The problem in the assumption about the existing noise

The coordinate time series of the GPS stations usually show complex non-linear behaviour, and the associated noise is more complex than simple white noise. Analysis of continuous GPS time series by Mao et al. (1999) and Williams et al. (2004) has indicated that the uncertainty associated with frequency-dependent noise is mostly analogous to a combination of white and flicker noise. The complication is often related to geophysical phenomena such as offsets due to earthquakes, post-seismic transient behaviour after earthquakes, and more noise-like phenomena such as cyclic water table changes. It can also originate from offsets due to change in the receiver, antenna, or antenna radome (Herring, 2003). Other candidates to explain non-linearity in position time series may be side effects caused by the succession of GPS satellite block types (Ge et al., 2005), and contributions from higher order ionospheric terms (Kedar et al., 2003).

References

Ge, M., Gendt, G., Dick, G., Zhang, F. P., and Reigber, C. (2005). Impact of GPS satellite antenna offsets on scale changes in global network solutions. Geophysical research letters, 32(6), L06310. American Geophysical Union. doi:10.1029/2004GL022224.

Herring, T. (2003). MATLAB Tools for viewing GPS velocities and time series. GPS solutions, 7(3), 194-199. Springer.

Kedar, S., Hajj, G. A., Wilson, B. D., and Heflin, M. B. (2003). The effect of the second order GPS ionospheric correction on receiver positions. Geophysical research letters, 30(16), 1829. American Geophysical Union. doi:10.1029/2003GL017639.

Mao, A., Harrison, C. G. A., and Dixon, T. H. (1999). Noise in GPS coordinate time series. Journal of Geophysical Research, 104(B2), 2797-2816. American Geophysical Union. doi:10.1029/1998JB900033.

Williams⁠, S. D. P., Bock, Y., Fang, P., Jamason, P., Nikolaidis, R. M., Prawirodirdjo, L., Miller, M., et al. (2004). Error analysis of continuous GPS position time series. Journal of geophysical research, 109(B3), B03412. American Geophysical Union. doi:10.1029/2003JB002741.