A critical discussion on parametric and nonparametric regression methods applied to Hipparcos-FK5 residuals

López

2013

A&A

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Context. The International Astronomical Union (IAU) recommendations regarding the International Celestial Reference Frame (ICRF) realizations require the construction of radio sources catalogs obtained using very-long-baseline interferometry (VLBI) methods. The improvement of these catalogs is a necessary procedure for the further densification of the ICRF over the celestial sphere. Aims. The different positions obtained from several catalogs using common sources to the ICRF make it necessary to critically revise the different methods employed in improving the ICRF from several radio sources catalogs. In this sense, a revision of the analytical and the statistical methods is necessary in line with their advantages and disadvantages. We have a double goal: first, we propose an adequate treatment of the residual of several catalogs to obtain a homogeneous catalog; second, we attempt to discern whether a combined catalog is homogeneous. Methods. We define homogeneity as applied to our problem in a dual sense: the first deals with the spatial distribution of the data over the celestial sphere. The second has a statistical meaning, as we consider that homogeneity exists when the residual between a given catalog and the ICRF behaves as a unimodal pure Gaussian. We use a nonparametrical method, which enables us to homogeneously extend the statistical properties of the residual over the entire sphere. This intermediate adjustment allows for subsequent computation of the coefficients for any parametrical adjustment model that has a higher accuracy and greater stability, and it prevents problems related with direct adjustments using the models. On the other hand, the homogeneity of the residuals in a catalog is tested using different weights. Our procedure also serves to propose the most suitable weights to maintain homogeneity in the final results. We perform a test using the ICRF-Ext2, JPL, and USNO quasar catalogs. Results. We show that a combination of catalogs can only be homogeneous if we configure the weights carefully. In addition, we provide a procedure to detect inhomogeneities, which could introduce deformities, in these combined catalogs.Conclusions. An inappropriate use of analytical adjustment methods provides erroneous results. Analogously, it is not possible to obtain homogeneous-combined catalogs unless we use the adequate weights.

“…b) Rotation plus deformation model: the vector field of the residuals may be developed in vectorial spherical harmonics using first order truncation; see Marco (2004a).…”

Section: Parametrical Regression Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Homogenization in compiling ICRF combined catalogs

López

2013

A&A

Self Cite

“…Equivalently, orthogonality is not preserved when we go from the theoretic-continuous case to the practical-discrete) and inefficient (if a higher order of development is needed, all the coefficients of lower order must be recomputed). See, for example, [8,14]. We consider these topics in Section 3.…”

Section: Hipparcos-ucac4mentioning

confidence: 99%

“…It is necessary to highlight that this catalogue contains approximately 118000 visible wavelengths stars. In order to assure the continuity of the Celestial Reference Systems, different authors have carried out the study of the relations between HCRF and the FK5 (see [3][4][5]8] among others).…”

Section: Introductionmentioning

confidence: 99%

Fixed Point Method to Analyze Differences between Hipparcos and ICRF2

Abstract and Applied Analysis

Ortí

2014

From 1998, the International Astronomical Union (IAU) adopted a new Celestial Reference System: the International Celestial Reference System (ICRS). The first optical materialization was the Hipparcos catalogue, defining the Hipparcos Celestial Reference Frame (HCRF). The compilation of subsequent radio sources catalogues culminated in the current representation of the ICRF, the ICRF2 catalogue that is not sufficiently dense to cover all astrometrical purposes. Linking Hipparcos and ICRF2 is essential to uniformize the reference regardless of whether it is visible (HCRF) or not (ICRF). Many working groups provide their own complementary catalogs, some of whose sources are also in the ICRF2, with different reduction processes for positions. The point is that they provide information in more than one reference for a small number of objects. Some of these projects have been used by us to study the Hipparcos-ICRF2 differences: a certain number of couples of catalogs can be interrelated using a set of parameters. With these couples, we build a closed cycle with the same ending and departure couple. The parameters obtained from each couple affect the next; thus we have an iterative process whose fixed point is the solution that stabilizes it, providing a preliminary link for Hipparcos-ICRF2.

“…See, in particular, the primary contribution of Mignard & Morando (1990) and their further update of that paper, Mignard & Klioner (2012), within the context of the Hipparcos-FK5 comparison. This issue was also studied by us in Marco et al (2004), where we truncate the VSH development up to the first order, which is enough to determine the rotational and deformation parameters. We also used VSH in the frame of ICRF in Martinez et al (2009).…”

Section: Introductionmentioning

confidence: 99%

Application of Vector Spherical Harmonics and Kernel Regression to the Computations of Omm Parameters

López

2015

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The high quality of Hipparcos data in position, proper motion, and parallax has allowed for studies about stellar kinematics with the aim of achieving a better physical understanding of our galaxy, based on accurate calculus of the Ogorodnikov-Milne model (OMM) parameters. The use of discrete least squares is the most common adjustment method, but it may lead to errors mainly because of the inhomogeneous spatial distribution of the data. We present an example of the instability of this method using the case of a function given by a linear combination of Legendre polynomials. These polynomials are basic in the use of vector spherical harmonics, which have been used to compute the OMM parameters by several authors, such as Makarov & Murphy, Mignard & Klioner, and Vityazev & Tsvetkov. To overcome the former problem, we propose the use of a mixed method (see Marco et al.) that includes the extension of the functions of residuals to any point on the celestial sphere. The goal is to be able to work with continuous variables in the calculation of the coefficients of the vector spherical harmonic developments with stability and efficiency. We apply this mixed procedure to the study of the kinematics of the stars in our Galaxy, employing the Hipparcos velocity field data to obtain the OMM parameters. Previously, we tested the method by perturbing the Vectorial Spherical Harmonics model as well as the velocity vector field.