Direction Cosines Research Articles

Design method toward creating a three-dimensional asymmetric compound parabolic concentrator

Ideal three-dimensional concentration has been sought for decades in the solar and optical worlds. Nonimaging optics has been able to achieve this thermodynamic maximum concentration limit with certain symmetrical designs, but three-dimensional concentration in which acceptance angles are not symmetric has been a challenge for researchers. Our study outlines a new design approach that hopes to move toward the development of an ideal 3D asymmetric concentrator based on the current asymmetric compound parabolic concentrator (ACPC) design principles. A geometric scheme to revolve a variable ACPC curve about a central axis is presented. The 3D ACPC is compared with a standard compound parabolic concentrator (CPC) in a tilted and angular truncated case. Each design was characterized for performance by examining the angular acceptance/illumination region in angular direction cosine space. Ideal performance was demonstrated for the 3D ACPC design for an off axis circular Lambertian acceptance region in direction cosine plots, whereas the CPC designs failed to maintain a circular Lambertian distribution. High-aperture tilt angles demonstrated an interesting “flaring” of the aperture, which caused a decline in ideal performance. Despite design deformations at high-aperture angles, the 3D ACPC design method presented here is a step toward ideal 3D asymmetric concentration.

MIDDLE RESOLUTION REMOTE SENSING IMAGE CHANGE DETECTION BASED ON VECTOR ANALYSIS OF MIDLINE CHANGE

Abstract. The extraction and timely updating of land use /cover information is a key issue in remote sensing change detection. The change vector analysis (CVA) is a better method of change detection. However, the CVA method is the blindness of artificial choice of threshold. Moreover, the direction cosine of CVA cannot represent the unique point in change vector space and it can’t distinguish the change category effectively. In order to avoid this defect, the midline vector is added to CVA method. In this paper, we use the midline change vector analysis (MCVA) method to detect the land use /cover change in multi temporal remote sensing images. We proposed the two-step threshold method to get the optimal threshold and determine the change and the unchanged region of the difference remote sensing image. We chose Hefei city of Anhui Province as the study area, and adopted two Landsat5 TM images in 2000 and 2008 year as experiment data. We use the MCVA and two-step threshold method to achieve remote sensing change detection. In order to compare the detection accuracy between MCVA method and the traditional post classification comparison method, the paper choose the same area (178 pixels × 180 pixels) in the two images to analyse the accuracy, and compare the accuracy of MCVA method with that of the traditional post classification comparison method based on SVM. The experiment results show that the MCVA method has higher overall accuracy, lower allocation disagreement and quantity disagreement. What’s more, the overall accuracy of MCVA method can reach nearly 60%, much higher than the traditional post classification comparison method (less than 40%). And the MCVA method can effectively avoid the problem of change vector direction cosine values are not unique, and the result is much better than the traditional post classification (SVM) comparison method. It indicates that MCVA is a more effective method in land use / cover change detection for middle resolution multispectral images.

An Investigation of Poorly Studied Open Cluster NGC 4337 Using Multicolor Photometric and Gaia DR2 Astrometric Data

Abstract We present a comprehensive analysis (photometric and kinematical) of the poorly studied open cluster NGC 4337 using 2MASS, WISE, APASS, and Gaia DR2 databases. By determining the membership probabilities of stars, we identified the 624 most probable members with membership probability higher than 50% by using proper motion and parallax data taken from Gaia DR2. The mean proper motion of the cluster is obtained as and μ y = 1.49 ± 0.006 mas yr−1. We find the normal interstellar extinction toward the cluster region. The radial distribution of members provides a cluster radius of 7.′75 (5.63 pc). The estimated age of 1600 ± 180 Myr indicates that NGC 4337 is an old open cluster with a bunch of red giant stars. The overall mass function slope for main-sequence stars is found as within the mass range 0.75−2.0 , which is in fair agreement with Salpeter’s value (x = 1.35) within uncertainty. The present study demonstrates that NGC 4337 is a dynamically relaxed open cluster. Using the Galactic potential model, Galactic orbits are obtained for NGC 4337. We found that this object follows a circular path around the Galactic center. Under the kinematical analysis, we compute the apex coordinates (A, D) by using two methods: (i) the classical convergent point method and (ii) the AD-diagram method. The obtained coordinates are (A conv, D conv) = (96.°27 ± 0.°10, 13.°14 ± 0.°27) and (A ◦, D ◦) = (100.°282 ± 0.°10, 9.°577 ± 0.°323) respectively. We also computed the Velocity Ellipsoid Parameters, matrix elements (μ ij ), direction cosines (l j , m j , n j ), and the Galactic longitude of the vertex (l 2).

