Cosine Matrix Research Articles

A Tourist Destination Recommender System for Nepali Tourism Industry

Tourism is one of the major sources of revenue in developing countries with natural beauty like Nepal. Understanding tourist preferences is essential to optimize this industry. Many places suffer obscurity due to not being recommended to the tourists who would’ve liked the destination. Our goal is to analyse what every tourist likes and recommend them accordingly. In case of Nepal, since there are a lot of under-explored potential tourist destinations and not many data available for the reviews and ratings, the data becomes sparse and limited. To tackle the challenge, our system utilizes a blend of content-based and collaborative filtering, which is known as hybrid filtering. The system leverages the strengths of Cosine Similarity, k-Nearest Neighbors, and Matrix Factorization to personalize recommendations based on user preferences and available destination information even in a sparse as well as limited dataset. This approach not only tackles the under-exploration of hidden gems but also presents a scalable framework applicable to any domain with limited data, potentially impacting personalized recommendations across various industries.

Robust Attitude Estimation for Low-Dynamic Vehicles Based on MEMS-IMU and External Acceleration Compensation.

Attitude determination based on a micro-electro-mechanical system inertial measurement unit (MEMS-IMU) has attracted extensive attention. The non-gravitational components of the MEMS-IMU have a significant effect on the accuracy of attitude estimation. To improve the attitude estimation of low-dynamic vehicles under uneven soil conditions or vibrations, a robust Kalman filter (RKF) was developed and tested in this paper, where the noise covariance was adaptively changed to compensate for the external acceleration of the vehicle. The state model for MEMS-IMU attitude estimation was initially constructed using a simplified direction cosine matrix. Subsequently, the variance of unmodeled external acceleration was estimated online based on filtering innovations of different window lengths, where the acceleration disturbance was addressed by tradeoffs in time-delay and prescribed computation cost. The effectiveness of the RKF was validated through experiments using a three-axis turntable, an automatic vehicle, and a tractor tillage test. The turntable experiment demonstrated that the angle result of the RKF was 0.051° in terms of root mean square error (RMSE), showing improvements of 65.5% and 29.2% over a conventional KF and MTi-300, respectively. The dynamic attitude estimation of the automatic vehicle showed that the RKF achieves smoother pitch angles than the KF when the vehicle passes over speed bumps at different speeds; the RMSE of pitch was reduced from 0.875° to 0.460° and presented a similar attitude trend to the MTi-300. The tractor tillage test indicated that the RMSE of plough pitch was improved from 0.493° with the KF to 0.259° with the RKF, an enhancement of approximately 47.5%, illustrating the superiority of the RKF in suppressing the external acceleration disturbances of IMU-based attitude estimation.

Quaternion-Based Attitude Estimation of an Aircraft Model Using Computer Vision.

Investigating aircraft flight dynamics often requires dynamic wind tunnel testing. This paper proposes a non-contact, off-board instrumentation method using vision-based techniques. The method utilises a sequential process of Harris corner detection, Kanade-Lucas-Tomasi tracking, and quaternions to identify the Euler angles from a pair of cameras, one with a side view and the other with a top view. The method validation involves simulating a 3D CAD model for rotational motion with a single degree-of-freedom. The numerical analysis quantifies the results, while the proposed approach is analysed analytically. This approach results in a 45.41% enhancement in accuracy over an earlier direction cosine matrix method. Specifically, the quaternion-based method achieves root mean square errors of 0.0101 rad/s, 0.0361 rad/s, and 0.0036 rad/s for the dynamic measurements of roll rate, pitch rate, and yaw rate, respectively. Notably, the method exhibits a 98.08% accuracy for the pitch rate. These results highlight the performance of quaternion-based attitude estimation in dynamic wind tunnel testing. Furthermore, an extended Kalman filter is applied to integrate the generated on-board instrumentation data (inertial measurement unit, potentiometer gimbal) and the results of the proposed vision-based method. The extended Kalman filter state estimation achieves root mean square errors of 0.0090 rad/s, 0.0262 rad/s, and 0.0034 rad/s for the dynamic measurements of roll rate, pitch rate, and yaw rate, respectively. This method exhibits an improved accuracy of 98.61% for the estimation of pitch rate, indicating its higher efficiency over the standalone implementation of the direction cosine method for dynamic wind tunnel testing.

