Noise content assessment in GNSS coordinate time-series with autoregressive and heteroscedastic random errors

Proper representation of the stochastic process of the Global Navigation Satellite System (GNSS) coordinate time-series lays a foundation for realistic velocities estimates and their uncertainties, as well as identifications of functional effects, generally called periodic/offset signals. Various noise models (e.g. autoregressive process) have been used to describe the stochastic process of GNSS data. A realistic stochastic model prefers proper consideration of individual error characteristics of observations. The usual autoregressive (AR) noise model assumes its white-noise components sharing the same constant variances, which might degrade the modelling accuracy of stochastic process. Through using a generalized autoregressive conditional heteroscedasticity (GARCH) process to quantify variance variation of the white-noise components, our current investigation has constituted an AR-GARCH noise model to realize the stochastic model and subsequent noise content assessment. This noise framework and its adjustment algorithm are further considered in the identifications of functional effects. For evaluating the performance of our current algorithm, 500 emulated real time-series were used, they consist of a linear trend, seasonal periodic signals, offsets, gaps (up to 10 per cent) and an AR-GARCH noise process. The algorithm's identification power for functional effects was investigated within a case study in the absence of periodic/offset signals. Furthermore, the algorithm's results were compared with the current state-of-the-art noise models (e.g. white plus flicker noise) using 15 real GNSS coordinate time-series. The results demonstrated that the presented stochastic model has been identified as a preferred noise model. Its model's algorithm can offer reliable noise content although sporadic unidentified periodic/offset signals are still masked in time-series. Moreover, the error volatility of white-noise components was identified via an autoregressive conditional heteroscedasticity Lagrange multiplier (ARCH LM) test and confirmed in the time-series.