M. J. Martínez

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

In this paper we present an analysis of the differences between the Hipparcos and FK5 catalogues. We study parametric and nonparametric methods with two main objectives: first, to determine whether or not there is a pure rotation between the two catalogues, and to decide which model best represents the residuals; second, to give a practical formulation to reduce positions between the two systems at any point on the celestial sphere.

Homogenization in compiling ICRF combined catalogs

Part of this work was supported by a grant P1-1B2009-07 from Fundacio Caixa Castello BANCAIXA and a grant P1-061I455.01/1 from Bancaja.

Accurate Analytical and Statistical Approaches to Reduce O-C Discrepancies in the Precessional Parameters

The Hipparcos catalog provides a reference frame at optical wavelengths for the new International Celestial Reference System (ICRS). This new reference system was adopted following the resolution agreed at the 23rd IAU General Assembly held in Kyoto in 1997. Differences in the Hipparcos system of proper motions and the previous materialization of the reference frame, the FK5, are expected to be caused only by the combined effects of the motion of the equinox of the FK5 and the precession of the equator and the ecliptic. Several authors have pointed out an inconsistency between the differences in proper motion of the Hipparcos-FK5 and the correction of the precessional values derived from VLBI and lunar laser ranging (LLR) observations. Most of them have claimed that these discrepancies are due to slightly biased proper motions in the FK5 catalog. The different mathematical models that have been employed to explain these errors have not fully accounted for the discrepancies in the correc- tion of the precessional parameters. Our goal here is to offer an explanation for this fact. We propose the use of independent parametric and nonparametric models. The introduction of a nonparametric model, combined with the inner product in the square integrable functions over the unitary sphere, would give us values which do not depend on the possible interdependencies existing in the data set. The evidence shows that zonal studies are needed. This would lead us to introduce a local nonparametric model. All these models will provide independent corrections to the precessional values, which could then be compared in order to study the reliability in each case. Finally, we obtain values for the precession corrections that are very consistent with those that are currently adopted.

APPLICATION OF VECTOR SPHERICAL HARMONICS AND KERNEL REGRESSION TO THE COMPUTATIONS OF OMM PARAMETERS

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.

ANALYSIS OF SYSTEMATIC DIFFERENCES OF ASTROMETRIC CATALOGS IN A BAND

We first establish theoretical arguments that give consistency to a method of homogenization for astrometric catalogs that may be applied to domains other than the usual complete sphere. The work domain consists of bands having a constant width and containing a great circle. The proposed adjustment requires prescribed values on these band boundaries that are subject to uncertainties, so it is desirable that the adjustment depend as little as possible on these uncertainties. We then solve this problem in the case of a band containing any great circle, for which it is necessary to determine a new functional basis in order to expand the systematic differences in spherical coordinates.

A Statistical Approach to Determine the Values of the Correction for the Precession

The Hipparcos catalogue [1] provides a reference frame at optical wavelengths for the new ICRS. The adoption of this new reference system was decided following a resolution that was agreed at the 23rd IAU assembly held in Kyoto in 1997. Differences in the Hipparcos system of proper motions and the previous materialization of the reference frame, the FK5, are expected to be caused only by the combined effects of the motion of the equinox of the FK5 and the Luni‐solar and planetary precession. Several authors have, however, pointed out an inconsistency in the differences in proper motion of the FK5‐Hipparcos with the Δp of the Luni‐solar precession as determined from VLBI and LLR, and most of them have claimed that these discrepancies are due to slightly biased proper motions in the FK5 catalogue [3], [5].The different mathematical models employed to explain these errors have not completely accounted for the previous discrepancies in the precessional parameters. Our goal is to offer an explanation for this ...

A Numerical Method for the Dynamical Correction of Celestial Reference Frames from Non-Regular Samples

The aim of this paper is to analyze the orientation errors of a celestial reference system. These errors can be obtained by analyzing the differences between the observed and calculated positions for a set of selected minor planets. The classical methods do not work well if the sample is non-homogeneous on the region covered by the observations. In this paper a new algorithm based on a new class of spatial estimators and an appropriate reconstruction operator is proposed.