assessed using non-parametric Spearman’s correlation to identify the strength, direction, and similarity of regional-specific drought events. The temporal lag interdependence between meteorological and agricultural droughts was assessed using a non-parametric Spearman’s cross correlation function (SCCF). The findings revealed that the GARCH model with a skewed Student’s t distribution effectively captured conditional temporal volatility and asymptotic behavior in the precipitation series. The model’s sensitivity enabled the incorporation of temporal fluctuations related to droughts and extreme meteorological events. The Bhalme and Mooley Drought Index (BMDI-6) and Z-Score Index (ZSI-6) were the most applicable indices for drought monitoring. Spearman’s cross-correlation analysis revealed that meteorological droughts influenced agricultural droughts with a time lag of up to 4 months. Full article

A fundamental limitation of maximum likelihood and Bayesian methods under model misspecification is that the asymptotic covariance matrix of the pseudo-true parameter vector ${\mathsf{\theta }}_{*}$ is not the inverse of the Fisher information, but rather the sandwich covariance matrix ${\displaystyle \frac{1}{n}}{\mathbf{A}}_{*}^{-1}{\mathbf{B}}_{*}^{\phantom{-1}}{\mathbf{A}}_{*}^{-1}$, where ${\mathbf{A}}_{*}$ and ${\mathbf{B}}_{*}$ are the sensitivity and variability matrices, respectively, evaluated at ${\mathsf{\theta }}_{*}$ for training data record ${\omega }_1,\dots ,{\omega }_n$. This paper makes three contributions. First, we review existing approaches to robust posterior sampling, including the open-faced sandwich adjustment and magnitude- and curvature-adjusted Markov chain Monte Carlo (MCMC) simulation. Second, we introduce a new sandwich-adjusted MCMC method. Unlike existing approaches that rely on arbitrary matrix square roots, eigendecompositions or a single scaling factor applied uniformly across the parameter space, our method employs a parameter-dependent learning rate $\lambda \left(\mathsf{\theta }\right)$ that enables direction-specific tempering of the likelihood. This allows the sampler to capture directional asymmetries in the sandwich distribution, particularly under model misspecification or in small-sample regimes, and yields credible regions that remain valid when standard Bayesian inference underestimates uncertainty. Third, we propose information-theoretic diagnostics for quantifying model misspecification, including a strictly proper divergence score and scalar summaries based on the Frobenius norm, Earth mover’s distance, and the Herfindahl index. These principled diagnostics complement residual-based metrics for model evaluation by directly assessing the degree of misalignment between the sensitivity and variability matrices, ${\mathbf{A}}_{*}$ and ${\mathbf{B}}_{*}$. Applications to two parametric distributions and a rainfall-runoff case study with the Xinanjiang watershed model show that conventional Bayesian methods systematically underestimate uncertainty, while the proposed method yields asymptotically valid and robust uncertainty estimates. Together, these findings advocate for sandwich-based adjustments in Bayesian practice and workflows. Full article

This paper presents a near real-time implementation of the Karhunen–Loève Transform (KLT) for Radio Frequency Interference (RFI) mitigation in microwave radiometry. KLT is a powerful, data-adaptive technique capable of adjusting to various signal types by estimating the covariance matrix of the incoming signal and segmenting its eigenvectors to form an effective RFI basis. In this paper, the KLT is evaluated with real signals in laboratory conditions, aiming to characterize its performance in realistic conditions. To that effect, the dual Rx/Tx capability of a Pluto SDR is used to generate and capture RFI. The main mitigation metrics are computed for the KLT and other commonly used mitigation methods. In addition, while previous studies have shown the effectiveness of offline processing of recorded I/Q data, real-time mitigation is often necessary. Given the computational cost of eigendecomposition, this work introduces a low-complexity solution using the “economy covariance” approach alongside asynchronous covariance decomposition. The proposed implementation, realized within the GNU Radio framework, demonstrates the practical feasibility of real-time KLT-based mitigation and underscores its potential for improving signal integrity in digital radiometers operating under dynamic RFI conditions. Full article

As a key technology for the fifth-generation of mobile communications, massive MIMO systems enable massive user access via large-scale arrays. However, their dense deployment extends the near-field (NF) region, introducing new localization complexities. Based on an exact spherical wavefront model, this paper proposes a multiple-cumulant-matrices-based method for NF source localization using a Co-centered Orthogonal Loop and Dipole (COLD) array. Firstly, following the physical numbering of array elements, we can construct multiple polarization cumulant matrices, which can then be cascaded into a long matrix. Next, the signal subspace can be obtained through eigen-decomposition of this long matrix, from which the horizontal and vertical components can be further separated. By applying ESPRIT, joint angle, range, and polarization parameters can be estimated. In addition, the asymptotic variances for joint spatial and polarization parameters are analyzed. Compared with existing NF polarization algorithms, the proposed method exhibits better parameter estimation and is consistent with a theoretical asymptotic performance. Full article

Hierarchical clustering analysis (HCA) is a widely used unsupervised learning method. Limitations of HCA, however, include imposing an artificial hierarchy onto non-hierarchical data and fixed two-way mergers at every level. To address this, the current work describes a novel rootlets hierarchical principal component analysis (hPCA). This method extends typical hPCA using multivariate statistics to construct adaptive multiway mergers and Riemannian geometry to visualize nested dependencies. The rootlets hPCA algorithm and its projection onto the Poincaré disk are presented as examples of this extended framework. The algorithm constructs high-dimensional mergers using a single parameter, interpreted as a p-value. It decomposes a similarity matrix from GL(m, ℝ) using a sequence of rotations from SO(k), k << m. Analysis shows that the rootlets algorithm limits the number of distinct eigenvalues for any merger. Nested clusters of arbitrary size but equal correlations are constructed and merged using their leading principal components. The visualization method then maps elements of SO(k) onto a low-dimensional hyperbolic manifold, the Poincaré disk. Rootlets hPCA was validated using simulated datasets with known hierarchical structure, and a neuroimaging dataset with an unknown hierarchy. Experiments demonstrate that rootlets hPCA accurately reconstructs known hierarchies and, unlike HCA, does not impose a hierarchy on data. Full article

In recent years, phase linking (PL) methods in radar time-series interferometry (TSI) have proven to be powerful tools in geodesy and remote sensing, enabling the precise monitoring of surface displacement and deformation. While these methods are typically designed to operate on a complete network of interferograms, generating such networks is often challenging in practice. For instance, in non-urban or vegetated regions, decorrelation effects lead to significant noise in long-term interferograms, which can degrade the time-series results if included. Additionally, practical issues such as gaps in satellite data, poor acquisitions, or systematic errors during interferogram generation can result in incomplete networks. Furthermore, pre-existing interferogram networks, such as those provided by systems like COMET-LiCSAR, often prioritize short temporal baselines due to the vast volume of data generated by satellites like Sentinel-1. As a result, complete interferogram networks may not always be available. Given these challenges, it is critical to understand the applicability of PL methods on these incomplete networks. This study evaluated the performance of two PL methods, eigenvalue decomposition (EVD) and eigendecomposition-based maximum-likelihood estimator of interferometric phase (EMI), under various network configurations including short temporal baselines, randomly sparsified networks, and networks where low-coherence interferograms have been removed. Using two sets of simulated data, the impact of different network structures on the accuracy and quality of the results was assessed. These patterns were then applied to real data for further comparison and analysis. The findings demonstrate that while both methods can be effectively used on short temporal baselines, their performance is highly sensitive to network sparsity and the noise introduced by low-coherence interferograms, requiring careful parameter tuning to achieve optimal results across different study areas. Full article