The empirical Earth rotation model from VLBI observations^*

National Astronomical Observatory of Japan, Mizusawa, 2-12, Hoshigaoka-cho, Mizusawa-ku, Oshu-shi, Iwate-ken, 023-0861, Japan e-mail: leonid.petrov@lpetrov.net

Received: 25 February 2006
Accepted: 13 December 2006

Abstract

Aims.An alternative to the traditional method for modeling the kinematics of the Earth's rotation is proposed. The purpose of developing the new approach is to provide a self-consistent and simple description of the Earth's rotation in a way that can be estimated directly from observations without using intermediate quantities.

Methods.Instead of estimating the time series of pole coordinates, the UT1–TAI angles, their rates, and the daily offsets of nutation, the method for estimating coefficients of the expansion of a small perturbational rotation vector into basis functions is proposed. The resulting transformation from the terrestrial coordinate system to the celestial coordinate system is formulated as the product of the a priori matrix of a finite rotation and an empirical vector of a residual perturbational rotation. In the framework of this approach, the specific choice of the a priori matrix is irrelevant, provided the angles of the residual rotation are small enough to neglect their squares. The coefficients of the expansion into the B-spline and Fourier bases, together with estimates of other nuisance parameters, are evaluated directly from observations of time delay or time range in a single least square solution.

Results.This approach was successfully implemented in a computer program for processing VLBI observations. The dataset from 1984 through 2006 was analyzed. The new procedure adequately represents the Earth's rotation, including slowly varying changes in UT1–TAI and polar motion, the forced nutations, the free core nutation, and the high frequency variations of polar motion and UT1.