Cosine Matrix Research Articles

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>

Rotation vector and directional cosine matrix in problems of satellite attitude control

For many years, three rotation angles of moving vehicles: roll, pitch, and yaw have been used for attitude determination and control. However, in the last years due to appearance of new airspace applications such as strapdown inertial navigation systems (INS) and spacecrafts new quaternion (Q)-based methods appeared. Conventional and new modern methods have some features that can attract or repel developers. Nevertheless, some new techniques of classical mechanics can be tried to use them for vehicle attitude determination and control purposes with the expectation to get more effective results. The article presents a rotation vector (RV) and proposes a way of using it for satellite attitude control. This method is compared with conventional method of attitude control using three rotation angles. The ratio is shown between RV control and modern method of satellite attitude control using quaternion. Analytical and simulation results are presented.

SINS attitude algorithm based on moving-window overdetermined polynomial fitting of gyro outputs

The attitude algorithm is the most important part of the whole strapdown inertial navigation processing. It calculates the attitude of certain parameterization by integrating the gyro outputs or measurements in a specifically tailored way according to the attitude kinematic differential equation. The measurements or some angular velocity models obtained by fitting these measurements are often assumed free of errors in order to assess the numerical errors only. However, the gyro outputs and hence the models from them are by no means free of measurement errors. It is more often than not that the measurement errors dominate the numerical ones in practice. In this study, with coping with the measurement errors as the focus, we aim to improve the angular velocity model which is used as input in an attitude integration algorithm. This is achieved by exploiting the potential of overdetermined least-squares polynomial fitting. In order to avoid reducing the update rate by incorporating more measurements, the moving window trick is employed to re-use measurements in the previous update interval. The conventional attitude algorithm with second-order approximation in solving the differential equation of the equivalent rotation vector is employed as an example; however, the proposed method can be readily applied to other parameterizations such as direction cosine matrix, quaternion or Rodrigues parameters, and other high order approximations in solving the differential equation widely studied recently.

Relative controllability of a stochastic system using fractional delayed sine and cosine matrices

In this paper, we study the relative controllability of a fractional stochastic system with pure delay in finite dimensional stochastic spaces. A set of sufficient conditions is obtained for relative exact controllability using fixed point theory, fractional calculus (including fractional delayed linear operators and Grammian matrices) and local assumptions on nonlinear terms. Finally, an example is given to illustrate our theory.

An algorithm for solving of Euler parameters differential equations system

The design an optimal numerical method for solving a system of ordinary differential equations simultaneously is described in this paper. System of differential equations was represented by a system of linear ordinary differential equations of Euler’s parameters called quaternions. The components of angular velocity were obtained by the experimental way. The angular velocity of the centre of gravity was determined from sensors of acceleration located in the plane of the centre of gravity of the machine. The used numerical method for solving was a fourth-order Runge-Kutta method. The stability of solving was based on the orthogonality of a direct cosine matrix. The numerical process was controlled on every step in numerical integration. The algorithm was designed in the C# programming language.

An improved uncertainty principle for functions with symmetry

Chebotarëv proved that every minor of a discrete Fourier matrix of prime order is nonzero. We prove a generalization of this result that includes analogues for discrete cosine and discrete sine matrices as special cases. We establish these results via a generalization of the Biró–Meshulam–Tao uncertainty principle to functions with symmetries that arise from certain group actions, with some of the simplest examples being even and odd functions. We show that our result is best possible and in some cases is stronger than that of Biró–Meshulam–Tao. Some of these results hold in certain circumstances for non-prime fields; Gauss sums play a central role in such investigations.

Immersion and Invariance Adaptive Control for Spacecraft Pose Tracking via Dual Quaternions

This paper addresses the simultaneous attitude and position tracking of a target spacecraft in the presence of general unknown bounded disturbances in the framework of dual quaternions, which provides a concise and integrated description of the coupled rotational and translational motions. By virtue of the newly introduced dual direction cosine matrix, the dimension of the dual quaternion-based relative motion dynamics written in vector/matrix form can be lowered to six. Treating the disturbances as unknown parameters, a modular adaptive pose tracking control scheme composed of two separately designed parts is then derived. One part is the adaptive disturbance estimator designed based on the immersion and invariance theory. Driven by the disturbance estimation errors, it can realize exponential convergence of the estimations and has the nice “parameter lock” property, which can hardly be expected in the conventional certainty equivalent adaptive controllers. The other part is a proportional-derivative-like pose tracking controller where the estimated disturbances are directly used. The closed-loop stability of the relative motion system under different kinds of disturbances is proven by Lyapunov stability analysis. Simulations and comparisons with two previous dual quaternion-based controllers demonstrate the novel features and performance improvements of the proposed control scheme.

