Search Results (29)

Reliable short-term position forecasting may provide anticipatory state information for collision-risk assessment, communication management, and prediction-assisted control in Internet of Things (IoT)-enabled unmanned aerial vehicles (UAVs); these downstream functions are not evaluated directly here. This study reformulates UAV position prediction as a flight-wise, multi-horizon, three-dimensional forecasting problem and tests whether position, velocity, gravity-resolved acceleration, and quaternion-orientation histories improve predictive accuracy while measuring model-level edge-inference cost rather than end-to-end system latency. The dataset contains 3100 AirSim flights with high-rate kinematic, inertial, attitude, pressure, and magnetic-field measurements under variable horizontal wind. The reported generalization is flight-disjoint within one AirSim domain; route/scenario disjointness and transfer to physical UAVs are not established. Signals are converted to a common navigation frame, gravity-resolved, low-pass filtered, resampled to 50 Hz, and partitioned by flight identifier before normalization and window construction. Each learned model receives 2 s of history and predicts the complete next 1 s trajectory, with errors evaluated at 0.1, 0.5, and 1.0 s. The sensor-enriched LSTM (LSTM-PVAQ) is compared under matched conditions with persistence, constant-velocity, constant-acceleration, extended Kalman filter, reduced-feature LSTM, GRU, temporal convolutional network (TCN), and compact Transformer baselines. LSTM-PVAQ achieved 3D RMSE values of 0.043, 0.168, and 0.371 m at 0.1, 0.5, and 1.0 s, respectively. At 1 s, its RMSE was 21.7% lower than LSTM-PV, 13.1% lower than GRU-PVAQ, 9.3% lower than TCN-PVAQ, and 16.8% lower than Transformer-PVAQ. Its one-second ADE and FDE were 0.216 and 0.339 m. On a Raspberry Pi 5 CPU using one FP32 thread and batch size one, median neural forward-pass latency was 0.88 ms, well below the 20 ms model-update interval. The results show that gravity-resolved inertial and orientation histories improve multi-horizon prediction, while TCN-PVAQ remains an attractive lower-latency alternative. Full article

Caregiver–patient traceability is essential for measuring care workload and interaction time in shared hospital rooms, where a single caregiver attends multiple patients and manual documentation is intrusive, time-consuming, and prone to errors. This paper proposes a non-invasive smart bedside sensing approach based on a commercial smartwatch with integrated Ultra-Wideband (UWB) radio worn by the caregiver and two compact UWB localization anchors deployed near the monitored beds. The classification approach uses a compact smartwatch feature set comprising three-axis magnetometer measurements and a four-component orientation quaternion provided by the device through Magnetic, Angular Rate, and Gravity (MARG)-based sensor fusion. No device is required to be worn by the patients. The system was evaluated in a shared hospital room measuring approximately $5.0\times 4.8$ m, with two hospital beds separated by 1.3–1.7 m. Three datasets involving two caregiver participants were included in the evaluation. Several supervised learning approaches were evaluated, including Long Short-Term Memory (LSTM) networks, a hybrid Convolutional Neural Network plus LSTM (CNN+LSTM) architecture, Extreme Gradient Boosting (XGBoost), and a non-linear Support Vector Machine (SVM). XGBoost and SVM achieved the best overall performance, reaching a macro F1-score of 0.97. The results demonstrate that compact wrist-worn magnetic and MARG-derived orientation signals can accurately identify the attended bed, supporting scalable and objective caregiver–patient traceability in shared hospital rooms with minimal infrastructure. Full article

This article presents a detailed study of the two-dimensional quaternion fractional Fourier transform (2D QFRFT) and investigates its role in the probabilistic analysis of quaternion-valued signals. The 2D formulation is constructed by applying fractional Fourier transforms independently along each spatial dimension, thereby extending classical 2D Fourier and fractional Fourier frameworks to the quaternion domain. Key analytical properties of the 2D QFRFT, including linearity, shift behavior, differentiation, convolution, and energy relations, are summarized based on existing results in the literature. Furthermore, the transform is employed to define and analyze fundamental probabilistic quantities, such as expected value and normalized probability distributions, within the 2D quaternion fractional transform domain. These results provide a systematic 2D extension of existing quaternion transform-based probabilistic models and offer a clear theoretical foundation for the representation and analysis of 2D quaternion-valued signals in non-commutative settings. Full article

