Combining multiple arcs for orbit determination using normal equations

2021 ◽  
Author(s):  
Flavien Mercier ◽  
Shambo Bhattacharjee ◽  
Félix Perosanz ◽  
Jean-Michel Lemoine
Keyword(s):  
Least Squares ◽  
Global Solution ◽  
Orbit Determination ◽  
Simple Problem ◽  
Test Case ◽  
Minimal Set ◽  
Normal Equations ◽  
The One ◽  
Gnss Constellation ◽  
Recursive Solutions

<p>The normal equations are widely used to combine elementary least squares solutions, to solve very large problems which are not possible to handle directly. The principle is to reduce each problem to a minimal set of parameters present in the global problem, without removing the corresponding information, and connect them. For instance, one important application is the combination over years of daily network solutions, as performed for the ITRF (Altamimi et al., 2016) [1].</p><p>The approach can also be used in orbit determination to connect arcs solutions in order to construct the solution of a global arc. This was applied for example for GPS constellation solutions as in the article written by Beutler et al. (1996) [2]. Due to the size of the problems, it is interesting to divide for example a three days solution into three one day solutions. Another advantage is that the one day solutions are usually efficiently processed by the orbit determination software. For rapid or ultra-rapid GNSS products this is also very interesting, as the solutions are needed very often for small shifts of the global arc (for example 24 hours arcs, shifted every 6 hours in the case of ultra-rapid products). A further extension is to construct recursive solutions from these elementary arcs, leading to a filter similar to a Kalman filter.</p><p>We propose a unified methodology, associated with an efficient implementation compatible with our least squares software GINS, allowing us to solve the various problems ranging from arc connection to sequential filtering. The final objective is to construct efficient GNSS ultra-rapid products.</p><p>The application on a simple problem consisting in connecting different SLR arcs is shown, as a test case to develop and implement the methodology. In this case, the global solution can also be directly constructed for validation purposes. This study includes the construction of the solution at the end points of the elementary arcs, and also the recovery of the global solution state vectors at every epoch.</p><p>The next step will be to implement more complex parameterizations (including measurement parameters, which are not present in the SLR test case), and to apply this for GNSS constellation solutions.</p>

Theoretical accuracy of the last squares method in the isotope dilution analysis

1984 ◽  
Vol 49 (4) ◽  
pp. 805-820
Author(s):  
Ján Klas
Keyword(s):  
Least Squares ◽  
Isotope Dilution ◽  
Least Squares Method ◽  
Isotope Dilution Analysis ◽  
Straight Line ◽  
The One ◽  
Two Parameter ◽  
Theoretical Accuracy

The accuracy of the least squares method in the isotope dilution analysis is studied using two models, viz a model of a two-parameter straight line and a model of a one-parameter straight line.The equations for the direct and the inverse isotope dilution methods are transformed into linear coordinates, and the intercept and slope of the two-parameter straight line and the slope of the one-parameter straight line are evaluated and treated.

scholarly journals Pathways to relativistic curved momentum spaces: de Sitter case study

2016 ◽  
Vol 25 (02) ◽  
pp. 1650027 ◽  
Author(s):  
Giovanni Amelino-Camelia ◽  
Giulia Gubitosi ◽  
Giovanni Palmisano
Keyword(s):  
Momentum Space ◽  
Hopf Algebras ◽  
Affine Connection ◽  
Planck Scale ◽  
Test Case ◽  
De Sitter ◽  
Group Manifold ◽  
The One ◽  
Natural Test

Several arguments suggest that the Planck scale could be the characteristic scale of curvature of momentum space. As other recent studies, we assume that the metric of momentum space determines the condition of on-shellness while the momentum space affine connection governs the form of the law of composition of momenta. We show that the possible choices of laws of composition of momenta are more numerous than the possible choices of affine connection on a momentum space. This motivates us to propose a new prescription for associating an affine connection to momentum composition, which we compare to the one most used in the recent literature. We find that the two prescriptions lead to the same picture of the so-called [Formula: see text]-momentum space, with de Sitter (dS) metric and [Formula: see text]-Poincaré connection. We then show that in the case of “proper dS momentum space”, with the dS metric and its Levi–Civita connection, the two prescriptions are inequivalent. Our novel prescription leads to a picture of proper dS momentum space which is DSR-relativistic and is characterized by a commutative law of composition of momenta, a possibility for which no explicit curved momentum space picture had been previously found. This momentum space can serve as laboratory for the exploration of the properties of DSR-relativistic theories which are not connected to group-manifold momentum spaces and Hopf algebras, and is a natural test case for the study of momentum spaces with commutative, and yet deformed, laws of composition of momenta.

