On Application of the Kalman Filter and the Least Squares Collocation in Earth Rotation Investigations1

Geophysical processes which excite variations in the orientation of the Earth have an irregular nature therefore a stochastic approach to the description of Earth rotation seems to be the most appropriate. We describe here a simple stochastic model for the Chandler wobble, originally proposed by Jeereys (1940), then prove its advantage over the sinusoidal modeling by performing the goodness-of-t statistical test. On the basis of this model two kinds of techniques may be elaborated for smoothing, combining, and prediction of polar motion series, namely the least squares collocation (LSC) and the Kalman lter (KF). The paper contains a summary of comparison of these two methods. 1. STOCHASTIC MODEL FOR THE CHANDLER WOBBLE A number of diierent approaches can be developed in the frame of the stochastic modeling of Earth rotation. In the present paper the LSC and the KF are both considered as based on a stochastic model for the Chandler wobble derived directly from the dynamical equation of polar motion. Let us denote by p = (x y) T the terrestrial location of the Celestial Ephemeris Pole (CEP), x-axis being in the direction of the International Earth Rotation Service (IERS) Reference Meridian and y-axis being in the direction 90 E longitude. Then geophysical perturbations of the CEP may be described by the following linear diierential equation (Brzezi nski, 1992) _ p = ?! c 1=2Q c 1 ?1 1=2Q c p + ! c 1=2Q c 1 ?1 1=2Q c x; where ! c and Q c are the frequency and the quality factor of the Chandler wobble and x = (1 2) T is the equatorial eeective angular momentum function expressing excitation processes. Let us assume that the Chandler wobble is driven by the isotropic zero-mean white noise process x with spectral density matrix S c I, where I is the 2 2 unit matrix. The 1 Published in Capitaine N. et al.