Advances in visual recognition have relied on increasingly deep and wide convolutional neural networks (CNNs), which often introduce substantial computational and memory costs. This review summarizes recent progress in parameter-efficient CNN design across three directions: hypercomplex representations with cross-channel weight sharing, axial attention mechanisms, and real-valued architectures using separable convolutions. We highlight how these approaches reduce parameter counts while maintaining or improving accuracy. We further analyze our contributions within this landscape. Full hypercomplex neural networks (FHNNs) employ hypercomplex layers throughout the architecture to reduce latency and parameters, while representational axial attention models (RepAA) extend this efficiency by generating additional feature representations. To mitigate the remaining overhead of spatial hypercomplex operations, we introduce separable hypercomplex networks (SHNNs), which factorize quaternion convolutions into sequential vectormap operations, lowering parameters by approximately $50\%$. Finally, we compare these models with popular efficient architectures, such as MobileNets and SqueezeNets, and demonstrate that our residual one-dimensional convolutional networks (RCNs) achieve competitive performance in image classification and super-resolution with significantly fewer parameters. This review highlights emerging strategies for reducing computational overhead in CNNs and outlines directions for future research. Full article

Despite the popularity of electroencephalograms (EEGs) as tools for assessing brain health, they can sometimes be abstract and prone to noise, making them difficult to interpret. The following work aims to implement a Quaternion Convolutional Neural Network (QCNN) to detect abnormal EEGs obtained from a database that includes both people with excellent mental health and individuals with different types of mental illnesses. Unlike other approaches in which the QCNN is used exclusively for image processing, in the present work, a unique architecture with mainly quaternionic layers is proposed, specifically designed for the classification of time-varying signals. Using the database “The TUH EEG Abnormal Corpus”, the signals are preprocessed using the Wavelet Transform, a mathematical tool capable of performing simultaneous time and frequency analysis, configured with a level 4 decomposition value. Subsequently, the results are subjected to a partial spectrogram-type treatment to integrate the energy parameter into the analysis. They are then conditioned in each of the elements of the quaternion and processed by the QCNN, leveraging quaternion algebra to maintain the relationships between its elements, both in the input and in the convolutional product. In this way, it is possible to obtain significant percentages in the precision, recall, and accuracy metrics with values higher than 77%. Its performance, which uses 4 times less computational memory, allows the QCNN to be considered an alternative for classifying EEG signals. Finally, a comparison of the proposed model was made with other architectures commonly used in the literature, as well as with developments in other research and with a hybrid model whose performance places it at the highest classification standard, not to mention the ability of the QCNN to preserve multi-channel dependencies in EEG signals in a more natural way, achieving parameter efficiencies by leveraging quaternion algebra, reducing the computational cost compared to real-valued CNNs. Full article

The rapid evolution of virtual reality systems and the broader metaverse landscape has prompted growing research interest in biometric authentication methods for user verification. These solutions offer an additional layer of access control that surpasses traditional password-based approaches by leveraging unique physiological or behavioral traits. Current literature emphasizes analyzing controller position and orientation data, which presents challenges when using convolutional neural networks (CNNs) with non-continuous Euler angles. The novelty of the presented approach is that it addresses this limitation. We propose a modality transformation approach that generates acceleration and angular velocity signals from trajectory and orientation data. Specifically, our work employs algebraic techniques—including quaternion algebra—to model these dynamic signals. Both the original and transformed data were then used to train various CNN architectures, including Vanilla CNNs, attention-enhanced CNNs, and Multi-Input CNNs. The proposed modification yielded significant performance improvements across all datasets. Specifically, F1-score accuracy increased from 0.80 to 0.82 for the Comos subset, from 0.77 to 0.82 for the Quest subset, and notably from 0.83 to 0.92 for the Vive subset. Full article