Error Analysis of Accelerometer- and Magnetometer-Based Stationary Alignment

This paper revisits the stationary attitude initialization problem, i.e., the stationary alignment, of Attitude and Heading Reference Systems (AHRSs). A detailed and comprehensive error analysis is proposed for four of the most representative accelerometer- and magnetometer-based stationary attitude determination methods, namely, the Three-Axis Attitude Determination (TRIAD), the QUaternion ESTimator (QUEST), the Factored Quaternion Algorithm (FQA), and the Arc-TANgent (ATAN). For the purpose of the error analysis, constant biases in the accelerometer and magnetometer measurements are considered (encompassing, hence, the effect of hard-iron magnetism), in addition to systematic errors in the local gravity and Earth magnetic field models (flux density magnitude, declination angle, and inclination angle). The contributions of this paper are novel closed-form formulae for the residual errors (normality, orthogonality, and alignment errors) developed in the computed Direction Cosine Matrices (DCM). As a consequence, analytical insight is provided into the problem, allowing us to properly compare the performance of the investigated alignment formulations (in terms of ultimate accuracy), as well as to remove some misleading conclusions reported in previous works. The adequacy of the proposed error analysis is validated through simulation and experimental results.

Coarse alignment of marine strapdown inertial navigation system using the location of fitted parametric circle of gravity movement

AbstractThis paper presents a novel estimation method for coarse alignment of a marine strapdown inertial navigation system (SINS) under mooring conditions. The properties of gravitational motion are used to improve the accuracy of coarse alignment. The parametric motion of gravitational apparent is a circle that is on the surface of a sphere. The location of this parametric circle is dependent on the definition of the reference frames and the initial angles of SINS. In the method proposed here the initial direct cosine matrix is calculated only from the location of the gravity motion parametric circle. The novelty of this paper is to provide a new method for estimating the gravity motion trajectory in inertial frame, as well as direct extraction of the initial direct cosine matrix from this estimated trajectory. Simulation and testing show that the proposed method is suitable for coarse alignment in mooring conditions.

Attitude reconstruction from strap-down rate gyros using power series

AbstractThis paper introduces a power series based method for attitude reconstruction from triad orthogonal strap-down gyros. The method is implemented and validated using quaternions and direction cosine matrix in single and double precision implementation forms. It is supposed that data from gyros are sampled with high frequency and a fitted polynomial is used for an analytical description of the angular velocity vector. The method is compared with the well-known Taylor series approach, and the stability of the coefficients’ norm in higher-order terms for both methods is analysed. It is shown that the norm of quaternions’ derivatives in the Taylor series is bigger than the equivalent terms coefficients in the power series. In the proposed method, more terms can be used in the power series before the saturation of the coefficients and the error of the proposed method is less than that for other methods. The numerical results show that the application of the proposed method with quaternions performs better than other methods. The method is robust with respect to the noise of the sensors and has a low computational load compared with other methods.

국립무용단의 무용작품 주제 분석: 빅데이터 분석

Purpose: The purpose of this study is to examine dance themes performed by the National Dance Company of Korea (NDCK). Research questions were (1) What is the main theme of the dance works performed by the NDCK from 1962 to 2015? (2) Do the dance themes vary with a specific period? (3) Do the dance themes of the NDCK change with NDCK directors?<BR> Method: Data were descriptions of the dance pamphlet collected from 1962 to 2015, which were uploaded on digital archive service offered from NDCK. Data analysis consisted of 4 steps: Step1, authors had transformed contents of pamphlets collected into the text file. Step2, authors conducted the morpheme analysis through a program written by Python. Step3, authors created the co-occurrence matrix and direction cosine matrix by KrKwic & KrTitle programs. Step4, authors analyzed centrality and visualization by UCINET & Pajek programs.<BR> Results: The results showed that keywords of dance themes were dance, human, human life, form, Korea, which appeared frequently from 1962 to 2015. Words with a high degree of centrality were human, works, human life. It means choreographic themes of the NDCK represented human life in association with historical fact. Also, the results of the study indicated that dance themes of NDCK varied with the historical period of dance. Also, the findings of this study showed that directors of the NDCK had some common themes in their choreography but these themes were performed differently using their symbolic material.<BR> Conclusion: In summary, NDCK works is to create works related to human life. When looking at dance works by time, various themes are performed, but there is no significant difference in the flow of dance themes. It seems that they are performed with similar themes. The theme of the NDCK is found to be different according to each leader through characteristic words.