Method of preliminary solution of the problem of space robot navigation by onboard astronomical measurements using the butterworth filter

A method of preliminary solution of the problem of space robot navigation based on the results of measurements carried out using its onboard optronic equipment is presented. The initial data of the navigation problem are the directional cosines of the space robot orientation vector in the absolute geocentric equatorial coordinate system with reference to time during one revolution. Analytical expressions are obtained for determining unknown parameters of the motion of the space robot center of mass in the form of Keplers elements of the orbit. It is shown that to determine the right ascension of the ascending node, the inclination and the semi-major axis of the orbit of the space robot, information about the orientation of its radius vector at various times is used, and to determine the perigee argument, the moment of passing the perigee and the eccentricity of the orbit, the angular orbital speed of the space robot is used, which is determined by the results of evaluating the speed of change in the orientation of its radius vector over time. The presented results can be used in the development of software for navigation systems that allow autonomous determination of the parameters of the space robots orbit using onboard electro-optical sensors in the absence of a priori information about the parameters of the reference orbit or signals from satellite radio navigation systems.

Retrospective of Roland Shack's global view of diffraction [Invited

In April of 1972, Professor Roland Shack presented a series of four colloquium talks at the Optical Sciences Center at the University of Arizona in which he reformulated scalar diffraction theory in terms of the direction cosines of the propagation vectors of the angular spectrum of plane waves described by the Fourier integral transform of the diffracting aperture. The fourth lecture, entitled Radiometry and Lambert's Law, described diffuse reflectance and surface scatter phenomena as merely a diffraction phenomenon caused by random phase variations in the system pupil function. In 1974, he elegantly condensed these four lectures into a single colloquium talk entitled A Global View of Diffraction. This paper is intended to provide a compilation showing the further development of that work over the last 46 years.

Stochastic subspace identification based data‐driven approach for monitoring electromechanical dynamics from phasor measurement units

This study proposes to extend the numerical algorithm for subspace state space system identification (N4SID) for power grid electromechanical dynamics monitoring using the multi-channel noisy synchrophasor measurements. The oscillation modes, mode shapes, participation factors and coherent groups are estimated in a comprehensive manner. It consists of five key steps: (i) estimation of power system state subspace model via N4SID; (ii) electromechanical modes discrimination from the trivial modes by developing the generalised inverse and mode assurance criterion; (iii) calculations of the mode shapes using the estimated states and output subspace matrices; (iv) estimation of participation factors estimated by the calculated mode shapes and (v) the generator coherency identification by developing the direction cosine denoted coherency inductor. Test results on the IEEE 16-machine 68-bus test system and the practical China Southern power Grid using field synchrophasor measurements are performed. Comparison results with other existing methods show that the proposed method achieves better accuracy and efficiency for power system electromechanical dynamics monitoring in the presence of measurement noise.

