Stochastic modeling of length of day and universal time

We propose a general stochastic model for the UT1/LOD system and derive the corresponding Kalman filter model. This stochastic model consists of an arbitrary sum of continous time autoregressive moving average (ARMA) processes, each chosen to characterize a different frequency band. The transition matrix which corresponds to the overall system and the time-dependent process noise covariance matrix are derived.Based on the general formulation, several models for UT1 were derived from spectral analysis of the Space 92 UT1 series (Gross,1993). Using Space 92 as the reference series, the candidate models were compared based on their ability to predict UT1 and LOD up to 30 days in the absence of data. These candidate models were compared with the JPL operational Kalman Earth Orientation Filter (KEOF) which assumes a random walk model for LOD (Morabito et al.,1987). The results of the comparison revealed that autoregressive modeling the 40–50 day oscillation in the LOD reduces the LOD prediction error by 10prediction.