Maximum likelihood estimates of polar motion parameters

Two estimators developed by Jeffreys (1940, 1968) are described and used in conjunction with polar-motion data to determine the frequency (Fc) and quality factor (Qc) of the Chandler wobble. Data are taken from a monthly polar-motion series, satellite laser-ranging results, and optical astrometry and intercompared for use via interpolation techniques. Maximum likelihood arguments were employed to develop the estimators, and the assumption that polar motion relates to a Gaussian random process is assessed in terms of the accuracies of the estimators. The present results agree with those from Jeffreys' earlier study but are inconsistent with the later estimator; a Monte Carlo evaluation of the estimators confirms that the 1968 method is more accurate. The later estimator method shows good performance because the Fourier coefficients derived from the data have signal/noise levels that are superior to those for an individual datum. The method is shown to be valuable for general spectral-analysis problems in which isolated peaks must be analyzed from noisy data.