Direction Cosines Research Articles

A Novel Method for Eliminating the Strip-Shaped Interferences in Aeromagnetic Anomaly Based on Convolutional Neural Network

The strip-shaped interferences in aeromagnetic data pose great adverse effects on data interpretation. In literature, a number of methods have been proposed to deal with this problem. However, existing methods still have some limitations. Inspired by the ability of deep learning techniques to extract features from data, this study presents a novel convolutional neural network (CNN)-based method to eliminate the strip-shaped interferences in aeromagnetic data. The proposed method uses the U-Net structure to establish the whole network. The use of up–down sampling and skip connection enables the network to extract multiscale strip-shaped interferences with complex distribution and morphological characteristics. The basic theoretical formulas of the network and its architecture are presented, along with the construction method of the training dataset. Afterward, the presented method is tested on several synthetic examples and real aeromagnetic data collected in Jining, Inner Mongolia, and is compared with the conventional directional cosine filter to display its advantage in accuracy. The results demonstrate that the presented method can eliminate the strip-shaped interferences in aeromagnetic data effectively while preserving the features due to the real geological sources without any subjective parameters.

Algorithm of the autonomous initial alignment of sins with sequential filtering

An algorithm for an autonomous initial alignment of a strapdown inertial navigation system on a fixed or limitedly movable base is proposed and considered. It sequentially uses two Kalman averaging filters in. The first one determines one column of the directing cosines matrix (DCM) between the axes of the associated with the object and the geographical accompanying bases by the signals of the accelerometers. The second filter determines the second column of the matrix based on the gyroscope signals and the obtained estimates of the direction cosines. The third column is determined from known ratios. From the resulting DCM, the heading, pitch and roll angles are determined. Information signals for solving the problem are obtained by averaging a small interval (5 s) at the end of the Kalman filter transition process. This allows minimizing errors from changing the position of the object during the measurement time, which can reach tens of minutes. The advantage of the algorithm is the independence of errors from the object heading. It is shown that pre-smoothing of signals improves accuracy. The algorithm makes it possible to determine the orientation angles, and then the direction cosines at a measurement time insufficient to complete the transient evaluation process by the Kalman filter. The conducted field experiments confirm the good characteristics of the alignment on a fixed and vibrating base, achieved using the algorithm.

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.

Accuracy estimation of the calculating algorithm the satellite’s orbit of earth remote sensing

Transformations of the coordinate systems in which the reference vectors of the initial navigation information - the flow of sunlight and the Earth's magnetic field are set - into the coordinate system of the sun-synchronous orbit of the Earth's remote sensing satellite by matrix and analytical methods are considered. The influence of the accuracy of calculating the direction cosines of the satellite orientation matrices on the accuracy of determining its orientation angles and the scanning accuracy is estimated. The estimation of the influence on the accuracy of determining the satellite orientation of the sensor errors of the primary navigation information and the features of the matrix orientation algorithm is carried out. Analytical dependencies are obtained that allow one to evaluate the influence of the noted factors depending on the position of the satellite in its orbit and the motion of the Earth along the ecliptic.

Analytical ray tracing based on Hamilton principal function and conjugate variable pairs.

A transformation method based on optical Hamilton equations is proposed for 3D ray tracing in axially inhomogeneous gradient-index (GRIN) media with cylindrical symmetry. For a given GRIN field, the optical conjugate variable pairs of physical space can be transformed into a virtual space by applying canonical transformation. The virtual trace can be simply solved as a uniform expression regardless of what the GRIN field is, and one can inversely transform it into the physical space. The transformation is intimately related to a Hamilton principal function, called the S function, which simultaneously gives the real ray trace and its conjugate. The "conjugate trace" displays the direction cosines of the ray trace and thus shows the information about propagation direction at every point, and it can be independently derived from the S function without knowing the real trace. In addition, as two special dimension-reduction cases, the S function is also applicable for 2D structures with only axial inhomogeneity or cylindrical symmetry.

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.

