This paper investigates the qualitative behavior of semilinear Hilfer-nabla fractional discrete time systems characterized by inherent memory effects. The considered model employs the Hilfer-type fractional difference operator, which interpolates between the Riemann-Liouville and Caputo nabla operators and provides additional flexibility through the order and type parameters. By transforming the system into an equivalent fractional Volterra summation equation, an explicit representation of the solution is obtained via discrete multi-parameter Mittag-Leffler functions using the Picard’s successive approximation method. Based on this representation, sufficient conditions ensuring the existence, uniqueness, finite-time stability, and attractive stability of the system are derived. Finally, two numerical examples are presented to validate the theoretical findings and illustrate the effectiveness of the proposed stability criteria.
In this paper, an adaptive correlated Gaussian approximation filter (A-CGAF) is introduced for nonlinear state estimation problems when there are correlated noises of process and measurement. Classical statistics-fixed filtering techniques have to rely on a priori knowledge of static noise correlation; otherwise, their performance will be degraded. This paper seeks to improve the problem by developing a new algorithm that takes advantage of a neural network to estimate the noise cross-correlation in an online fashion based on a correlated Gaussian approximation filter structure. The effectiveness of the approach is demonstrated through simulations conducted under static, sudden, and gradually changing noise cross-correlation environments. Simulation results show that the proposed A-CGAF has superior estimation accuracy, robustness, and fast convergence performance compared with the fixed statistics-based competitors. More specifically, it delivers a 20.43
In this paper, we introduce the working of signals, systems, and signal processing on totally weighted graphs. We discuss some real-world systems on graphs by considering sensing points as vertices, connection between sensing points as edges, assigning signal values as vertex weight, measure of connection between vertices as edge weight, and try to ensure the efficiency of the system by assigning a signal condition on each vertex. By suggesting a matrix representation for this system, we try to connect the matrix energy as a measure of the energy of the signal and system. In addition, signal processing is represented on totally weighted graphs considering a different type of edge weight. Also, discussed are the sampling of analog signal and representation of the digitalized signal on totally weighted graph. We also consider the energy of signal, system, and signal processing matrix as a measure of efficiency.
Robust adaptive filtering is a key technique for sparse system identification. However, traditional algorithms struggle to balance robustness, convergence speed, and steady-state accuracy under impulsive and heavy-tailed noise. The logarithmic Student’s t-based filtering method offers good robustness to impulsive noise due to its heavy-tailed error modeling, but its fixed zero-centered symmetric assumption introduces steady-state bias under nonzero-mean noise and does not fully leverage the system’s sparsity prior. To address this, we propose the Logarithmic Student’s t-based Generalized Maximum Variable-Center Correntropy (LSGMVCC) algorithm, which dynamically adjusts the error distribution center using a sliding-window median to compensate for nonzero-mean bias. Additionally, we introduce a sparsity-enhanced variant, SN-LSGMVCC, incorporating a sparsity-aware regularization term for improved convergence and steady-state accuracy in sparse system identification. Simulation results demonstrate that the proposed algorithms achieve faster convergence and lower steady-state mean square deviation under various non-Gaussian noise environments, significantly enhancing the robust identification performance of sparse systems.
The growing deployment of unmanned aerial vehicles in sensitive fields such as military operations demands high levels of image security and authentication. To address the increasing risk of tampering, this study proposes a robust watermarking and encryption framework designed to ensure both the integrity and confidentiality of unmanned aerial vehicles images. The proposed hybrid technique integrates non-subsampled shearlet transform, QR decomposition and multi-level singular value decomposition for robust and imperceptible watermark embedding. To further secure the data, double random phase encoding is applied for encryption, followed by compression using compressive sensing to enable efficient storage and transmission. The framework is evaluated using standard image quality and security metrics under various attack conditions. Experimental results demonstrate that the method preserves the visual quality of unmanned aerial vehicles images after decryption and offers strong resilience to common signal processing and noise attacks. The watermark remains reliably detectable, with minimal loss of image fidelity. The proposed framework ensures secure transmission and authentication of unmanned aerial vehicles images while maintaining high image quality. Its layered architecture shows significant potential for deployment in real-time unmanned aerial vehicles—based applications, especially where security and data integrity are critical.