In this research work, we focus on the one-dimensional quaternion linear canonical transform (1-D QLCT). Under certain conditions, we first derive the symmetry property of the 1-D QLCT for real signals. The new form of the convolution theorem related to this transformation is proposed. We develop this convolution definition to derive the correlation theorem for the 1-D QLCT. We then show that the direct connection between the quaternion convolution and quaternion correlation definitions permits us to provide a different way for proving the correlation theorem concerning the 1-D QLCT. Finally, we present a simple application of the convolution theorem to the study of quaternion swept-frequency filter analysis. Full article

In this paper, we describe the associative and commutative algebra or the (2,2)-model of quaternions with application in color image enhancement. The method of alpha-rooting, which is based on the 2D quaternion discrete Fourier transform (QDFT) is considered. In the (2,2)-model, the aperiodic convolution of quaternion signals can be calculated by the product of their QDFTs. The concept of linear convolution is simple, that is, it is unique, and the reduction of this operation to the multiplication in the frequency domain makes this model very attractive for processing color images. Note that in the traditional quaternion algebra, which is not commutative, the convolution can be chosen in many different ways, and the number of possible QDFTs is infinite. And most importantly, the main property of the traditional Fourier transform that states that the aperiodic convolution is the product of the transform in the frequency domain is not valid. We describe the main property of the (2,2)-model of quaternions, the quaternion exponential functions and convolution. Three methods of alpha-rooting based on the 2D QDFT are presented, and illustrative examples on color image enhancement are given. The image enhancement measures to estimate the quality of the color images are described. Examples of the alpha-rooting enhancement on different color images are given and analyzed with the known histogram equalization and Retinex algorithms. Our experimental results show that the alpha-rooting method in the quaternion space is one of the most effective methods of color image enhancement. Quaternions allow all colors in each pixel to be processed as a whole, rather than individually as is done in traditional processing methods. Full article

The application of robot technology in the automatic transportation process of packaging bags is becoming increasingly common. Point cloud registration is the key to applying industrial robots to automatic transportation systems. However, current point cloud registration models cannot effectively solve the registration of deformed targets like packaging bags. In this study, a new point cloud registration network, DCDNet-Att, is proposed, which uses a variable weight dynamic graph convolution module to extract point cloud features. A feature interaction module is used to extract common features between the source point cloud and the template point cloud. The same geometric features between the two pairs of point clouds are strengthened through a bottleneck module. A channel attention model is used to obtain the channel attention weights. The attention weight of each spatial position is calculated, and a rotation translation structure is used to sequentially obtain quaternions and translation vectors. A feature fitting loss function is used to constrain the parameters of the neural network model to have a larger receptive field. Compared with seven methods, including the ICP algorithm, GO-ICP algorithm, and FGR algorithm, the proposed method had rotation errors (MAE, RMSE, and Error of 1.458, 2.541, and 1.024 in the ModelNet40 dataset, respectively) and translation errors (MAE, RMSE, and Error of 0.0048, 0.0114, and 0.0174, respectively). When registering the ModelNet40 dataset with Gaussian noise, the rotation errors (MAE, RMSE, and Error) were 2.028, 3.437, and 2.478, respectively, and the translation errors (MAE, RMSE, and Error) were 0.0107, 0.0327, and 0.0285, respectively. The experimental results were superior to those of the other methods, and the model was effective at registering packaging bag point clouds. Full article

The one-dimensional quaternion fractional Fourier transform (1DQFRFT) introduces a fractional-order parameter that extends traditional Fourier transform techniques, providing new insights into the analysis of quaternion-valued signals. This paper presents a rigorous theoretical foundation for the 1DQFRFT, examining essential properties such as linearity, the Plancherel theorem, conjugate symmetry, convolution, and a generalized Parseval’s theorem that collectively demonstrate the transform’s analytical power. We further explore the 1DQFRFT’s unique applications to probabilistic methods, particularly for modeling and analyzing stochastic processes within a quaternionic framework. By bridging quaternionic theory with probability, our study opens avenues for advanced applications in signal processing, communications, and applied mathematics, potentially driving significant advancements in these fields. Full article