Topology optimization for three-dimensional design of segmented permanent magnet arrays

This paper proposes a topology optimization formulation for the three-dimensional (3-D) design of segmented permanent magnet (PM) arrays. Specifically, the proposed formulation aims to find an optimal 3-D structural topology of PM segments and their discrete magnetization directions. To achieve this, a design variable is defined in the vector form of a Cartesian coordinate system. The magnitude of the design variable vector determines a PM density, and the directional cosines of the vector determine PM magnetization directions. To acquire a segmented PM design with discrete magnetization directions, a PM strength penalization scheme is proposed. In this scheme, a PM strength is controlled using a minimum distance function between a magnetization direction and target discrete directions. Here, the minimum distance function is approximated using the p-norm for sensitivity calculation. To validate the effectiveness of the proposed formulation, three design examples are provided. In the first example, a two-dimensional (2-D) dipole Halbach cylinder is designed to confirm that the proposed formulation can be applied for a 2-D design problem. The second example aims to design 3-D dipole PM arrays with a cuboid cavity. In the third example, a 3-D PM arrays are designed for maximizing the magnetic force acting on a soft ferromagnetic material.

Light trapping by the dark matter

Considering the dark matter as self-gravitating Bose-Einstein condensate in a gravito-chemical equilibrium state, we have studied the light trajectory through the halo. Found that depending on the initial direction cosine of the light ray, there are three types of trajectories: (a) the refracted light i.e. light which can refracts away from the halo to the out side, (b) the trapped light i.e. light that is trapped into the halo i.e. an observer, situated outside of the halo, can not observe it and (c) the reflected light: in this case the halo behaves as a perfect reflector to the outside light. The light trapping can introduce asymmetry in the observed spectrum and modify the apparent number of stars in a dark matter dominated galaxy.

Estimating Mo, Cu, Ni, Cd Contents in the Crop Leaves Growing on Small Land Plots Using Satellite Data

ABSTRACT The main goal of this research was to estimate heavy metals (HMs) (molybdenum (Mo), copper (Cu), nickel (Ni), cadmium (Cd)) contents in crop leaves through multispectral satellite imagery. During the acquisition of a SPOT 7 satellite image (28 July 2017) in situ sampling (38 samples) was done from the leaves of potatoes and beans growing close to the mining town of Kajaran (Armenia). To estimate HMs contents, multivariate regression (multiple linear regression (MLR), partial least squares regression (PLSR)), and artificial neural network (ANN) were used. As input data for the models raw, atmospherically corrected (Dark Object Subtraction (DOS)) and hyperspherical direction cosines (HSDC) normalized values of SPOT 7 spectral data in combination with one or combined log10, multiplicative scatter correction (MSC), standard normal variate transform (SNV) preprocessing methods were utilized. The best results were obtained for Cu using MLR (R2 cal. = 0.79, R2 CV = 0.70, RMSEcal. = 11.27, RMSECV = 13.47) and ANN (R2 Train ≈ 0.80, R2 Test ≈ 0.72, RMSETrain ≈ 11, RMSETest ≈ 13) models in case of bean leaves. The results are quite optimistic, however, further research with the use of high spatial/spectral resolution satellite images is needed to improve the accuracy of models.

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.

Method for extraction of airborne LiDAR point cloud buildings based on segmentation.

The LiDAR technology is a means of urban 3D modeling in recent years, and the extraction of buildings is a key step in urban 3D modeling. In view of the complexity of most airborne LiDAR building point cloud extraction algorithms that need to combine multiple feature parameters, this study proposes a building point cloud extraction method based on the combination of the Point Cloud Library (PCL) region growth segmentation and the histogram. The filtered LiDAR point cloud is segmented by using the PCL region growth method, and then the local normal vector and direction cosine are calculated for each cluster after segmentation. Finally, the histogram is generated to effectively separate the building point cloud from the non-building.Two sets of airborne LiDAR data in the south and west parts of Tokushima, Japan, are used to test the feasibility of the proposed method. The results are compared with those of the commercial software TerraSolid and the K-means algorithm. Results show that the proposed extraction algorithm has lower type I and II errors and better extraction effect than that of the TerraSolid and the K-means algorithm.

