Rational Polynomial Research Articles

SATELLITE IMAGING DIRECTION ANGLES ESTIMATION METHOD BASED ON RATIONAL POLYNOMIAL COEFFICIENTS

Abstract. Satellite imaging direction angles, including the azimuth angle and the incidence angle, are the basic information used for satellite camera network structure analysis. They play an important role in 3D reconstruction using satellite images. In this paper, a satellite imaging direction angle estimation method based on rational polynomial coefficients is proposed for use when the satellite imaging direction angles are not available. Using rational polynomial coefficients, a vertical line on the ground is projected into the image plane, and the satellite imaging direction angles are estimated by analyzing the projection. Satellite images acquired by SPOT6, SOPT7 and Pleiades with different satellite imaging direction angles were used to test the feasibility of the proposed method. The experimental results were analyzed in detail combined with the method and the data. The experimental results show that the azimuth angle estimation error is less than 1.30 degrees, and the incidence angle estimation error is less than 0.83 degrees. This level of accuracy is sufficient for satellite camera network structure analysis.

Exchange rates in India: current account monetarism in a nonlinear context

Abstract The Indian exchange rate system has evolved from a pegged system to the current managed float. The study examines the presence of a long-run equilibrium in the monthly Indian exchange rate (Rs/USD) using a current account monetary model (or flexible price monetary model) while accounting for different nonlinearities over the period January 1993 to January 2014 (pre-inflation targeting period). The nonlinear adjustment to disequilibria is modelled using a nonlinear error correction model (NLECM). The nonlinear current account monetarism (CAM) model includes nonlinear transformations of long-run dynamics in the ECM to account for different nonlinearities: multiple equilibria (cubic polynomial function), nonlinear mean reversion (rational polynomial function), and smooth and gradual regime switches (exponential smooth transition autoregressive (ESTAR) function). The NLECM-ESTAR model outperforms other alternatives based on model and forecast performance measures, implying the existence of nonlinear mean reversion and smooth transition across different periods of overvaluation and undervaluation of the exchange rate. This implies the presence of asymmetric adjustment to the movements from the long-run equilibrium, but the nature of such transitions is smooth and not abrupt. The paper also establishes the uniqueness of the long-run equilibrium. A comparison to the sticky price monetary model could not be made due to stationary exchange rate disequilibrium.

CALIBRATION AND VALIDATION OF THE ADVANCED LAND OBSERVING SATELLITE-3 “ALOS-3”

Abstract. The “Advanced Land Observing Satellite-3” (ALOS-3, nicknamed “DAICHI-3”) is the next high-resolution optical mission as a successor of the optical mission by the Advanced Land Observing Satellite (ALOS, “DAICHI”) in Japan Aerospace Exploration Agency (JAXA), and will be launched in Japanese Fiscal Year 2020. ALOS-3 is now under developing the flight model. The major missions of ALOS-3 are (1) to contribute safe and secure social including provision for natural disasters, and (2) to create and update geospatial information in land and coastal areas. To achieve the missions, the “WIde-Swath and High-resolution optical imager” (WISH, as a tentative name) is mounted on ALOS-3, which consists of the high-resolution panchromatic- and multispectral-bands.This paper introduces the overview of ALOS-3’s mission and the calibration and validation plan at JAXA. The standard product is the system corrected data using the sensor models, which will be provided from the sensor development team. Therefore, the sensor calibration is directly affected to the accuracies of the standard product. In addition, the sensor model based the Rational Polynomial Coefficient will be contained with level 1B2 standard product that can be used to process an ortho rectification and three-dimensional measurement from ALOS-3 images. As the target accuracy of WISH’s standard products, the geometric accuracies are less than 5 m in horizontal without ground control point (GCP), and 1.25 m in horizontal and 2.5 m in vertical with GCPs (1 sigma), and the radiometric accuracy is ± 10 % as absolutely and ± 5 % as relatively for multispectral band.

