On the performance of position-domain sidereal filter for 30-sec kinematic GPS to mitigate multipath errors

Yuji Itoh and Yosuke Aoki (Earthquake Research Institute, The University of Tokyo)
Earth, Planets and Space (2022) 74:23 https://doi.org/10.1186/s40623-022-01584-8

 GPS coordinates of everywhere on the ground and its temporal change (i.e., northward, eastward, and upward motion of the ground) have been widely used to identify crustal deformation associated with earthquake and volcano activities. Daily coordinates (e.g., F5 solution of GSI, Japan) have been used in most cases, but we can obtain coordinates at a much finer interval (e.g., 1 or 30 seconds). Subdaily coordinates produced by the kinematic GPS analysis play a crucial role in capturing crustal deformation during great earthquakes and volcano eruptions as well as fast transient deformation following them in detail. However, their precision is a few to several centimeters, which has been considered difficult to capture sub-centimeter deformation. One of the major positioning error sources is multipath. GPS determines the position of ground sites by measuring the distance between multiple satellites and the site on the ground using carrier-wave radiated from GPS satellites. However, on the ground, we always record the direct wave as well as the detoured wave due to the reflection on the ground, building and trees simultaneously, which is called multipath. The multipath effects depend on the geometrical relationship between the satellites, the ground observation site, and reflection bodies around it, so it can be mitigated by taking the temporal difference of coordinates, which is called sidereal filter. For the future application of the kinematic GPS to capturing small crustal deformation, this study investigates characteristics of multipath and performance of sidereal filter by employing an environment mostly free from atmospheric delay, which is another major positioning error source.
 Our analysis of correlation coefficient from two data set recorded during different time periods demonstrates that multipath yield periodic coordinate fluctuations with a period from 500 to 100,000 seconds while fluctuation at the shorter period does not well repeat over the time. By applying the sidereal filter, the coordinate fluctuations at the long period are highly mitigated (See the left and center panels of Figure). Furthermore, removal of short-period fluctuation from a sidereal filter slightly improved reduction of coordinate fluctuation and avoided lift of power spectrum density at the shorted period. Coordinate fluctuation after sidereal filtering is about 6 mm or below, which exhibits the nearly lowest noise level of kinematic GPS coordinates achievable by the standard analysis setting.

Figure. (left) Fluctuation of kinematic GPS coordinates drawn as color. Red color indicates the fluctuation of coordinates in the direction of north, east or up. On the other hand, blue color indicates the fluctuation of coordinates in the direction of south, west or down. Coordinates excluded from our analysis are shown as drawn by green. Top, middle, and bottom rows indicate results with different baselines (i.e., pair of two sites). Left, center and right columns indicate north, east, and up components. We expect that these plots are drawn by white uniformly because the length of the baselines should not change over time, but actually we can see some patterns of colors due to the fluctuation of coordinates. (middle) Fluctuation of kinematic GPS coordinates after sidereal filtering drawn as color. The plots drawn with the lighter colors indicate that the coordinate fluctuation has been mitigated by sidereal filtering. (Right) Power spectrum density (PSD) before and after the sidereal filter application. Many peaks in the PSDs before the sidereal filtering at the longer period than 500 seconds (black) are mostly alleviated in the PSDs after the filtering (green and red). Meanwhile, the lift of PSDs at the shorter period than 500 seconds (green) occurred when the short-period fluctuation is not removed from the sidereal filter. Such feature is not found when the sidereal filter with the short-period fluctuation removal is used (red).