Search Results (268)

In this paper, we introduce and investigate a new class of r-circulant matrices whose entries are generated by higher-order Fibonacci numbers. Explicit representations of the eigenvalues of these matrices are derived by means of the Binet formula together with the structural properties of r-circulant matrices. Based on these representations, a closed-form expression for the determinant is obtained. In addition, several summation identities involving higher-order Fibonacci numbers are established, including formulas for partial sums, sums of squares, and weighted sums. These identities play a fundamental role in the derivation of the norm expressions and spectral estimates of the matrices. Furthermore, several matrix norms, including the Euclidean (Frobenius) norm, the 1-norm, the ∞-norm, and the spectral norm, are investigated in detail. Lower and upper bounds for the spectral norm are obtained for both cases $\left|r\right|\ge 1$ and $\left|r\right|<1$ by employing Hadamard product techniques and classical norm inequalities. Finally, numerical examples are presented to illustrate and validate the theoretical results. Full article

Low Earth orbit (LEO) satellite systems provide ubiquitous global connectivity for massive grant-free random access Internet of Things (IoT) applications. Full frequency reuse (FFR) improves spectrum efficiency in spectrum sharing scenarios but introduces severe adjacent beam and cross-system co-channel interference. Meanwhile, the high mobility of LEO satellites hinders accurate instantaneous channel state information (iCSI) acquisition, and random direction-of-arrival (DOA) estimation errors cause statistical CSI (sCSI) mismatch, which degrades beamforming performance and makes it difficult to balance transmission robustness, user fairness, and onboard computational complexity. To address these issues, we propose a low-complexity Hybrid Optimized Robust Beamforming (HORBA) algorithm. We first construct a robust joint optimization model to characterize the coupling effects of DOA errors, outdated CSI, and multi-dimensional interference, with constraints on per-user minimum SINR and cross-system interference temperature. Then, based on the block coordinate descent framework, we decouple the original non-convex problem into two convex subproblems, which are solved via generalized eigenvalue decomposition and first-order Taylor expansion, combined with an adaptive sampling mechanism that balances accuracy and complexity. Simulation results verify that our algorithm outperforms typical benchmarks in sum rate and robustness, maintains low onboard processing complexity, and effectively alleviates edge user rate polarization. Full article

This study examines the temporal evolution of low-carbon energy production in the European Union (EU27) using annual data for 1990–2022, focusing on the dynamic interaction between nuclear, renewable, and biofuel production at the EU aggregate level. After evaluating stochastic properties via Augmented Dickey–Fuller (ADF) tests and assessing long-run cointegration through the Johansen framework, short-run interactions are modeled using a Vector Autoregression (VAR) of order one. Dynamic responses and innovation variances are analyzed using impulse response functions (IRFs) and forecast error variance decomposition (FEVD). The Augmented Dickey–Fuller (ADF) results suggest both series are I(1). The Johansen test fails to reject the null of no cointegration, implying that there is no stable long-run equilibrium relationship between the two series over 1990–2022. VAR-based IRFs show small, short-lived cross-responses that dissipate within a few years. FEVD results indicate that variance shares are horizon-dependent and sensitive to the Cholesky ordering. Granger causality tests provide limited evidence of short-run directional predictability. A Zivot–Andrews test does not reject the unit-root-with-break null. These findings suggest that nuclear and renewables follow largely independent dynamics in the EU27 aggregate. A key limitation is that EU27 aggregation masks cross-country heterogeneity (e.g., Germany vs. France) and excludes policy variables, prices, and demand-side drivers. The estimated VAR(1) satisfies the stability condition: all eigenvalues of the companion matrix lie inside the unit circle (modulus < 1), confirming that the system is dynamically stable. Full article