EPR Analysis of Cu2+ ion Doped Potassium borodicitrate Single Crystal

In our present investigation single crystals of Potassium borodicitrate (KBDC) (for a fixed content- host lattice) with Cu2+, a guest species, as a dopant (at four 0.2, 0.5, 1 and 2 g) in weight ratio have been synthesized at room temperature by using slow evaporation method. These as-synthesized 4 crystals have been subjected to Electron Paramagnetic Resonance (EPR) studies. The EPR spectrum shows that 0.5 g dopant KBDC give a 4 equidistant hyperfine lines with the perfect symmetry confirms that the localization of Cu2+, a paramagnetic impurity, within it reveals that the maximum absorption of EPR signals happens at 0.5 g Cu2+ than any other concentrations with reference to 20° in horizontal plane than the normal and vertical recording in the same angular projection. The Spin Hamiltonian calculations are used to obtain spectroscopic field splitting factor g-tensor values, gxx = 2.0421, gyy = 2.1962, gzz = 2.2827 and hyperfine splitting factor A-tensor values Axx = 150, Ayy = 112 and Azz = 134. The K–O bond length associated with directional cosines of gzz tensor reveal that the Cu2+ is located interstitially. This optimized single crystal has furtherance been subjected to Single cystal X-ray diffraction (SXRD), Fourier transform infrared Spectrascopy (FTIR). Scanning electron microscope (SEM) Energy dispersive X-ray analysis (EDAX) and compared with pure KBDC single crystal. The XRD unit cell crystalline parameter variations reveal that there is doping effect of Cu2+ into the host lattice brings forth structural coordination of Cu2+ with KBDC. The FTIR confirms that complexation of host and guest through molecular interactions in the finger print region. The EDAX mapping shows Cu2+ presence in the crystal. HIGHLIGHTS SXRD are taken to confirm that structure of pure KBDC and Cu2+ doped KBDC are same The spin Hamiltonian parameters of KBDC-Cu2+ single crystal are calculated through EPR spectra On analyzing the spectra, it is found that the doped ion site location symmetry is identified as interstitial and experience orthorhombic local field symmetry In addition to the above studies FTIR and EDX confirms the presence of Cu2+ ion GRAPHICAL ABSTRACT

A sweep-based low-rank method for the discrete ordinate transport equation

The dynamical low-rank (DLR) approximation is an efficient technique to approximate the solution to matrix differential equations. Recently, the DLR method was applied to radiation transport calculations to reduce memory requirements and computational costs. This work extends the low-rank scheme for the time-dependent radiation transport equation in 2-D and 3-D Cartesian geometries with discrete ordinates discretization in angle (SN method). The reduced system that evolves on a low-rank manifold is constructed via the “unconventional” basis update & Galerkin integrator to avoid a substep that is backward in time, which could be unstable for dissipative problems. The resulting system preserves the information on angular direction by applying separate low-rank decompositions in each octant where angular intensity has the same sign as the direction cosines. Then, transport sweeps and source iteration can efficiently solve this low-rank-SN system. The numerical results in 2-D and 3-D Cartesian geometries demonstrate that the low-rank solution requires less memory and computational time than solving the full rank equations using transport sweeps without losing accuracy.

Measurement of the polarisation of single top quarks and antiquarks produced in the t-channel at sqrt{s} = 13 TeV and bounds on the tWb dipole operator from the ATLAS experiment