Change detection in multispectral images based on fusion of change vector analysis in posterior probability space and posterior probability space angle mapper

Change vector analysis in posterior probability space (CVAPS) has been introduced recently as an effective method for change detection. CVAPS is based on the length of change and its direction in a posterior probability (PP) space. However, CVAPS is prone to similar direction cosine values. An approach to analyzing change by combining CVAPS and a new method called posterior probability space angle mapper (PSAM) is proposed in this study. PSAM establishes the similarity between two PP vectors of a pixel for two different dates by calculating the angle between them. This research presents a new change-detection algorithm based on combining CVAPS and PSAM (CVAPSAM), which is able to fully exploit change vectors in a PP space. While CVAPS uses a suitable threshold value to detect changes, CVAPSAM does not need to set a threshold. In addition, it reduces the similar direction cosine values source of error in identifying ‘from-to’ classes.

On a Dual Direct Cosine Simplex Type Algorithm and Its Computational Behavior

The goal of this paper is to propose a dual version of the direct cosine simplex algorithm (DDCA) for general linear problems. The proposed method has not artificial variables, so it is different from both the two-phase method and big-M method. Our technique solves the dual Klee–Minty problem via two iterations and solves the dual Clausen problem via four iterations. The power of the proposed algorithm is evident from the extensive experimental results on benchmark problems adapted from NETLIB. Preliminary results indicate that this dual direct cosine simplex algorithm (DDCA) reduces the number of iterations of the two-phase method.

ESPRIT-Based DOA Estimation with Spatially Spread Long Dipoles and/or Large Loops

The radiation efficiency of short electric dipole and small magnetic loop is low. Therefore, the long electric dipole and large magnetic loop for direction of arrival (DOA) estimation are investigated in this study. A novel array composed of long electric dipole, large magnetic loop, or a hybrid long electric dipole and large magnetic loop is proposed. Then a corresponding algorithm based on ESPRIT is proposed to estimate the two-dimensional (2D) DOA. The proposed array has eight elements. The first four elements and other four elements construct the rotational invariant property. Then, the 2D direction cosine can be estimated accurately but with ambiguity. After that, the ambiguous value is instituted into the spatially spread vector sensor for spatial phase compensation. Then, the steering vector of the collocated orthogonal vector sensor is obtained to calculate a fake coarse DOA estimation. By comparing the above ambiguous fine estimation with the fake coarse estimation, the closest estimation is taken as the finally 2D DOA estimation. The computation of the proposed algorithm is small due to a lack of angle searching. Moreover, the long dipole has high radiation efficiency, and the spatially spread vector sensor has low mutual coupling. Simulation results demonstrate the effectiveness of the proposed algorithm.

Human Posture Recognition Method Based On Skeleton Vector With Depth Sensor

This paper proposes a human body gesture recognition method. The method collects bone information of the human body through the Kinect depth sensor, and then uses the direction cosine method for feature extraction.Finally, the feature vector is sent to the BP neural network for training and recognition. In the case of less sample training, the system can still accurately identify the five postures of standing, sitting, leaning forward, leaning backward and underarm. The input is composed of low-dimensional bone information, so the speed and recognition response speed during network training is better than the conventional RGB image recognition method. Experiments show that the recognition rate and real-time performance of the system can meet the needs of practical applications.

CARTESIAN VECTOR DIRECTION COSINES AS THE MULTI-OPTIONAL HYBRID FUNCTIONS OPTIMAL DISTRIBUTION

It is made an attempt to discover an explainable plausible reason for the existence of the conditions of optimality for Cartesian vector direction cosines, having importance in energy mechanical engineering, with the help of the multi-optional hybrid functions entropy conditional optimality doctrine. Substantiation is made in terms of the calculus of variations theory with the help of the special hybrid-optional effectiveness functions uncertainty measure, which includes the hybrid functions entropy of the traditional Shannon’s style. In the studied cases, the simplest variational problems solutions, which are the numbers known as the direction cosines of a Cartesian vector, are stipulated by the specified natural logarithmic quadratic forms. It is proposed to evaluate the uncertainty/certainty degree of the magnitude and direction of a Cartesian vector with the use of the objective functional. This is a new insight into the scientific explanation of the well-known dependency derived in another way. The developed theoretical contemplations and mathematical derivations are finalized with a simplest numerical example for the variated value of the multi-optional hybrid function resulting in the objective functional.