The Estimation of Aquifer Properties From Reservoir Performance in Water-Drive Fields

1977 ◽  
Vol 99 (2) ◽  
pp. 345-352 ◽  
Author(s):  
A. T. Chatas
Keyword(s):  
Least Squares ◽  
Material Balance ◽  
Dimensionless Form ◽  
Simultaneous Solution ◽  
Method Of Least Squares ◽  
Normal Equations ◽  
Aquifer Parameters ◽  
Reservoir Performance ◽  
Analytical Functions ◽  
Aquifer Properties

The purpose of this paper is to indicate a method for estimating values of specified aquifer parameters from an investigation of the reservoir performance of an associated oilfield. To achieve this objective an analysis was made of the simultaneous solution of the material-balance and diffusivity equations, followed by an application of the method of least squares. Three analytical functions evolved, which in dimensionless form were numerically evaluated by computer and tabulated herein. Application of the proffered method requires the simultaneous solution of the three normal equations developed in the paper.

THE CALIBRATION OF AN ARRAY OF ACCELEROMETERS

2011 ◽  
Vol 35 (2) ◽  
pp. 251-267 ◽  
Author(s):  
Dany Dubé ◽  
Philippe Cardou
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Least Squares ◽  
Calibration Method ◽  
Calibration Procedure ◽  
Rigid Bodies ◽  
New Method ◽  
Scale Factors ◽  
Array Calibration ◽  
The One

An accelerometer-array calibration method is proposed in this paper by which we estimate not only the accelerometer offsets and scale factors, but also their sensitive directions and positions on a rigid body. These latter parameters are computed from the classical equations that describe the kinematics of rigid bodies, and by measuring the accelerometer-array displacements using a magnetic sensor. Unlike calibration schemes that were reported before, the one proposed here guarantees that the estimated accelerometer-array parameters are globally optimum in the least-squares sense. The calibration procedure is tested on OCTA, a rigid body equipped with six biaxial accelerometers. It is demonstrated that the new method significantly reduces the errors when computing the angular velocity of a rigid body from the accelerometer measurements.

scholarly journals Crystal structure ofO-ethylN-(ethoxycarbonyl)thiocarbamate

2015 ◽  
Vol 71 (10) ◽  
pp. o782-o783 ◽  
Author(s):  
Matthew J. Henley ◽  
Alex M. Schrader ◽  
Victor G. Young ◽  
George Barany
Keyword(s):  
Crystal Structure ◽  
Hydrogen Bonds ◽  
Least Squares ◽  
Title Compound ◽  
Compound C ◽  
The One ◽  
Related Compounds ◽  
Centrosymmetric Dimers

The title compound, C6H11NO3S, provides entries to novel carbamoyl disulfanes and related compounds of interest to our laboratory. The atoms of the central O(C=S)N(C=O)O fragment have an r.m.s. deviation of 0.1077 Å from the respective least-squares plane. While several conformational orientations are conceivable, the crystal structure shows only the one in which the carbonyl and the thiocarbonyl moieties areantito each other across the central conjugated C—N—C moiety. Pairs of 2.54 Å N—H...S=C hydrogen bonds between adjacent molecules form centrosymmetric dimers in the crystal.

scholarly journals Numerical solutions for unsteady gravity-driven flows in collapsible tubes: evolution and roll-wave instability of a steady state

1999 ◽  
Vol 396 ◽  
pp. 223-256 ◽  
Author(s):  
B. S. BROOK ◽  
S. A. E. G. FALLE ◽  
T. J. PEDLEY
Keyword(s):  
Shallow Water ◽  
Numerical Solutions ◽  
Godunov Method ◽  
Test Case ◽  
Interesting Phenomenon ◽  
One Dimensional ◽  
Collapsible Tubes ◽  
Highly Nonlinear ◽  
Pressure Area ◽  
The One