A simultaneous measurement of the three components of the top-quark and top-antiquark polarisation vectors in t-channel single-top-quark production is presented. This analysis is based on data from proton–proton collisions at a centre-of-mass energy of 13 TeV corresponding to an integrated luminosity of 139 fb−1, collected with the ATLAS detector at the LHC. Selected events contain exactly one isolated electron or muon, large missing transverse momentum and exactly two jets, one being b-tagged. Stringent selection requirements are applied to discriminate t-channel single-top-quark events from the background contributions. The top-quark and top-antiquark polarisation vectors are measured from the distributions of the direction cosines of the charged-lepton momentum in the top-quark rest frame. The three components of the polarisation vector for the selected top-quark event sample are {P}_{x^{prime }} = 0.01 ± 0.18, {P}_{y^{prime }} = −0.029 ± 0.027, {P}_{z^{prime }} = 0.91 ± 0.10 and for the top-antiquark event sample they are {P}_{x^{prime }} = −0.02 ± 0.20, {P}_{y^{prime }} = −0.007 ± 0.051, {P}_{z^{prime }} = 0.79 ± 0.16. Normalised differential cross-sections corrected to a fiducial region at the stable-particle level are presented as a function of the charged-lepton angles for top-quark and top-antiquark events inclusively and separately. These measurements are in agreement with Standard Model predictions. The angular differential cross-sections are used to derive bounds on the complex Wilson coefficient of the dimension-six mathcal{O} tW operator in the framework of an effective field theory. The obtained bounds are CtW ∈ [−0.9, 1.4] and CitW ∈ [−0.8, 0.2], both at 95% confidence level.

A novel effectiveness evaluation method of smokescreen jamming based on the fusion of directional gradients and local texture features

Smokescreen jamming is one of the most common types of interference in optical imaging. However, there are few tools available to assess the effectiveness of optical imaging in the presence of smoke screen interference, and most of them are qualitative in nature. There is an urgent need for targeted quantitative assessment methods. Therefore, a novel effectiveness evaluation method of smoke screen jamming (EEMSSJ) based on the histogram of oriented gradient and local binary pattern feature is proposed. According to the influence on the tracking effect, the proposed method weights and fuses the directional gradient histogram feature, texture feature, cosine similarity, and luminance feature of the image and finally obtains the EEMSSJ index. The EEMSSJ index provides a quantitative assessment of the effectiveness of smoke screen interference from an image perspective, which can effectively improve the accuracy of the analysis and judgment of the smokescreen jamming situation and provide a strong reference basis for making timely adjustments to the interference deployment. The effectiveness of the proposed method and the EEMSSJ index are validated by experiments. Experimental results show that the EEMSSJ index can achieve a high level of agreement with the subjective assessment of the experimental data and possess high sensitivity and robustness. The EEMSSJ index provides a more accurate representation of the dynamic disturbance of the smoke screen than the correlation assessment method and the multi-scale structural similarity method.

Head impacts in non-helmeted sports: Measuring and locating the impact force

Mild traumatic brain injury within contact sports is a growing concern due to the serious risk of injury and concussion. Extensive research is being conducted looking into head kinematics during impacts in non-helmeted contact sports utilizing instrumented mouthguards, allowing researchers to record accelerations and velocities of the head during and after an impact. This does not, however, allow the location of the impact on the head, and its magnitude and orientation, to be determined. This research proposes and validates an algorithm using rigid body dynamics that approximates the impact force and determines its location and orientation from instrumented mouthguard kinematic data. Impact data captured from an experimental laboratory test using an instrumented mouthguard and five finite element simulations are used to validate the algorithm. The obtained results from both validation methods highlight the effectiveness of the proposed impact magnitude and location algorithm as impact locations were calculated within 12 mm of the impact center for all conducted tests. Additionally, components of force unit vectors (direction cosines) obtained from the algorithm were within ±0.03, which equates to less than 11% of the components of applied force unit vectors, highlighting the accuracy of impact direction vector established from the algorithm. This algorithm has the potential to significantly aid researchers conducting field tests within non-helmeted sports by reducing the time required to analyze and determine head impact locations.

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.

3D Stokes parameters for vector focal fields

The study is devoted to the application of the formalism of 3D Stokes parameters to the near-focal structured fields described with Richards–Wolf vector focusing theory. The distribution of the local polarization properties of these fields is characterized in the plane perpendicular to optical axes. The linear polarization parameter is explored, first tested by comparing basic loosely and tightly focused Gaussian beams and then, getting deeper insight into its descriptive capabilities, applied to different spatial modes. The distributions of the linear polarization parameter and directional cosines of polarization ellipses’ planes in the transverse plane are presented.

