2:15 PM - 2:30 PM
[SGD01-15] On the performance of sidereal filter for 30-sec kinematic GPS to mitigate multipath errors
Keywords:Kinematic GPS, Multipath, Sidereal filter
1. Introduction
The noise level of kinematic Global Positioning System (GPS) coordinates is much higher than that of static daily coordinates. Therefore, it needs to be improved to capture details of small sub-daily tectonic deformation. One of the dominant error sources of kinematic GPS is multipath, which is the delay of carrier-phase due to reflection on the ground and other objects around the antenna. The sidereal filter is a well-known method to mitigate multipath effects by exploiting the repeatability of the geometrical relationship between GPS constellation and reflective bodies around the antenna. Many studies have investigated the characteristics of multipath and performance of the sidereal filter, but most of them focused only on seismic frequency and ignored longer periods. Their analyses are possibly contaminated with other error sources, including atmospheric disturbances, because they usually have employed Precise Point Positioning. With the increasing interest in applying kinematic GPS to subdaily postseismic deformation studies, we investigate the characteristics of multipath errors and the performance of sidereal filter using 30-sec kinematic coordinates with a length of nearly five days in an environment mostly free from atmospheric disturbances.
2. Method
We employ the differential positioning to focus on the multipath effect as error sources. A baseline we use consists of two GNSS sites, POTS and POTM. The approximate baseline length is 3 m, short enough to cancel most atmospheric and ionospheric disturbances. We obtain kinematic coordinates between 01 January 2019 and 31 December 2019. We split the year-long time series into 430770-seconds-long blocks, an integer multiple of the sub-sidereal satellite repeat period 86154 seconds estimated by a previous study. First, we assess the repeatability of kinematic coordinates, fundamental in applying the sidereal filter, by computing the correlation coefficient between arbitrary two blocks out of 73 blocks in total. We also calculate the correlation coefficient of two blocks after lowpass filtering with several different cut-off periods between 100 and 20,000 seconds to examine if longer-period fluctuations have better temporal repeatability than shorter-period fluctuations. Next, we apply a sidereal filter by subtracting a time series of one block from its neighbor. We also employ a lowpass-filtered sidereal filter to test if the performance of the sidereal filter is improved by discarding short-period fluctuations.
3. Results and Discussion
Correlation of lowpass-filtered time series with the longer cut-off period is generally better. However, in most pairs of blocks, variance reduction by sidereal filtering is largest when applying the lowpass filter to the sidereal filter with the cut-off period of 500 seconds, not with the longest one among tested. It is because longer-period fluctuations have smaller amplitudes. We find several peaks of power spectral density (PSD) at a period between 500 and 100,000 seconds. The standard (i.e., non-lowpass-filtered) sidereal filtering efficiently mitigates them, whereas it does not mitigate but enhance PSD fluctuations with periods shorter than 500 seconds. These data analyses suggest that this short-period fluctuation of kinematic coordinates is less likely due to multipath. It is also supported by a simple multipath model from the reflection at a horizontal surface beneath the antenna. Our results recommend lowpass filtering to the sidereal filter, which previous studies have empirically done. Because the cut-off period should depend on each site's physical environment and other error sources contaminate the data, a careful design of the sidereal filter is required in its application to postseismic deformation studies.
The noise level of kinematic Global Positioning System (GPS) coordinates is much higher than that of static daily coordinates. Therefore, it needs to be improved to capture details of small sub-daily tectonic deformation. One of the dominant error sources of kinematic GPS is multipath, which is the delay of carrier-phase due to reflection on the ground and other objects around the antenna. The sidereal filter is a well-known method to mitigate multipath effects by exploiting the repeatability of the geometrical relationship between GPS constellation and reflective bodies around the antenna. Many studies have investigated the characteristics of multipath and performance of the sidereal filter, but most of them focused only on seismic frequency and ignored longer periods. Their analyses are possibly contaminated with other error sources, including atmospheric disturbances, because they usually have employed Precise Point Positioning. With the increasing interest in applying kinematic GPS to subdaily postseismic deformation studies, we investigate the characteristics of multipath errors and the performance of sidereal filter using 30-sec kinematic coordinates with a length of nearly five days in an environment mostly free from atmospheric disturbances.
2. Method
We employ the differential positioning to focus on the multipath effect as error sources. A baseline we use consists of two GNSS sites, POTS and POTM. The approximate baseline length is 3 m, short enough to cancel most atmospheric and ionospheric disturbances. We obtain kinematic coordinates between 01 January 2019 and 31 December 2019. We split the year-long time series into 430770-seconds-long blocks, an integer multiple of the sub-sidereal satellite repeat period 86154 seconds estimated by a previous study. First, we assess the repeatability of kinematic coordinates, fundamental in applying the sidereal filter, by computing the correlation coefficient between arbitrary two blocks out of 73 blocks in total. We also calculate the correlation coefficient of two blocks after lowpass filtering with several different cut-off periods between 100 and 20,000 seconds to examine if longer-period fluctuations have better temporal repeatability than shorter-period fluctuations. Next, we apply a sidereal filter by subtracting a time series of one block from its neighbor. We also employ a lowpass-filtered sidereal filter to test if the performance of the sidereal filter is improved by discarding short-period fluctuations.
3. Results and Discussion
Correlation of lowpass-filtered time series with the longer cut-off period is generally better. However, in most pairs of blocks, variance reduction by sidereal filtering is largest when applying the lowpass filter to the sidereal filter with the cut-off period of 500 seconds, not with the longest one among tested. It is because longer-period fluctuations have smaller amplitudes. We find several peaks of power spectral density (PSD) at a period between 500 and 100,000 seconds. The standard (i.e., non-lowpass-filtered) sidereal filtering efficiently mitigates them, whereas it does not mitigate but enhance PSD fluctuations with periods shorter than 500 seconds. These data analyses suggest that this short-period fluctuation of kinematic coordinates is less likely due to multipath. It is also supported by a simple multipath model from the reflection at a horizontal surface beneath the antenna. Our results recommend lowpass filtering to the sidereal filter, which previous studies have empirically done. Because the cut-off period should depend on each site's physical environment and other error sources contaminate the data, a careful design of the sidereal filter is required in its application to postseismic deformation studies.