An Analysis of the Kinematics and Dynamics Performance of a New Type of Three-Pronged Sliding Universal Coupling

The three-pronged sliding universal coupling is a new kind of three-pronged coupling. The purpose of this study is to demonstrate that, compared with a traditional unequal angular velocity universal coupling (such as the Hooke universal coupling), the universal coupling has the superior characteristics of constant angular speed transmission, simple structure and strong transmission capacity by performing kinematic and dynamic analysis of the new three-pronged sliding constant angular velocity universal coupling. It provides a broad prospect for applications in automotive and other fields. To study its kinematic and dynamic characteristics, directional cosine matrices are utilized as tools to analyze the coordinate systems by establishing simplified geometric models and corresponding motions. Through the analysis of the motions of the input and output shafts and employing the method of single-force element, a set of equilibrium equations for the forces acting on the output shaft and the input shaft are formulated for solution analysis. The research indicates that during the rotation process, there exists a small angular difference between the input shaft and the intermediate shaft, demonstrating the quasi-constant angular velocity characteristics of the new tripod sliding universal coupling. The curves of the forces and force moment acting on each component of the coupling approximate sinusoidal curves. The optimal operating angle range for the new tripod universal coupling is at angle , during which the system exhibits good transmission and mechanical performance. It can be widely used in the automobile industry, tie steel industry and other occasions that require angular transmission. It is especially used in high-speed operation and large transmission capacity.

Optimal design and experiments of a novel bobbin thread-hooking mechanism with RRSC (revolute–revolute–spherical–cylindrical) spatial four-bar linkage

Abstract. To solve the problem of low supply of bobbin thread and frequent bobbin changes existing in current embroidery machines, a novel bobbin thread-hooking mechanism with an RRSC (revolute–revolute–spherical–cylindrical) spatial four-bar linkage is proposed which can achieve a large number and continuous supply of bobbin thread. Based on the analysis of the chain stitch formation principle, the design requirements for motion trajectory and posture of the hooking mechanism are proposed. The methods of direction cosine matrix and mechanism identity condition are applied in kinematics modeling and analysis of the RRSC mechanism. The optimization design model and computer-aided software are developed, then the human–computer interaction optimization method is used to obtain optimal solutions to meet working requirements. The physical prototype is machined and a test bench is built. The virtual simulation and prototype high-speed camera kinematics tests are conducted. The results verify the correctness of mechanism design and show good application feasibility of the mechanism.

ANOVA approximation with mixed tensor product basis on scattered points

In this paper we consider an orthonormal basis, generated by a tensor product of Fourier basis functions, half period cosine basis functions, and the Chebyshev basis functions. We deal with the approximation problem in high dimensions related to this basis and design a fast algorithm to multiply with the underlying matrix, consisting of rows of the non-equidistant Fourier matrix, the non-equidistant cosine matrix and the non-equidistant Chebyshev matrix, and its transposed. Using this, we derive the ANOVA (analysis of variance) decomposition for functions with partially periodic boundary conditions through using the Fourier basis in some dimensions and the half period cosine basis or the Chebyshev basis in others. We consider sensitivity analysis in this setting, in order to find an adapted basis for the underlying approximation problem. More precisely, we find the underlying index set of the multidimensional series expansion. Additionally, we test this ANOVA approximation with mixed basis at numerical experiments, and refer to the advantage of interpretable results.

A Novel Method for Spatial Structural Kinematic Analysis

Kinematic analysis is the first task that needs to be solved for further real-life problems such as machine dynamics and durability, machine balancing, and optimization, chemistry, etc. Currently, there are many methods to analyze the kinematic problem, for instance: vector graphics method, vector-analytic method, or Dennavit-Hartenberg-Craig matrix method. Although each method has its advantages, they have mostly encountered difficulties in establishing equations associated with complicated spatial structures. This research proposed a novel method, entitled “'perpendicular projection method” to solve the problem of spatial structural kinematic analysis. This is an approximate solution method that combines the use of generalized coordinates and direction cosine matrices. With this method, the problem of kinematic analysis of spatial structures will be solved simply and easily by establishing connection equations as well as simulating the motion of spatial structures. This method was then applied in conducting the kinematic analysis of a spatial mechanism with 1 rotating joint (R), 1 ball joint (S), 1 translational joint (P), and one cylindrical joint (C). The calculated results, including the velocity, acceleration of generalized coordinates, angular velocity, angular acceleration of the links, velocity, and acceleration of the center of mass of the links, showed the efficiency of the proposed method.