Parameter Optimization and Experiment of Soil Cleaning Device on Apple Seedling-Lifting Machine Based on Spatial RSSR Mechanism

HighlightsThe spatial four-bar linkage mechanism is applied to the apple orchard seedling-lifting machines.The dimension synthesis of spatial four-bar mechanism is applied to the design of agricultural machinery.A new type of soil cleaning device for apple orchard seedling-lifting machines was designed.Compared with the traditional soil cleaning device, the new soil cleaning device with optimized parameters causes less damage to root system and provides a more stable performance.Abstract. To solve the problems of poor working conditions, incomplete root systems, and low seedling-lifting efficiencies of apple orchard seedling-lifting machines, a new type of shaking soil-cleaning device was proposed, in which a spatial four-bar linkage (RSSR) was used instead of a traditional planar linkage. By means of the direction cosine matrix, the position and pose of the spatial four-bar mechanism of the device were analyzed, and the functional relationship was obtained. A fast Fourier transform (FFT) was used to synthesize a periodic function of the spatial four-bar linkage, a numerical atlas was established, and the dimensions were selected by means of fuzzy recognition. A genetic algorithm (GA) was used to optimize the identified parameters, and the optimized mechanisms was compared with the traditional planar linkage mechanism. The results showed that the maximum positive and negative errors of the first curve fitting groups were 0.43% and 0.67%, respectively, and those of the second curve fitting group were 0.79% and 0.50%, respectively, which met the operating and precision requirements. The structure of the new oscillating soil cleaning device is compact. Meanwhile, moderate lengths of the main roots, dense root hair, and complete root systems were achieved. The results showed that the taproots remained intact, and they were between 120 and 150 mm long. Due to the small sample size, the damage rate of the seedlings was zero, and the seedlings produced by the two models met the agronomic requirements. Thus, the requirements of agricultural operations are met by the optimized mechanism. This design concept can provide ideas for follow-up spatial RSSR four-bar mechanism design, and the optimized size parameters can provide a reference for the follow-up design and research of seedling and soil clearing devices. Keywords: Dimension synthesis, Genetic algorithm, Numerical atlas method, Oscillating soil cleaning device, Spatial RSSR mechanism.

Trajectory Tracking Control of Quadrotor via Minimum Projection Method

Abstract In this paper, we consider a nonlinear tracking controller design problem for a quadrotor. For the controller design, we design a tracking control Lyapunov function (TCLF) based on the minimum projection method. However, it is not clear whether we can design the TCLF for a quadrotor by the method. In particular, it is difficult to calculate the TCLF without reducing the amount of computation. We show that the use of the orthogonal property of the direction cosine matrix in the quadrotor dynamics has the effect of reducing the computation. Finally, we demonstrate the computer simulation for a given trajectory.

Rotation vector and directional cosine matrix in problems of satellite attitude control

Rotation vector and directional cosine matrix in problems of satellite attitude control

Hybrid Dynamic Pharmacophore Models as Effective Tools to Identify Novel Chemotypes for Anti-TB Inhibitor Design: A Case Study With Mtb-DapB.

Antimicrobial resistance (AMR) is one of the most serious global public health threats as it compromises the successful treatment of deadly infectious diseases like tuberculosis. New therapeutics are constantly needed but it takes a long time and is expensive to explore new biochemical space. One way to address this issue is to repurpose the validated targets and identify novel chemotypes that can simultaneously bind to multiple binding pockets of these targets as a new lead generation strategy. This study reports such a strategy, dynamic hybrid pharmacophore model (DHPM), which represents the combined interaction features of different binding pockets contrary to the conventional approaches, where pharmacophore models are generated from single binding sites. We have considered Mtb-DapB, a validated mycobacterial drug target, as our model system to explore the effectiveness of DHPMs to screen novel unexplored compounds. Mtb-DapB has a cofactor binding site (CBS) and an adjacent substrate binding site (SBS). Four different model systems of Mtb-DapB were designed where, either NADPH/NADH occupies CBS in presence/absence of an inhibitor 2, 6-PDC in the adjacent SBS. Two more model systems were designed, where 2, 6-PDC was linked to NADPH and NADH to form hybrid molecules. The six model systems were subjected to 200 ns molecular dynamics simulations and trajectories were analyzed to identify stable ligand-receptor interaction features. Based on these interactions, conventional pharmacophore models (CPM) were generated from the individual binding sites while DHPMs were created from hybrid-molecules occupying both binding sites. A huge library of 1,563,764 publicly available molecules were screened by CPMs and DHPMs. The screened hits obtained from both types of models were compared based on their Hashed binary molecular fingerprints and 4-point pharmacophore fingerprints using Tanimoto, Cosine, Dice and Tversky similarity matrices. Molecules screened by DHPM exhibited significant structural diversity, better binding strength and drug like properties as compared to the compounds screened by CPMs indicating the efficiency of DHPM to explore new chemical space for anti-TB drug discovery. The idea of DHPM can be applied for a wide range of mycobacterial or other pathogen targets to venture into unexplored chemical space.