Modified Integer Sine Transforms. Construction Method and Separable Directional Adaptive Transforms for Intra Prediction in Image/Video Coding

The author proposes a matrix method for constructing a modified order 8 integer sine type VII transform. Based on the method, two modified order 8 integer sine type VII transforms are constructed and algorithms for fast implementation of 8-point modified integer sine type VII transforms are developed, which require only integer operations. These algorithms have low computational complexity that is 4.5 and 10.9 times less than that of the known algorithm. These transforms have higher coding performance in terms of quality and compression ratio than the known sine transforms do. Algorithms for fast implementation of 2D 8-point separable directional integer cosine and modified adaptive sine transforms for intra prediction with low computational complexity are developed, and their computational complexity is 4.62 and 8.24 times lower than that of the known algorithms.

P-wave reflection-moveout approximation for horizontally layered media of arbitrary moderate anisotropy

We present an approximate nonhyperbolic P-wave moveout formula applicable to horizontally layered media of moderate or weak anisotropy of arbitrary symmetry and orientation. Anisotropy symmetry and its orientation may differ from layer to layer. Instead of commonly used Taylor-series expansion of the square of the reflection traveltime in terms of the square of the offset, we use the weak-anisotropy approximation, in which the square of the reflection traveltime is expanded in terms of weak-anisotropy (WA) parameters. The resulting formula is simple, and it provides a transparent relation between the traveltimes and WA parameters. Along an arbitrarily chosen single surface profile, it depends, in each layer, on the thickness of the layer, on the reference P-wave velocity used for the construction of reference rays, and on three WA parameters specified in the Cartesian coordinate system related to the profile. In each layer, these three “profile” WA parameters depend on “local” WA parameters specifying anisotropy of a given layer in a local coordinate system and on directional cosines specifying the orientation of the local coordinate system with respect to the profile one. The number of local P-wave WA parameters may vary from three for transverse isotropy or six for orthorhombic symmetry to nine for triclinic symmetry. Our tests of the accuracy indicate that the maximum relative traveltime errors do not exceed 0.5% or 2.5% for weak or moderate P-wave anisotropy, respectively.

Algorithms for Fast Implementation of 4-Point Integer Sine Type Vii Transformswithout Multiplication and Separable Directional Adaptive Transforms for Intra Prediction in Image/Video Coding

The separable directional adaptive integer cosine and sine type VII transforms with 4×4 blocks are proposed for intra prediction in image and video coding. Algorithms for fast implementation of 2D 4-point separable directional integer cosine and sine transforms are developed. These algorithms require 7 times fewer multiplication operations and provide higher compression ratio than the well-known algorithms. Two order-4 integer sine type VII transforms are proposed, and algorithms are developed for fast implementation of 4-point integer sine type VII transforms, which require integer operations only. As compared to the known algorithm, these algorithms can significantly reduce the number of multiplication operations or avoid them at all. These integer sine transforms are very close to discrete sine type VII transform and have a higher compression ratio than the well-known sine transform accepted in standard H.265 does.

Leak localization in water distribution networks using classifiers with cosenoidal features

This paper presents a leak localization approach for water distribution networks using classifiers with pressure residuals as input features. This approach is based on applying a non-linear transformation to the residuals of the node pressures to increase the separability of the leak classes. The transformed features can be interpreted as the direction cosines in the subspace spanned by the residuals of the measured pressures. In order to illustrate the method, different tests were performed with MATLAB® applying four different classification algorithms on a synthetic dataset obtained from an EPANET model of the Hanoi network. Then, by considering the cosenoidal features, a significant improvement in the leak location error was achieved. In this way, the leak location error decreases by more than 97% compared to the use of residual features when accurate measurements are used, and about 50% when noisy measurements with 60 dB SNR are used.