GEOMETRIC ACCURACY EVALUATION OF THE ZY-3 STEREO MAPPING SATELLITE FOR 8 YEARS

Abstract. The Ziyuan-3 (ZY-3) is the first civil high-resolution optical stereoscopic mapping satellite developed by China. It was launched on January 9, 2012, and as of January 9, 2020, it has been in a continuous operation for 8 years in orbit. The direct geolocation performances of ZY-3 based on the Rational Polynomial Coefficients (RPC) model are discussed, and the monoscopic and stereoscopic geometric accuracy of ZY-3 with ground control point (GCP) have also been studied using a bundle block adjustment with the affine correction in image space. Through the analysis of 47 sets of ZY-3 stereo data in Harbin, China, it can be found that from 2012 to 2019, the ZY-3 geolocation accuracy without GCP remains stable, with an average planimetric accuracy of approximately 16.2m, an average elevation accuracy of about 7.5m. The internal accuracy of the panchromatic triplet images is better than 1.0 pixel, the planimetric accuracy and elevation accuracy of stereo triplets and and stereo pairs are better than 2.0 meters with control points. In general, the results show that the ZY-3 satellite has been in good and stable condition during in-orbit operation in the past 8 years, and the various test indicators have been able to meet the design specifications.

A NOVEL RPC BIAS MODEL FOR IMPROVING THE POSITIONING ACCURACY OF SATELLITE IMAGES

Abstract. High-precision satellite image geolocation is the basis for advanced processing of satellite image data. Aiming at the optimization of the satellite image positioning accuracy based on rational polynomial coefficients (RPC), we propose an RPC image-space bias model that combines object-space information. Based on a comprehensive analysis of the full-link error of the satellite image geometric imaging process, the real object coordinates are introduced into the RPC correction to make the bias model better fit the actual error. Experiments were performed using several image datasets from the Chinese satellite TianHui-1 (TH-1) and compared with the traditional RPC bias model. The results show that our model has strong robustness and can better correct image positioning errors. Compared with traditional bias models, it can improve the accuracy of plane positioning by approximately 1 pixel.

Estimation and improvement in the geolocation accuracy of rational polynomial coefficients with minimum GCPs using KOMPSAT-3A

ABSTRACT In this paper, we propose a method to regenerate Rational Polynomial Coefficients (RPCs) using KOMPSAT-3A imagery and to reduce the geolocation error using minimum ground control points (GCPs). To estimate the new RPCs, the physical sensor model fitted to KOMPSAT-3A imagery was utilized and virtual GCPs over the study area were created. The size of the virtual grid used was 20x20x20. To remove the sensor-related errors in physical sensor model, three different image correction models (image coordinate translation model, shift and drift model, and affine transformation model) were additionally applied. We evaluated our proposed method in two areas within Korea, one in urban (Seoul) and one in rural (Goheung) areas. The results showed that there was a significant improvement after applying the suggested approach in the two areas. The image coordinate translation model is suggested in terms of GCP requirement and expected errors estimated from the error propagation analysis using Gauss–Markov Model (GMM).

Modelling and identification of bolted truss structure with the use of design of experiment approach

The paper concerns identification process of the structural model of the multiple degrees of freedom bolted truss structure of complex geometry. In order to properly describe dynamic response of a system, both restraints and connections of the truss structure elements should be modelled as semi-rigid. On the basis of the simplified laboratory model of the overhead power line supporting structure the method of structural model parameters identification is presented. The experimental modal analysis, that involves Rational Fraction Polynomial method, results in modal model for five mode shapes in 72 degrees of freedom. The established finite element model of the construction includes elastic anchor joints and over 150 semi-rigid bolted connections of unknown values of parameters. Applying the enhanced Central Composite Inscribed design for three factors allows to determine the response surfaces and analyze the sensitivity of the individual modal parameters to the input structural parameters. The multi-criteria optimization minimize the quality function and provide the Pareto-optimal solutions. Finally, the identified structural numerical model is verified, comparing its modal parameters with the model determined experimentally.

Photometric multi-view mesh refinement for high-resolution satellite images

Modern high-resolution satellite sensors collect optical imagery with ground sampling distances (GSDs) of 30–50 cm, which has sparked a renewed interest in photogrammetric 3D surface reconstruction from satellite data. State-of-the-art reconstruction methods typically generate 2.5D elevation data. Here, we present an approach to recover full 3D surface meshes from multi-view satellite imagery. The proposed method takes as input a coarse initial mesh and refines it by iteratively updating all vertex positions to maximise the photo-consistency between images. Photo-consistency is measured in image space, by transferring texture from one image to another via the surface. We derive the equations to propagate changes in texture similarity through the rational function model (RFM), often also referred to as rational polynomial coefficient (RPC) model. Furthermore, we devise a hierarchical scheme to optimise the surface with gradient descent. In experiments with two different datasets, we show that the refinement improves the initial digital elevation models (DEMs) generated with conventional dense image matching. Moreover, we demonstrate that our method is able to reconstruct true 3D geometry, such as facade structures, if off-nadir views are available.