Study on a plane grating spectral imaging system with smile and keystone eliminated

Subject of study. For a grating-based imaging spectrometer, a method of using an off-axis lens to correct the smile and keystone is proposed and verified by simulation. Method. In the set coordinate system, the ratios of direction cosines of the refractive rays along the y-axis and z-axis are studied using the spatial ray tracing method. On this basis, the smile characteristics of a single refraction sphere and an off-axis lens have been analyzed. In order to verify the theory, a visible spectral imaging system without an off-axis lens and one with an off-axis lens have been optimized, respectively. Main results. The criterion of the smile sign has been given and discussed. For the spectral imaging system without an off-axis lens, good image quality and high spectral resolution have been achieved, which is less than 1 nm. The modulation transfer functions at the wavelengths of 400, 600, and 800 nm are greater than 0.5 at the Nyquist frequency. However, the maximums of the smile and keystone are greater than 0.07 and 0.06 mm, respectively, which are several times the unit size. For the spectral imaging system with an off-axis lens, the image quality is basically the same as the previous one. The obvious differences between the two systems are the smile and keystone. For the latter, the maximums of smile and keystone at all working wavelengths in all fields are close to 6.24 and 6.40 µm, which are less than half of the unit size. Practical significance. The smile and keystone caused by a plane grating can be corrected by an off-axis lens in a plane-grating-based imaging spectrometer, which provides a universal method for the design of a spectral imaging system.

Instability of opposite polarity charged dusty plasma with vortex-like distributed electrons

Electrons in space plasma may follow vortex-like distribution, that is why we have derived the three-dimentional (3D) nonlinear modified Zakharov–Kuznetsov (mZK), describing the propagation of dust acoustic solitary to the plasma system composed of four components, magnetized charged dust plasma with electrons modelled by vortex-like distribution. By using the reductive perturbation method, it has been found that both solitary wave amplitude and width are affected by the plasma parameters: graim charge ratio ρ, population parameter β, and temperature ratio σ. The small-k perturbation technique has also been applied to study the instability criterion and growth rate of this instability. Cyclotron frequency Ω, temperature ratio , direction cosine ( and ), and grain charge ratio ρ are found to modify the instability growth rate Γ.

The methodology for obtaining nonlinear and continuous three-dimensional topographic data using inertial and optical measuring instruments of unmanned ground systems

Topography is the study of an area on the earth's surface. This term relates to the land's slope or contour, which is the interval of elevation differences between two adjacent and parallel contour lines. Topography generally presents a three-dimensional model of object surface relief and an identification of land or hilly areas based on horizontal coordinates such as latitude and longitude, and vertical position, namely elevation. The topography is essential information that must be provided in the execution of building or road construction based on the ground contour. The problem which is the ground contour which can provide visualization topography as a three-dimensional (3D) condition of the ground contour is not normal (non-linear). Another problem is that the traditional measurement techniques with wheel rotation only measure distances and cannot represent the trajectory of the ground contour in 3D. The proposed in-depth evaluation of orientation estimation results in the topography accuracy level. This methodology consists of several processes; Inertia and orientation of an object, Distance measurement, Terrestrial topocentric – Euclidean transformation, and Topography visualization. This research designed a prototype and proposed a new visualization method of the ground contours to reconstruct a topography map between three algorithms; Direct Cosine Matrix-3D Coordinate, Madgwick-3D Coordinate, and Complementary Filter. The methodology was tested and evaluated intensively by direct observation at three measurement locations with different difficulty levels. As a result, the Direct Cosine Matrix-3D Coordinate is able to visualize the ground contours by reconstructing a topography map much better than other methods.