To address the sharp degradation in positioning accuracy and the lack of robustness of received signal strength indication (RSSI)-based indoor localization methods when both the reference RSSI and path-loss exponent are mismatched, a Differential Iterative Joint Estimation (DIJE) localization method is proposed in this paper. The proposed method first employs a differential model to eliminate the uncertainty caused by reference RSSI, transforming the maximum likelihood estimation (MLE) problem into a matrix eigenvalue problem to enable fast and high-accuracy target position estimation. Additionally, an alternating iterative optimization framework for target position and path-loss exponent is constructed to achieve adaptive joint estimation of model parameters and target coordinates, effectively suppressing localization performance degradation induced by parameter mismatch. In this paper, the Cramér–Rao Lower Bound (CRLB) under the dual-parameter uncertainty scenario is derived as a theoretical performance benchmark, and both simulation experiments and public real-world datasets are used to validate the method’s performance. The results demonstrate that the DIJE method can approach the theoretical limit under varying noise levels, access point (AP) densities, and complex indoor environments. Compared with classical algorithms such as RSDPE, MLE-TLLS, SOCP3, and LCJE, the DIJE method exhibits significant advantages in localization accuracy, robustness, and adaptability to initial parameters, and can meet the engineering requirements of high-accuracy and low-latency real-time indoor localization. Full article

Traditional sliding mode control (SMC) lacks an active mechanism for redistributing energy among state channels during transient convergence, resulting in a rigid trade-off between response speed, overshoot suppression, and energy efficiency. This paper proposes a virtual state coupled SMC method that introduces a dynamic virtual state with bilinear product coupling $x_1{x}_2$ into the sliding surface. Unlike conventional virtual states that serve as static linear combinations or observer-based estimates, the proposed virtual state evolves dynamically and establishes an active energy exchange channel between the real and virtual state dynamics. Linearization and Lyapunov-based analyses prove local asymptotic stability of the closed-loop system. The coupling strength $\gamma$ is shown to be decoupled from the linearized local eigenvalues and thus governs the energy–performance trade-off independently, while the condition $c>\gamma /4$ guarantees a non-vanishing domain of attraction. Simulations demonstrate that the proposed method achieves up to 53.2% control energy reduction under disturbance-free conditions compared with conventional SMC. Under persistent high-frequency disturbances, increasing $\gamma$ reduces oscillations by 54.2% at a controllable energy cost of 45.7%. Systematic parameter selection guidelines are provided, and Monte Carlo simulations (500 trials, $\pm 30\%$ parameter perturbations) confirm 100% convergence. The proposed method offers an independently adjustable energy–performance trade-off mechanism suitable for sensor-based motion systems with stringent transient and energy requirements. Full article

To improve the accuracy and stability of X-ray pulsar time-delay estimation for multi-scenario celestial remote sensing and navigation, this paper proposes a time-delay estimation method based on a waterfall-plot multi-criteria framework and develops an end-to-end simulation framework for multi-scenario applications. First, a pulsar profile waterfall-plot model is built, and principal component analysis is performed to characterize candidate periodic structures. The contribution rate of the principal eigenvalue is used to describe the overall significance of the candidate period, and the projection variance of the first principal component is used to measure the prominence of the candidate pattern in the principal subspace. Second, support vector regression is used to fit the peak track of the waterfall plot, and a regression slope is used to describe the geometric stability of the candidate period. These three indicators are fused for pulsar period and time-delay estimation. Tests based on Insight-HXMT satellite observation data show that, compared with the ${\chi }^2$ and $Z^2$ test methods, our method improves time-delay estimation accuracy by 68.68% and 50.43%, respectively. Multi-scenario navigation simulations indicate positioning improvements of approximately 0.83 km, 3.04 km, and 1.05 km in the Earth-orbiting, Earth–Moon transfer, and Mars approach scenarios, respectively. These results suggest that the proposed framework can improve pulsar time-delay estimation and may provide useful measurement support for celestial remote sensing and navigation. Full article

Although secondary control of direct current (DC) microgrids has been widely studied, traditional static current sharing may still cause severe voltage sag under large-signal constant power load (CPL) steps, and many distributed schemes rely on global topology information while showing limited transient disturbance rejection. To address these issues, this paper proposes an observer-assisted, stability-margin-driven prescribed-time distributed secondary control strategy for islanded DC microgrids. A dynamic CPL risk evaluation function updates current-sharing ratios according to converter operating margins, while a distributed prescribed-time observer estimates disturbance envelopes and alleviates high-frequency chattering. Local adaptive gains remove the explicit dependence of controller tuning on global Laplacian eigenvalue information. MATLAB R2024a-based numerical studies show that, under a 6000 W CPL stress scenario, the proposed method limits the maximum voltage drop to 3.37 V, compared with 24.60 V for the conventional virtual current derivative (VCD) method. Under heterogeneous line impedances and a non-ideal digital benchmark, the proposed method yields a normalized current-sharing error of 0.72%, whereas the VCD method exhibits milder voltage transients. These results support the algorithmic effectiveness and numerical robustness of the proposed strategy within the adopted validation environment. Full article