An asymptotic series for an integral

We obtain an asymptotic series $$\sum _{j=0}^\infty \frac{I_j}{n^j}$$ for the integral $$\int _0^1[x^n+(1-x)^n]^{\frac{1}{n}}\mathrm{{d}}x$$ as $$n\rightarrow \infty $$ , and compute $$I_j$$ in terms of alternating (or “colored”) multiple zeta values. We also show that $$I_j$$ is a rational polynomial in the ordinary zeta values, and give explicit formulas for $$j\le 12$$ . As a by-product, we obtain precise results about the convergence of norms of random variables and their moments. We study $$Z_n=\Vert (U,1-U)\Vert _n$$ as n tends to infinity and we also discuss $$W_n=\Vert (U_1,U_2,\dots ,U_r)\Vert _n$$ for standard uniformly distributed random variables.

An automated PCA-based approach towards optimization of the rational function model

The existence of several unnecessary and highly correlated coefficients in the rational function model (RFM), known as rational polynomial coefficients (RPCs), leads to an ill-posed design matrix. Under such a condition, any small perturbation, including errors in the problem’s input, causes drastic changes in the final results. The ill-posedness of the design matrix, intrinsic to the RFM problem, can be amplified due to the errors in the ground and image coordinates of the control points. The principal component analysis (PCA)-based RFM optimization method has already been applied to reduce the impact of ill-posedness of the design matrix. Despite its efficacy, the existence of a case-sensitive tunable threshold value in this method has overshadowed its efficiency. To address this problem, we propose an automated PCA-based RFM optimization, called APCA-RFM method, which is based on the thresholding ridge ratio criterion. In APCA-RFM, the data itself is used to obtain the threshold value and hence to separate the noise from the signal. Experiments conducted on different data sets demonstrated the high performance of the proposed method to come up with a solution to the challenge of an appropriate threshold value. Additionally, the experimental results proved the superiority of the proposed APCA-RFM in comparison with recently published methods dealing with the ill-posedness problem of RFM.

Exploring the Novel Continuum-Cancellation Leal-Method for the Approximate Solution of Nonlinear Differential Equations

This work presents the novel continuum-cancellation Leal-method (CCLM) for the approximation of nonlinear differential equations. CCLM obtains accurate approximate analytical solutions resorting to a process that involves the continuum cancellation (CC) of the residual error of multiple selected points; such CC process occurs during the successive derivatives of the differential equation resulting in an accuracy increase of the inner region of the CC-points and, thus, extends the domain of convergence and accuracy. Users of CCLM can propose their own trial functions to construct the approximation as long as they are continuous in the CC-points, that is, it can be polynomials, exponentials, and rational polynomials, among others. In addition, we show how the process to obtain the approximations is straightforward and simple to achieve and capable to generate compact, and easy, computable expressions. A convergence control is proposed with the aim to establish a solid scheme to obtain optimal CCLM approximations. Furthermore, we present the application of CCLM in several examples: Thomas–Fermi singular equation for the neutral atom, magnetohydrodynamic flow of blood in a porous channel singular boundary-valued problem, and a system of initial condition differential equations to model the dynamics of cocaine consumption in Spain. We present a computational convergence study for the proposed approximations resulting in a tendency of the RMS error to zero as the approximation order increases for all case studies. In addition, a computation time analysis (using Fortran) for the proposed approximations presents average times from 3.5 nanoseconds to 7 nanoseconds for all the case studies. Thence, CCML approximations can be used for intensive computing simulations.