Attitude Determination System with Rotation of Gyroscopes

A method of auto-compensation for the influence of constant biases in the output signals of gyroscopes in the system for determining the orientation of an object, based on the rotation of the gyroscopes relative to the object, is considered. The analysis of the obtained models of errors in determining the orientation and the simulation performed show the high efficiency of this method for improving the accuracy of readings. The proposed error model makes it quite easy to evaluate the efficiency of auto-compensation. It is shown that the problem may be reduced to integrating the direction cosine matrix that determine the position of the sensitive elements in the reference coordinate system.

Title: Hip and lower limbs 3D motion tracking using a double-stage data fusion algorithm for IMU/MARG-based wearables sensors

This paper presents an algorithm to estimate the relative orientation of body segments during 3D motion tracking, either as multiple individual body segments or as an articulated body chain. For this purpose, a double-stage data fusion algorithm (algorithm-based system) was implemented for inertial measurement units (IMU)/Magnetic Angular Rate and Gravity (MARG)-based wearable sensors during gait. The methodology considers two stages of complementary filters for the data fusion of the IMU/MARG sensors and a Proportional-Integral controller (PI) to incorporate the processed data. Quaternions were employed for the orientation estimation, a Direction Cosine Matrix quaternion-based (DCM) to estimate the relative orientation between the body mobile coordinate system and the inertial reference coordinate system, and Euler angles for the orientation representation. A customized Ambulatory Sensing Motion System (ASMS), consisting of seven monitoring devices was used for the evaluation. The double-stage algorithm-based system was compared with a digital motion processor (DMP) performance. Experimental results of the double-stage algorithm-based system indicated a 0.7° RMSE (M1) and 1° RMSE (M1-M7) with mean values lower than 1° concerning the DMP outcomes. Based on the Bland-Altman analysis, the level of agreement indicated that the double-stage algorithm-based system is neither underestimated nor overestimated and is suitable for the DMP outcome. No singularity conditions nor significant levels of noise or drift were observed in the conducted experiments. The results demonstrate the feasibility of using the proposed method for 3D human motion tracking of multiple body segments, individually or as an articulated body chain. Besides, it suits different IMU/MARG sensor-based wearable sensors.

Increasing the Accuracy of Orientation Determination Based on Auto-compensation of Errors

An increasing the accuracy of orientation determination of strapdown system based on the spatial rotation of gyroscopes relative to an object is considered. The subject of analysis is a mathematical model of the measurement errors of orientation angles, taking into account the constant biases of gyroscopes. The proposed error model makes it quite easy to evaluate the efficiency of auto-compensation. It is shown that the problem may be reduced to integrating the direction cosine matrix that determine the position of the sensitive elements in the reference coordinate system. The results of theoretical analysis and simulation confirm the high efficiency of this method for increasing the accuracy of measuring kinematic parameters.

Three Attitude Models and their Characterization in the Generic Multisensor Integration Strategy for Kinematic Positioning and Navigation

This research aims at further completing our novel Generic Multisensor Integration Strategy (GMIS) with the systematic development of three alternate attitude models, i.e., roll-pitch-heading (RPH), direction cosine matrix (DCM), and quaternion. The GMIS' potential for a true sensor level data fusion is leveraged to its full extent here by facilitating comprehensive error analysis framework in Kalman filtering. A comparative analysis between the solutions resulted from the GMIS associated with each attitude model have been analysed and compared through real road test data. The attitude models were found to perform very consistently, exhibiting the same behaviours in the residuals of the process noise and measurement vectors along with the estimated variance components. Besides, an analysis was conducted to investigate how each attitude model reacts to a sudden trajectory variation captured by the IMU. Each attitude model still performed consistently, but the DCM model in particular exhibited resistance to absorbing erroneous observations into its process noise estimates.

Vector methods for determination of rigid body orientation

Vector methods for determining the orientation of a rigid body using information about vectors in the reference and body-related coordinate systems are considered. The analysis is based on the least squares method in vector-matrix form. This approach allows us to consider the application of different methods of solving the problem from a single standpoint: matrix (using the directional cosine matrix), geometric (using the Gibbs vector), quaternion (using the quaternion of rotation). Numerical evaluation of the accuracy of eight orientation determination algorithms obtained on the basis of these methods was performed.