The Eigenspace method has been widely applied in the ultrasonic field, and this method can improve the resolution and achieve good robustness. However, all existing methods require the number of sources in the space to be known. This paper proposes a high-resolution direction-of-arrival (DOA) estimation method based on the Eigenspace theory with an unknown number of sources in the PM domain. The proposed method first decomposes the received signals of a circular array into orthogonal PM signals and then extends the Eigenspace method into the phase mode (PM) domain. Since the existing Eigenspace methods project the optimal beam scanning vector onto the signal subspace, the number of sources needs to be known in advance. However, in practical scenarios, the number of sources is unknown. The proposed method employs the combination term of the PM covariance matrix and its eigenvalues to perform power operations, which can approximately achieve the closed-form expressions of the relevant parameters for the signal subspace and the noise subspace. Finally, high-resolution DOA estimation is achieved under the condition of an unknown number of sources. Simulation and experimental results demonstrate the effectiveness of the proposed method in high-resolution DOA with an unknown number of sources. Full article

In this paper, we establish Lyapunov-type and Hartman–Wintner-type integral inequalities for boundary value problems involving a class of composite fractional integral operators. By employing an explicit Green function representation and sharp uniform bounds for the associated kernel, we derive necessary conditions for the existence of nontrivial solutions. A distinctive feature of the obtained results is the higher-order scaling behavior induced by the interaction of left- and right-sided components of the operator, which cannot be observed in classical one-sided fractional models. As applications, we obtain quantitative nonexistence criteria and explicit lower bounds for the principal eigenvalue of the corresponding eigenvalue problem. These estimates extend classical results to a higher-order fractional framework and highlight the influence of the domain geometry on the stability of the solutions. Full article

Real-time Direction of Arrival (DOA) estimation demands high computational throughput and numerical precision. Consequently, dedicated hardware accelerators are essential. This paper presents an architecture to accelerate the MUSIC algorithm using an improved complex bilateral Jacobi eigenvalue decomposition (EVD). First, we design a triangular systolic array for Hermitian matrices. It employs an output-stationary dataflow to enable efficient parallel covariance computation. Second, we propose an enhanced EVD algorithm. It replaces CORDIC approximations with direct analytical rotations. This significantly improves numerical stability and accuracy. Third, we introduce hardware optimizations. These include unit reuse, integrated termination conditions, and pre-stored steering vectors. These measures reduce resource consumption while maintaining full functionality. Experiments on a Xilinx Virtex-6 platform validate the design. The architecture achieves a root mean square error (RMSE) below $0.24°$ with 300 snapshots. Processing latency is only 76.17 µs. The design utilizes 10,775 LUTs and 73 DSP slices. This work balances accuracy, speed, and efficiency. It offers a practical solution for real-time, high-precision DOA systems. Full article

We derive the eigenvalue bounds for symmetric block-tridiagonal multiple saddle-point systems preconditioned with the symmetric positive definite (SPD) preconditioner proposed by J. Pearson and A. Potschka in 2024 and further studied by L. Bergamaschi and coauthors, and for double saddle-point problems with inexact Schur complement matrices. The analysis applies to an arbitrary number of blocks. We validate the proposed estimates with both synthetic and realistic test problems, and show the good performance of the proposed preconditioner under the condition that the Schur complements are accurately approximated. Full article