Discrete-binary configuration of metaheuristic algorithms for RFM optimization in the case of limited GCPs

Metaheuristic algorithms have been widely used in determining optimum rational polynomial coefficients (RPCs). By eliminating a number of unnecessary RPCs, these algorithms increase the accuracy of geometric correction of high-resolution satellite images. To this end, these algorithms use ordinary least squares and a number of ground control points (GCPs) to estimate RPCs. Due to the cost of GCP collection, using limited GCPs has become an attractive topic in various research studies. A configuration for RPC estimation using metaheuristic algorithms, namely, discrete-binary configuration for rational function model (DBRFM), is presented to find the optimal number and combination of RPCs in the case of limited GCPs. Based on the fact that the maximum number of RPCs is twice the number of GCPs, the particle/chromosome in the proposed configuration is composed of two binary and discrete parts. This configuration not only is compatible with the nature of the metaheuristic algorithms but also significantly reduces the search space. The proposed method has been tested on various types of remotely sensed data sets. The results of the experiments indicate the superiority of the DBRFM in comparison with the traditional binary configuration of metaheuristic algorithms.

Rational Chebyshev collocation method for solving nonlinear heat transfer equations

In this paper, the classical collocation method has been revisited and modified by using the Chebyshev polynomials for solving nonlinear differential equations. Linear and nonlinear terms are converted to algebraical equations with the aid of the matrix relations. Resulting equations are solved to get unknown coefficients of rational Chebyshev polynomials. We apply the proposed technique for solving nonlinear heat transfer equations. Obtained results reveal that the rational Chebyshev collocation method can be safely applied to different types of nonlinear ordinary differential equations arising in science and engineering.

Satellite-Imagery Geometric Accuracy Improvement Based on Direct Correction of Dominant Coefficients

An important and difficult point in the application of satellite imagery is refining the positioning model and improving the geometric accuracy. In this study, we focus on improvement in geometric accuracy and develop a new rational function model (<small>RFM</small>) refinement method. First, we derive the conversion relationship between the rigorous sensor model and the <small>RFM</small>, based on which we illustrate the approximate meaning of the zero-order and first-order terms of the rational polynomial coefficients (<small>RPCs</small>). Second, the correlation problem between <small>RPCs</small> and the influence of individual <small>RPCs</small> on geometric positioning accuracy are analyzed and verified. The dominant coefficients that determine geolocation are then identified. Finally, a new <small>RFM</small> refinement method based on direct correction of the dominant coefficients is proposed and validated. The experiments, conducted with <small>ZY3-02</small> satellite imagery, indicate that the proposed method can effectively improve the geometric accuracy of satellite images.

Polygonal finite element: A comparison of the stiffness matrix integration methods

This paper aims to determine which numerical integration method shows the best performance when integrating the polygonal finite element stiffness matrix. Hence, numerical comparisons were made between two existing methods, triangulation and quadrangulation, and two new quadrature rules developed by the authors called Polygonal Gauss–Legendre quadrature (PGL) and Rational Polynomial Gauss quadrature (RPG). In this study, PGL11Polygonal Gauss-Legendre quadrature. points and weights were obtained for polynomials of degree 3, 5, 6, 8 and 9, while RPG22Rational Polynomial Gauss quadrature. rules were calculated for rational polynomials of degree 8/8, 10/8 and 16/16. Briefly, the PGL rule showed the best performance, reducing the execution time in 38.6% at best (compared with the triangulation), also, its implementation is much more straightforward.

공기압 관로의 동적 모델링과 과도응답 특성 해석

The study deals with dynamic modeling and time domain simulation of pneumatic transmission pipes with a distributed parameter dissipative model that include frequency dependent viscous friction terms and heat transfer effects. The transient responses of pneumatic transmission pipes are considerably complex and difficult because the transcendent transfer functions consist of hyperbolic Bessel functions in the frequency domain. For the blocked pipes at the downstream, the pipes terminating into single valve and capacitance element pairs, transfer functions are derived, and their gain and phases are calculated theoretically. Based on the frequency responses of the theoretical transfer functions, we obtained approximated transfer functions with equal frequency responses using MATLAB. The approximated transfer functions with rational polynomials are accurate over the designated frequency ranges, and are used to analyze the time domain responses. The effects of varying parameters of the blocked pipe on the accuracy of the simulated responses are investigated.