On the hyperbolic Horadam matrix functions

In this study, we introduce a new class of the hyperbolic matrix functions which are called symmetrical hyperbolic Horadam sine and cosine matrix functions and we present some hyperbolic and recursive properties of these new matrix functions. In addition, we introduce quasi-sine Horadam matrix function and also define the matrix form of the metallic shofars that related to the hyperbolic Horadam sine and hyperbolic Horadam cosine matrix functions.

The error model based on the special Euclidean group SE(3) of the INS: Comparison and extension

In this paper, the error model based on the Lie group is investigated with main focus on the Special Euclidean group SE(3) based error model construction and filtering comparison for the inertial navigation system (INS). The conventional theory of the SE(3) based error model is only focused on the state error definition. Moreover, the attitude representation is usually used by Euler angle. In order to enrich the family of the SE(3) based error model of the INS, this paper is to establish a theoretical bridge that can connect the attitude estimation to the error model construction for the Lie group. For this theoretical bridge, the SE(3) based error model based on Rodrigues parameter and modified Rodrigues parameter is proposed to fill the gap of the family of the SE(3) based error model. Further, based on the integrity of the SE(3) based error model, a uniform error model is also proposed to unify the family of the SE(3) based error model using the attitude transformation and direction cosine matrix. The field tests are carried out to assess the comprehensive performance of the existing SE(3) based error model under different conditions for the INS.

Free vibrations of spatial frame structures: Analytical modelling and solution

This study analytically handles the three-dimensional free vibrations of spatial frames using the initial values method, considering the axial and shear deformations alongside rotary inertias, namely, torsional, in-plane bending and out-of-plane bending. To handle the spatial geometry, the direction cosine matrices are used. Validation is performed with three cases in total, one case available in the literature alongside two numerical examples that are solved analytically and compared to the finite element models. Excellent agreements are found between the analytical results and the results in the literature, as well as those obtained from the finite element models.

Generalization of orientation trajectories and force–torque profiles for learning human assembly skill

Constructing system models in industrial tasks is difficult, especially when multiple sensing information is involved. The peg-in-hole task is typically complex in industrial manufacturing. It is hard to model different assembly states precisely. Learning from demonstration can simplify the modelling process based on human demonstration. In this paper, we transfer a new kind of assembly skill to the robot. To intuitively represent the orientation of the assembly, we propose a novel expression named assembly-angle based on direction cosine and rotation matrix , which offers a good differential performance and avoids the singularity problem. Meanwhile, this approach can be encoded by the dynamic constraint dynamic movement primitives (DC-DMPs) method, which is proposed to consider the constraints among the assembly-angle during movement generalization . The RBF network is employed to generalize force–torque information to improve the accuracy of force–torque profiles prediction. We utilize the vision system and apply admittance control to locate the hole precisely. This proposed assembly skill learning framework can complete the task from random deviation of the pose, which makes it suitable for realistic assembly scenarios. To validate our method’s generalization ability , pegs of two kinds of materials were designed, and the deviations of the initial pose were set from small to large. The success rate was 93.75% for high stiffness assembly and 86.25% for low stiffness assembly. The result validated the effectiveness of our method in the peg-in-hole task. • Human assembly skills can be effectively transferred through the proposed framework. • Assembly-angle has a good generalization performance in the proposed framework. • DC-DMPs considers the dynamical constraints during movement generalization. • RBF network has a high prediction accuracy for forces and torques. • The proposed framework is verified on the aluminum and silicone peg assembly tasks.

GA-MKB:A Multi-kernel Boosting Learning Method based on Normalized Kernel Target Alignment and Kernel Difference

Concentrates on the problem that the traditional kernel target alignment(KTA) is not invariance under data translation in the feature space, a cosine matrix alignment method is proposed for kernel selection, which is called normalized kernel target alignment(NKTA). On the basis of normalized kernel target alignment and kernel difference, we propose a new multi-kernel boosting. Firstly, the value of NKTA is taken as the election rarget of the kernel function in each iteration of algorithm, which leads to a selective kernel fusion. Secondly, the kernel difference measure is used to construct the combination coefficient to increase the diversity of weak classifiers, and then improve the generalization performance of integrated strong classifiers. Finally, among the 6 data sets, the GA-MKB performed better than MKBoost-D1 under the accuracy of classification, and can improve the generalization performance of the integrated classifier compared with MKBoost-D2.