Convolution plays a pivotal role in the domains of signal processing and optics. This paper primarily focuses on studying the weighted convolution for quaternion linear canonical cosine transform (QLCcT) and its application in multiplicative filter analysis. Firstly, we propose QLCcT by combining quaternion algebra with linear canonical cosine transform (LCcT), which extends LCcT to Hamiltonian quaternion algebra. Secondly, we introduce weighted convolution and correlation operations for QLCcT, accompanied by their corresponding theorems. We also explore the properties of QLCcT. Thirdly, we utilize these proposed convolution structures to analyze multiplicative filter models that offer lower computational complexity compared to existing methods based on quaternion linear canonical transform (QLCT). Additionally, we discuss the rationale behind studying such transforms using quaternion functions as an illustrative example. Full article

The quaternion windowed linear canonical transform is a tool for processing multidimensional data and enhancing the quality and efficiency of signal and image processing; however, it has disadvantages due to the noncommutativity of quaternion multiplication. In contrast, reduced biquaternions, as a special case of four-dimensional algebra, possess unique advantages in computation because they satisfy the multiplicative exchange rule. This paper proposes the reduced biquaternion windowed linear canonical transform (RBWLCT) by combining the reduced biquaternion signal and the windowed linear canonical transform that has computational efficiency thanks to the commutative property. Firstly, we introduce the concept of a RBWLCT, which can extract the time local features of an image and has the advantages of both time-frequency analysis and feature extraction; moreover, we also provide some fundamental properties. Secondly, we propose convolution and correlation operations for RBWLCT along with their corresponding generalized convolution, correlation, and product theorems. Thirdly, we present a fast algorithm for RBWLCT and analyze its computational complexity based on two dimensional Fourier transform (2D FTs). Finally, simulations and examples are provided to demonstrate that the proposed transform effectively captures the local RBWLCT-frequency components with enhanced degrees of freedom and exhibits significant concentrations. Full article

The Fourier transform plays a crucial role in statistics, applied mathematics, and engineering sciences. In this study, we give a definition of the two-dimensional quaternion Fourier transform, which is an extension of the two-dimensional Fourier transform. We present a new convolution theorem including this transformation. We study the characteristic function in the setting of quaternion algebra and obtain the essential properties. Based on this, we seek the expected value, variance, covariance, and their basic relations to the two-dimensional quaternion Fourier transform. We illustrate the results by giving examples to see how the obtained results differ from the classical case. Full article

In this paper, we present a novel integral transform known as the one-dimensional quaternion quadratic-phase Fourier transform (1D-QQPFT). We first define the one-dimensional quaternion quadratic-phase Fourier transform (1D-QQPFT) of integrable (and square integrable) functions on $\mathbf{R}$. Later on, we show that 1D-QQPFT satisfies all the respective properties such as inversion formula, linearity, Moyal’s formula, convolution theorem, correlation theorem and uncertainty principle. Moreover, we use the proposed transform to obtain an inversion formula for two-dimensional quaternion quadratic-phase Fourier transform. Finally, we highlight our paper with some possible applications. Full article

Quaternion Fourier transform (QFT) has gained significant attention in recent years due to its effectiveness in analyzing multi-dimensional signals and images. This article introduces two-dimensional (2D) right-sided quaternion offset linear canonical transform (QOLCT), which is the most general form of QFT with additional free parameters. We explore the properties of 2D right-sided QOLCT, including inversion and Parseval formulas, besides its relationship with other transforms. We also examine the convolution and correlation theorems of 2D right-sided QOLCT, followed by several uncertainty principles. Additionally, we present an illustrative example of the proposed transform, demonstrating its graphical representation of a given signal and its transformed signal. Finally, we demonstrate an application of QOLCT, where it can be utilized to generalize the treatment of swept-frequency filters. Full article