Impacts on Noise Analyses of GNSS Position Time Series Caused by Seasonal Signal, Weight Matrix, Offset, and Helmert Transformation Parameters

Abstract

The noise characteristics of the Global Navigation Satellite System (GNSS) position time series can be biased by many factors, which in turn affect the estimates of parameters in the deterministic model using a least squares method. The authors assess the effects of seasonal signals, weight matrix, intermittent offsets, and Helmert transformation parameters on the noise analyses. Different solutions are obtained using the simulated and real position time series of 647 global stations and power law noise derived from the residuals of stacking solutions are compared. Since the true noise in the position time series is not available except for the simulated data, the authors paid most attention to the noise difference caused by the variable factors. First, parameterization of seasonal signals in the time series can reduce the colored noise and cause the spectral indexes to be closer to zero (much “whiter”). Meanwhile, the additional offset parameters can also change the colored noise to be much “whiter” and more offsets parameters in the deterministic model leading to spectral indexes closer to zero. Second, the weight matrices derived from the covariance information can induce more colored noise than the unit weight matrix for both real and simulated data, and larger biases of annual amplitude of simulated data are attributed to the covariance information. Third, the Helmert transformation parameters (three translation, three rotation, and one scale) considered in the model show the largest impacts on the power law noise (medians of 0.4 mm−k/4 and 0.06 for the amplitude and spectral index, respectively). Finally, the transformation parameters and full-weight matrix used together in the stacking model can induce different patterns for the horizontal and vertical components, respectively, which are related to different dominant factors.

Chameleonic Noise in GPS Position Time Series

“…These results are considerably different to those recently obtained by Chen et al. (2018) who reported PL amplitude changes at least two times larger, while still considering they used daily series instead of weekly as in our case. They noted a clear spatial dependence of the PL changes, with the largest PL reduction in areas of high density of stations and a PL increase elsewhere.…”

“…These results confirm the more limited observations recently made by Chen et al. (2018). These authors considered changes in the estimated PL noise amplitude and spectral index as offsets were added to synthetic series of different length.…”

“…Nonetheless, AnR1 asserts that this, our core finding, "is not anything new" even though this phenomenon is never mentioned by WH19 and it rules out any practical utilization of the WH19 approach using real data with offsets. We found only one prior study of the noise "whitening" effect of adding position offset parameters, the simulation by Chen et al (2018). Position offsets were one of several analysis options they examined, obtaining median impacts consistent with ours but with more limited insight into the underlying dynamics of the problem, which is our prime interest here.…”

“…Since Chen et al. (2018) used the full IGS network to compute the transformation parameters, their result reflects a network effect, that is, the transfer of common‐mode PL noise between different areas of the network. Such a strong network effect was demonstrated by Ray et al.…”

“…We found only one prior study of the noise “whitening” effect of adding position offset parameters, the simulation by Chen et al. (2018). Position offsets were one of several analysis options they examined, obtaining median impacts consistent with ours but with more limited insight into the underlying dynamics of the problem, which is our prime interest here.…”