Multi-Source Data Fusion Method for the Truss Structure Stability Measurement of Space Telescope

It is necessary for large aperture space telescopes to achieve high measurement accuracy for mechanical reference mounting surfaces, complex deformation conditions, and difficulty in describing spatial geometric properties. In this manuscript, we propose a measurement method for evaluating the deformation of the trusses structure by fusing multiple sources of data. The multi-source data are obtained from the theodolite, laser tracker, and photogrammetry systems. The datum alignment of the laser tracker and photogrammetry coordinate systems is achieved by establishing the transition coordinate system method of the datum platform, and the alignment accuracy (3σ) is about 8.8″, 5.1″ and 4.2″. Using the laser tracker to establish the relationship between the cubic mirror coordinate system and the geometric coordinate system of the mounting part, the fast and high-precision measurement of the mounting angle of the cubic prism is realized, and the measurement accuracy reaches 2″. The data from multiple sources are fused through datum transfer and alignment to establish a cosine matrix transfer chain between the mechanical characteristic coordinate system of each component and the transition coordinate system of the datum platform, and the Eulerian rotation angle is obtained to describe the angular relationship between the components after solving. Based on the Monte Carlo mathematical error modeling analysis, the datum transfer and alignment simulations were carried out, and related experiments were conducted. The experiments show that the transfer error (3σ) of the XYZ rotation angle is less than 20.6″ after the datum transfer, the maximum error is within 3″ compared to the simulation results, and the deviation of the comparison photographic measurement data is less than 7.6″. The datum transfer method combined with photogrammetry can describe the deformation trend of large-size trusses under different load conditions more objectively and reasonably.

Performance analysis of novel precoding matrix techniques for optical OFDM-based visible light communication systems

Visible Light Communication (VLC) exploits the renowned modulation scheme like orthogonal frequency division multiplexing (OFDM) to accomplish high data rate transmission. However, the optical OFDM system like DC biased optical OFDM (DCO-OFDM) is vulnerable to high peak to average power ratio (PAPR) which results in detrimental clipping distortion which in turn degrades the overall system performance. The limited dynamic range of the LEDs further agitates this issue. On these grounds, PAPR reduction techniques like precoding matrix schemes have been proposed for reducing the high amount of PAPR in DCO-OFDM system. In this paper, discrete Hartley Matrix transform (DHMT) precoded discrete Hartley transform (DHT)-based DCO-OFDM system is proposed for reducing PAPR. In addition, we comparatively investigate the PAPR performance of a new precoding technique like T- transform which is a hybrid combination of Walsh Hadamard transform (WHT) and Zadoff chu transform (ZCT) with other precoding matrix techniques like discrete cosine matrix transform (DCMT), discrete Fourier matrix transform (DFMT), Walsh Hadamard Matrix transform (WHMT) and DHMT. Furthermore, this paper derives the mathematical analysis corresponding to the time-domain signal formats for the precoded DCO-OFDM system which is exploiting complex Fourier signal processing and real trigonometric transform like DHT. From the simulated results, it can be surmised that when compared with other precoding techniques, DHMT precoded DHT-based DCO-OFDM system not only achieves a significant reduction in PAPR but also achieves a better bit error rate (BER) and spectral efficiency performance. Furthermore, less computational complexity is required to implement it.

Fast image watermarking based on signum of cosine matrix

<span>In the field of image watermarking, the singular value decomposition has good imperceptibility and robustness, but it has high complexity. It divides a host image into matrices of U, S, and V. Singular matrix S has been widely used for embedding and extracting watermark, while orthogonal matrices of U and V are used in decomposition and reconstruction. The proposed signum of cosine matrix method is carried out to eliminate the generation of the three matrices at each block and replace it with a signum of cosine matrix. The proposed signum of cosine matrix is performed faster on the decomposition and reconstruction. The image is transformed into a coefficient matrix C using the signum matrix. The C matrix values are closer to the S value of singular value decomposition which can preserve high quality of the watermarked image. The experimental results show that our method is able to produce similar imperceptibility and robustness level of the watermarked image with less computational time.</span>