Точний навігаційний алгоритм на основі кватерніонів, адаптований для моделювання сигналів акселерометрів і гіроскопів при низьких частотах дискретизації

Accelerometers and gyroscopes based on MEMS technology are promising for tracing motion in medicine, sport activities, human-machine interaction, robotics and many other areas due to the fact that they are self-containing and have a range of other advantages. Three orthogonally placed accelerometers and gyroscopes are combined into a single module fitted with a controller for processing the signals from inertial sensors. However, the same module may be suitable for one application and inapplicable for another, since the accuracy of tracking a motion trajectory depends not only on the error characteristics of the inertial sensors but also on the trajectory itself. Simulation may help decide whether an inertial measurement unit is a reasonable choice for a specific application or not. The idea is to allow the user to preset a desirable motion trajectory and error characteristics of the inertial sensors specified by their manufacturer. Then software simulates signals of real accelerometers and gyroscopes and computes a set of potential trajectories upon these signals. Upon the discrepancies between the prescribed and synthesized trajectories one can judge on applicability of the inertial sensors with the preset error characteristics for a specific task, without implementing a real device. The software should be based on well-known navigation equations, expressed via direction cosine matrices or quaternions. However, the equations are only valid for infinitesimal rotation angles. Their usage leads to cumulating errors in computation of some trajectories due to the fact that low-cost accelerometers and gyroscopes available on the market offer limited sample frequencies. The work reveals the problem related to usage of the above-mentioned equations, both analytically and by numerical experiments. Examples of trajectories irreproducible at low frequencies are shown. The work analyzes the reasons why some trajectories are irreproducible and shows that the reasons can scarcely be eliminated in case of rotation matrices. We have proposed amended equations universal for any trajectory and any sample frequency.

Rapid Measurement and Control of Nitrogen-Vacancy Center-Axial Orientation in Diamond Particles* *Supported by the National Key R&D Program of China (Grant No. 2017YFB0403602), the Nature Science Foundation of Jiangsu Province (Grant No. SBK2020041231), and the Suqian Sci&Tech Program (Grant No. K201912).

Determination and control of nitrogen-vacancy (NV) centers play an important role in sensing the vector field by using their quantum information. To measure orientation of NV centers in a diamond particle attached to a tapered fiber rapidly, we propose a new method to establish the direction cosine matrix between the lab frame and the NV body frame. In this method, only four groups of the ODMR spectrum peaks shift data need to be collected, and the magnetic field along ± Z and ± Y in the lab frame is applied in the meantime. We can also control any NV axis to rotate to the X, Y, Z axes in the lab frame according to the elements of this matrix. The demonstration of the DC and microwave magnetic field vector sensing is presented. Finally, the proposed method can help us to perform vector magnetic field sensing more conveniently and rapidly.

Representation of solutions of a second order delay differential equation

In this article, we study an inhomogeneous second order delay differential equation on the fractal set \(\mathbb{R}^{\alpha n}\) \((0&lt;\alpha\leq 1)\), based on the theory of local calculus. We introduce delay cosine and sine type matrix functions and give their properties on the fractal set. We give the representation of solutions to second order differential equations with pure delay and two delays.&#x0D; For more information see https://ejde.math.txstate.edu/Volumes/2020/72/abstr.html

Globally Asymptotic Stable Attitude Estimation with Application to MEMS Sensors

Aiming at the requirement of attitude information module with high precision, small size and low power consumption for the control of miniature UAV, a practical attitude estimation algorithm based on the micro-electro-mechanical sensor is proposed in this paper, which realizes the accurate estimation of the attitude of the UAV under the condition of low acceleration. A low-cost MEMS gyroscope, accelerometer, and magnetometer are used in the system. The Euler angle is obtained by the state observer method based on Direction Cosine Matrix (DCM) which can be got by fusing the sensor data. Firstly, based on the basic idea of TRIAD algorithm, a method to determine the attitude rotation matrix by accelerometer and magnetometric measurement is proposed. Compared with the traditional method, this method does not have to calculate the inverse of the matrix. Secondly, a state observer is intended to estimate the attitude of the system. The state observer doesn't have to observe the bias of the gyroscope, but still ensures the convergence of the Euler angle. Finally, the simulation based on the actual sampling data of the MEMS sensor shows that the output of the state observer designed in this paper still has high accuracy and good dynamic characteristics under the condition of gyroscope noise and bias.