EigenPlaces is a state-of-the-art visual place recognition (VPR) method that constructs training classes via SVD-based focal points, where a fixed focal distance D controls how far the focal point is placed from each cell center. However, this globally fixed D cannot adapt to the diverse scene geometries encountered across different urban environments. In this work, we systematically analyze the sensitivity of D across multiple benchmark datasets and reveal that the optimal D value is highly dataset-dependent, with performance gaps of up to 4.4 percentage points between the best and worst D choices. We then propose a depth-aware adaptive D strategy that leverages monocular depth estimation to compute per-cell focal distances, combined with quantile mapping to ensure sufficient variance in the assigned D values. By establishing a principled connection between visual sensor data and geometric training supervision, our method enhances the environmental perception reliability of intelligent sensing platforms. Experiments on three benchmarks (Pitts30k, AmsterTime, SF-XL) validate the dataset-dependent nature of D and confirm that our depth-aware approach achieves the best same-distribution performance among all tested configurations. We further conduct a multi-strategy ablation comparing depth raw, depth quantile, and SVD eigenvalue ratio approaches, providing practical guidance for adaptive focal distance selection in VPR training pipelines. Full article

This paper investigates the transient stability characteristics of a DC-coupled off-grid photovoltaic hydrogen production system. A nonlinear state-space model of the system is established by integrating the photovoltaic generation unit, the energy storage unit, and the electrolyzer unit. To enhance system dynamic performance, a virtual DC machine (VDCM) control strategy is introduced for the energy storage converter. Based on the nonlinear system model, a Takagi–Sugeno (TS) fuzzy model is constructed to approximate the system dynamics, and the largest estimated domain of attraction (LEDA) is derived using Lyapunov stability theory. Simulation studies are conducted to evaluate system stability under sudden photovoltaic power fluctuations caused by environmental disturbances, and the obtained LEDA is compared with the simulated attraction domain and the power boundary derived from the Lyapunov eigenvalue method. The results show that the LEDA obtained from the TS fuzzy model can effectively estimate the stability boundary of the system, although it remains slightly conservative. Furthermore, the impacts of VDCM control parameters and electrolyzer operating states on system stability are analyzed. Simulation results demonstrate that appropriate adjustment of system parameters can enlarge the LEDA and significantly improve the transient stability of the off-grid photovoltaic hydrogen production system. Full article

This paper addresses the problem of robust identification of gross errors affecting both measurements and network parameters in power system state estimation. The study is conducted within a steady-state framework and focuses on improving bad data identification in the presence of modeling and measurement uncertainties, explicitly accounting for the limited observability of gross errors. Building on an Extended Weighted Least Squares (EWLS) estimator and a theoretically refined eigenvalue-based clustering of dominant error components, a novel Bayesian identification framework is introduced. The proposed Bayesian approach assigns probabilities to competing gross error models, including scenarios involving multiple simultaneous errors, given the observed clusters of dominant errors. This probabilistic formulation enables a systematic and quantitative decision-making process for identifying the most likely sources of gross errors, extending existing deterministic or heuristic approaches. The methodology is evaluated through numerical simulations on the IEEE-14 bus test system, considering several gross error scenarios and significant parameter uncertainties. The results demonstrate that the proposed Bayesian framework enhances the interpretability and discriminative capability of gross error identification, highlighting its potential for robust bad data identification in power system state estimation. Full article

The critical brain hypothesis proposes that neural systems operate near a phase transition to optimize information processing. A key method for investigating this hypothesis is the phenomenological renormalization group (pRG), which looks for scale-invariant features across levels of coarse-graining. One such feature is the power-law scaling of eigenvalues of covariance matrices of coarse-grained variables. However, the estimation of this scaling exponent, $\mu$, often relies on linear regression over arbitrarily selected ranges of the plot of eigenvalues versus rank. This heuristic “eyeballing” introduces uncontrolled bias and complicates the interpretation of observed scaling relationships. In order to obtain a more robust estimation of $\mu$, we do not fit the standard eigenvalue-vs-rank relationship, but rather the density of eigenvalues, for which standard protocols exist for fitting power laws to empirical data distributions. We demonstrate this approach using a synthetic model that replicates the scaling signatures of neural data while providing control over the system’s exponents as well as neural data obtained from publicly available Neuropixels recordings. We also establish standards for the minimal data required to quantify power-law behavior in a pRG eigenvalue analysis. Our approach contributes a tool for understanding the fundamental limitations imposed by spatial and temporal constraints of experimental datasets, which is required to rigorously assess the neural criticality hypothesis. Full article