Unsteady flow in collapsible tubes has been widely studied for a number of different physiological applications; the principal motivation for the work of this paper is the study of blood flow in the jugular vein of an upright, long-necked subject (a giraffe). The one-dimensional equations governing gravity- or pressure-driven flow in collapsible tubes have been solved in the past using finite-difference (MacCormack) methods. Such schemes, however, produce numerical artifacts near discontinuities such as elastic jumps. This paper describes a numerical scheme developed to solve the one-dimensional equations using a more accurate upwind finite volume (Godunov) scheme that has been used successfully in gas dynamics and shallow water wave problems. The adapatation of the Godunov method to the present application is non-trivial due to the highly nonlinear nature of the pressure–area relation for collapsible tubes.The code is tested by comparing both unsteady and converged solutions with analytical solutions where available. Further tests include comparison with solutions obtained from MacCormack methods which illustrate the accuracy of the present method.Finally the possibility of roll waves occurring in collapsible tubes is also considered, both as a test case for the scheme and as an interesting phenomenon in its own right, arising out of the similarity of the collapsible tube equations to those governing shallow water flow.

Strategies for the reinterpretation of normative texts within the Hebrew Bible

2018 ◽  
Vol 3 (1) ◽  
pp. 1-31 ◽  
Author(s):  
Bernard M. Levinson
Keyword(s):  
The Other ◽  
Constitutional Theory ◽  
Test Case ◽  
Divine Revelation ◽  
Original Intent ◽  
Ten Commandments ◽  
Legal Innovation ◽  
Normative Statement ◽  
The One ◽  
Individual Accountability

Abstract Contemporary constitutional theory remains divided between competing approaches to the interpretation of normative texts: between originalism or original intent, on the one hand, and living constitution approaches, on the other. The purpose of this article is to complicate that problematic dichotomy by showing how cultures having a tradition of prestigious or authoritative texts addressed the problem of literary and legal innovation in antiquity. The study begins with cuneiform law from Mesopotamia and the Hittite Empire, and then shows how ancient Israel’s development of the idea of divine revelation of law creates a cluster of constraints that would be expected to impede legal revision or amendment. The well-known Decalogue, or Ten Commandments, provides a valuable test-case, with its normative statement that God punishes sinners across generations (vicariously extending the punishment due them to three or four generations of their progeny). A series of inner-biblical and post-biblical responses to that rule demonstrates, however, that later writers were able to criticize, challenge, reject, and replace it with the alternative notion of individual accountability. The article will provide a series of close readings of the texts involved, drawing attention to their legal language and hermeneutical strategies. The conclusions stress the remarkable freedom to modify ostensibly normative statements available to ancient judicial interpreters, despite the expected constraints of a formative religious canon attributed to divine revelation.

De Analfabetische Blik en de Geletterde Bril

2002 ◽  
Vol 68 ◽  
pp. 9-26 ◽  
Author(s):  
Jeanne Kurvers
Keyword(s):  
Young Children ◽  
Metalinguistic Awareness ◽  
Test Case ◽  
Writing Systems ◽  
Adult Readers ◽  
Research Project ◽  
Language Analysis ◽  
The One ◽  
Low Educated ◽  
Metalinguistic Knowledge

Until recently, studies about adults' metalinguistic knowledge nearly always dealt with adult readers. Since explanations about the development of children's metalinguistic knowledge are not conclusive about the influence of either (language) development or experience with written language. Adult illiterates form a nice test case for these contrasting hypotheses, since they are both experienced language users and inexperienced in the written code. Therefore, a research project was carried out to compare the metalinguistic knowledge of adult illiterates with another group of non-readers (young children) and with low-educated adult readers. The research project was carried out with 24 young pre-readers, 25 adult (true) illiterates and 23 adult readers with about four years of schooling. All groups were offered different tests of metalinguistic awareness on the phonological, lexical/semantic and discourse-level of language. Analysis of variance and posthoc analyses showed that, on the whole, there were hardly any differences between young children and all adults in the knowledge of linguistic entities (favouring the developmental hypotheses) while there were many significant differences between the no-nreaders on the one hand (both children and adults) and low-educated literates on the other hand. It is concluded that experience with writing systems plays a major role in triggering metalinguistic knowledge.

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