Overview of site-specific errors

The GPS antenna receives signals at different locations, depending on the direction and intensity of the incoming signals. The location of a phase measurement at the antenna is determined by both the physical design and complex-valued gain pattern of the antenna. The measurement location of signals from different azimuths and elevation angles is not generally an ideal sphere, but rather forms an inhomogeneous shape (Figure 3.8). The mean electromagnetic phase centre of the antenna is a virtual point that is generally referred to as the antenna phase centre (APC). By definition, the antenna reference point (ARP) of a GPS receiver is where the vertical physical axis of the antenna intersects the lowest point of the antenna. The offset between APC and ARP is defined as the phase centre offset (PCO). In practice, the actual phase centre differs from the APC, depending on the elevation angle, azimuth and frequency of the arriving signal. The differences between the actual phase centres and APC are called phase centre variations (PCV).

In GPS analysis, both PCO and PCV should be taken into account for the ob- servations. The PCO and PCV are usually determined using absolute calibration techniques [e.g. Wübbena et al., 1997; Bilich and Mader, 2010]., and the mean val- ues of PCO and PCV are provided in the IGS antenna files [Schmid et al., 2016]. The corrections provided by the IGS are the mean values for antenna/radome types; how- ever, different individual antennas of the same type may show different behaviours depending on the manufacturing conditions. It has been shown previously that indi- vidual calibration of the antennas can have significant impacts of up to 1 cm on the height estimates and smaller but still significant impacts on horizontal positions [e.g. Baire et al., 2014]. In addition to the differences in the antennas of the same types, the difference in the environment of where a calibration is performed and where the antenna is mounted to observe signals leads to errors in the modelling of PCO and

Antenna Reference Point (ARP) Antenna Phase Centre (APC)

Phase Centre Offset (PCO)

Phase Centre Variations (PCV)

Figure 3.8: Schematic diagram for antenna characteristics (adapted from Seeber [2003]).

PCV. The pillar on which the antenna is mounted also plays a role in introducing errors into the antenna PCV and PCO by scattering the electromagnetic field trans- mitted by the antenna. Depending on the properties of the pillar, the signal scattering changes the amplitude and phase of the GPS signal received by the antenna [Moore, 2015].

A radome is an enclosing structure that covers a GPS antenna to protect it from the surrounding environment (e.g. snow or animals). A radome is designed to cause minimum attenuation in the radio frequency waves. In practice, however, they intro- duce alterations to the antenna phase patterns as a result of several effects. The GPS signal is distorted when propagating through the dielectric wall of the radome, which leads to a bending in the angle of the signal arrived (boresight error). The curvature in the radome wall may cause folding of the antenna energy from its original polar- isation. Once the GPS signal arrives at the radome wall, part of it is reflected, thus causing a loss in signal strength. The signal strength is also lost when it propagates through the dielectric wall of the radome. Moore [2015] showed that an unmodelled radome results in a bias to the estimate of height of up to 2.5 cm for a signal ar- riving at an elevation angle of 10◦. Kaniuth and Huber [2003] showed that the GPS heights are underestimated by up to several centimetres when a radome is mounted around the GPS antenna, and that the effect is dependent on the elevation cut-off angle. By comparing the tropospheric zenith delay estimates between the solutions with different elevation cut-off angles, they also argued that the dependency of the radome effect on height parameter is also reflected in the tropospheric zenith delays. However, since they did not include large baselines in their solutions, they did not discuss the impact of the radome on the absolute tropospheric delay estimates.

3.2.1.2 Multipath error

Multipath is the effect in which the signal transmitted by the satellite is reflected by the environment around the receiver and thus arrives at the receiver via more than one path. Phase multipath errors can reach 1/4 cycle of the phase, and increase for linear combinations of the phase. The multipath error can be as high as about 22 cm for the phase ionosphere-free combination [e.g. Hofmann et al., 2001; Seeber, 2003; Moore, 2015]. A GPS satellite is visible by a receiver on the ground with a period slightly less than one sidereal day (on average for all the GPS satellites, 23 hours, 55 minutes and 53 seconds) [Agnew and Larson, 2007]. Therefore, multipath errors, which are mainly dependent on the observation geometry, have an almost sidereal periodicity [Bock, 1991; Choi et al., 2004]. As a result, unmodelled multipath effects can be aliased into other estimation parameters at the "GPS year", the required time for the satellite to repeat its inertial orientation with respect to the sun (about 351.2 days), and its harmonics [Ray et al., 2008].

Several pieces of research have been performed to investigate and/or reduce the effects of multipath, which are nicely summarized in Moore et al. [2014]. These works include ray-tracing approaches to model the environment around an antenna (the satellite-reflector-antenna geometry) [Byun et al., 2002; Lau and Cross, 2007], us- ing the spectral content of signal to noise ratio (SNR) to map the contributions of the different satellites to the multipath errors [Bilich and Larson, 2007], calibration of the near-field multipath during the estimation of PCV [Wübbena et al., 2006; Dilssner et al., 2001], calibration of far-field multipath by using a local network of temporary stations [Wübbena et al., 2011], prediction of the multipath using the sidereal peri- odicity of GPS satellites [Choi et al., 2004], and derivation of a day-to-day correlated multipath correction model by statistical analysis of carrier-phase residuals [Wu and Hsieh, 2010]. Another technique for mitigating the multipath errors, which we use in this thesis, is to use stacks of one-way (undifferenced) phase residuals from the historical datasets for each station to generate a site-specific correction map. This em- pirical technique helps to map not only the multipath effect, but also antenna phase centre and radome modelling deficiencies and any other site-specific effects.