COORDINATE TRANSFORMATIONS OF THREE-PHASE VARIABLES USING QUATERNIONS

Among the variety of modern approaches to the mathematical description of the power quality indicators during the processes of transmission, distribution, conversion and calculation of the ac electric power, the representation of three-phase models in the form of a purely imaginary quaternion located in a separate subspace of the four-dimensional hypercomplex space allows, in relation to the generally accepted method of analyzing linear circuits, for example, symmetrical components with the selection of a direct, reverse and zero phase sequence for the fundamental harmonic, to take into a more complete account the features of energy consumption, especially in the presence of distortion in the modified forms of harmonic signals. In addition, the division of the quaternion into scalar (real) and partial (imaginary) makes it possible to significantly simplify the subsequent analytical processing of synthesis of a power converters control signals for active filtering and power supply of autonomous loads of an arbitrary type, including a single-phase configuration, by extracting from its composition individual components responsible for both the amplitude-phase asymmetry and the nonlinearity of the characteristics.
 
 The main algorithmic principles of organizing control structures as part of three-phase systems of various functional purposes, as a rule, are based on the conversion of reference signals and current values ​​of measured currents and voltages into state coordinates obtained by rotating the three-dimensional space plane by a given angle. At the same time, the calculated ratios for the numerical determination of the initial variables transformed by rotation in the quaternion basis are a function of only four kinematic parameters, which, other things being equal, leads to a simplification of the control law in relation to the traditional vector-matrix approach using nine direction cosines with six connection equations. In this regard, this paper is devoted to the applied problems of implementing linear transformations by E. Clarke and R.H. Park in terms of four-dimensional hypercomplex numbers, in compliance with the additional requirement of the invariance of scalar quantities after the transition.

Decorrelated Debiased Converted Measurement Kalman Filter for Phased Array Radar Tracking System

In this article, the target tracking of phased array radars with measurements specified in the direction cosine coordinate system is considered. The converted measurement Kalman filter is a widely adopted technique since it allows tracking in the coordinate system in which the dynamics of targets are described. The converted measurement Kalman filter has two types of inherent bias: conversion and estimation biases. The compensation of conversion bias has been examined by earlier studies using the debiasing technique in the presence of estimation bias. This article, therefore, introduces decorrelated debiased converted measurement Kalman filter (DDCMKF) in the direction cosine coordinate system to relieve the estimation bias. The decorrelation between the Kalman gain and measurement residual by applying conditioning on predicted position estimates is first introduced. The range-rate measurement is subsequently incorporated as a pseudo-measurement form after the derivation of decorrelated converted position. Finally, a sequential DDCMKF in direction cosine coordinates is developed using the derived converted position and range-rate measurement models. Adopting sequential filtering for incorporating the range-rate measurement reduces computation complexity and alleviates its strong nonlinearity. Numerical simulations are conducted to evaluate the performance of DDCMKF against other types of tracking filters in the direction cosine coordinate system. Simulation results show that the proposed DDCMKF achieves preferable error performance while maintaining consistency, especially in short-range tracking with relatively large direction cosine errors.

Overtaking Interactions of Multi-Ion Acoustic Shock Waves in a Magnetized Degenerate Plasma: An Application in White Dwarfs

Overtaking interactions are examined of multi-ion acoustic shock waves in magnetized degenerate quantum plasmas comprising inertial non-relativistic heavy and light ions having positive charges ultra-relativistic degenerate inertialess electrons. A Burgers’ equation governs the nonlinear excitation of multi-ion acoustic shock waves in a plasma model at hand. The Cole-Hopf transformation and the exponential function have been used to study the overtaking interactions of multi-ion acoustic shock waves in two modes (i.e., the fast and the slow modes). Numerically, the compressive ion-acoustic shock waves exist for the fast mode, but the rarefactive ion-acoustic shock waves exist for the slow mode. A numerical simulation demonstrates that the overtaking interactions of multi-ion acoustic shock waves and their electric fields are remarkably modified with the effectiveness of the charge states of heavy ions and light ions. Furthermore, the amplitude and the steepness of multi-ion acoustic shock waves increase with the decrease in the directional cosines of the multi-ion acoustic shock waves vector along the z-axis. Numerical simulations of overtaking interaction are employed to significantly highlight the physical features of multi-ion acoustic shock waves in astrophysical situations such as white dwarfs and neutron stars.