Fast Statistical Approaches To Geodetic Time Series Analysis

We present fast algorithms for estimating common parameters in geodetic time series based on statistical approaches to assess the impact of temporal correlations. One such assessment is based on the characteristics of the time series residuals averaged over different durations and with the statistical characteristics extrapolated with a first-order Gauss-Markov process to infinite averaging time. This approach circumvents a limitation of spectral methods, which cannot reliably account for the impact of temporal correlations over periods longer than the length of a given time series. The subsequent fast approach is the use of a Kalman filter with process noise values determined from the first-order Gauss-Markov characteristics to estimate all parameters. These methods are particularly useful for assessing long and numerous geodetic time series, which are nowadays ubiquitous, because they are much less computationally intensive than comprehensive methods, such as maximum likelihood estimators. Our approaches are compared to other commonly used programs, such as Hector, to understand the speed and impact of outliers on the algorithms, and to provide advice and suggestions on the uses of such algorithms in operational geodetic processing.