Thermodynamic potential for quark-qluon plasma with finite quark mass and chemical potential

We summarize the derivation of the finite temperature, finite chemical potential thermodynamic potential in the bag-model approximation to quantum chromodynamics (QCD) that includes a finite s-quark mass in the Feynman diagram contributions for both zero-order and two-loop corrections to the quark interaction. The thermodynamic potential for quarks in QCD is a desired ingredient for computations of the equation of state in the early universe, supernovae, neutron stars, and heavy-ion collisions. The 2-loop contributions are normally divergent and become even more difficult in the limit of finite quark masses and finite chemical potential. We describe various means to interpolate between the low and high chemical potential limits. Although physically well motivated, we show that the infinite series Padé rational polynomial interpolation scheme introduces spurious poles. Nevertheless, we show that lower order interpolation schemes such as polynomial interpolation reproduce the Padé result without the presence of spurious poles. We propose that in this way one can determine the equation of state for the two-loop corrections for arbitrary chemical potential, temperature and quark mass. This provides a new realistic bag-model treatment of the QCD equation of state. We compute the QCD phase diagram with up to the two-loop corrections. We show that the two-loop corrections decrease the pressure of the quark-gluon plasma and therefore increase the critical temperature and chemical potential of the phase transition. We also show, however, that the correction for finite s-quark mass in the two-loop correction serves to decrease the critical temperature for the quark-hadron phase transition in the early universe.

Mathematical Model for Strength Prediction of Concrete under Influence of GGBS and Fly Ash

There are many variables of concrete that affect its strength gaining characteristics. This study is a research to use the early compressive strength test result to evaluate compressive strength at different ages. Proper use of the early day compressive strength result to predict characteristic strength of normal weight concrete has been investigated. A simple model capable of predicting the compressive strength of concrete at any age is proposed for locally available aggregate concrete. The model develops a rational polynomial equation having only two coefficients. This study also proposes a simple justified relationship between the coefficient (strength at infinite time) with the strength values of concrete of a particular day. This relation almost make simple to understand and reliable to any the concrete strength prediction model. The developed model is validated for commonly used for local aggregate concrete. Data used in this study are collect from some previous studies of research scholars and recent experimental works of us at RCC lab of MBM Engineering College Jodhpur. along with data sets of conventional concrete (CC), we have also considered influence and variation of GGBS and FLYASH in Conventional concrete and we have selected the various data sets for M1 ( GGBS & FLY ASH ),M2( GGBS ) & M3( FLY ASH) member group .The research carried with the model using different data exhibit reliable prediction of concrete strength at different ages (7, 14, 28 days.) with good accuracy.

Feasibility of Replacing the Range Doppler Equation of Spaceborne Synthetic Aperture Radar Considering Atmospheric Propagation Delay with a Rational Polynomial Coefficient Model.

Usually, the rational polynomial coefficient (RPC) model of spaceborne synthetic aperture radar (SAR) is fitted by the original range Doppler (RD) model. However, the radar signal is affected by two-way atmospheric delay, which causes measurement error in the slant range term of the RD model. In this paper, two atmospheric delay correction methods are proposed for use in terrain-independent RPC fitting: single-scene SAR imaging with a unique atmospheric delay correction parameter (plan 1) and single-scene SAR imaging with spatially varying atmospheric delay correction parameters (plan 2). The feasibility of the two methods was verified by conducting fitting experiments and geometric positioning accuracy verification of the RPC model. The experiments for the GF-3 satellite were performed by using global meteorological data, a global digital elevation model, and ground control data from several regions in China. The experimental results show that it is feasible to use plan 1 or plan 2 to correct the atmospheric delay error, no matter whether in plain, mountainous, or plateau areas. Moreover, the geometric positioning accuracy of the RPC model after correcting the atmospheric delay was improved to better than 3 m. This is of great significance for the efficient and high-precision geometric processing of spaceborne SAR images.

A Rational Polynomial Tracking Control Approach to a Common System Representation for Unmanned Aerial Vehicles

This article presents a rational polynomial tracking control approach to a common system representation for unmanned aerial vehicles (UAVs). First, we newly provide a common system representation of kinematic models for straight and orbit paths. A polynomial representation is introduced to describe the common system. To stabilize the polynomial system, we design a rational polynomial controller using a sum-of-squares (SOS)-based design framework. A set of stabilization conditions considering a real actuator saturation is represented in terms of SOS, where a relaxation for the SOS design conditions is brought by considering practical operation domains. The SOS-based design framework is applied to path stabilization for a real UAV platform (a parafoil wing-type UAV). Experimental results demonstrate the capabilities of the proposed SOS-based design framework in path stabilization of real-world complex UAVs.