GPS-only Gravity Field Recovery with GOCE, CHAMP, and GRACE
Precise orbit determination (POD) of Low Earth Orbiters (LEOs) using GPS data is required to solve for the long-wavelength part of the Earth's gravity field. This is evident for missions uniquely relying on the GPS tracking technique such as the past gravity mission CHAMP. GPS-based POD is also important for the recently terminated gravity mission GOCE, where the low-degree coefficients of GOCE-only gravity field solutions are exclusively determined from GPS data, because the measurements of the core instrument, the three axis gravity gradiometer, are band-limited. As positions of low Earth orbiters (LEOs) may be determined from GPS measurements at each observation epoch by geometric means only, it is attractive to derive such kinematic positions in a first step and to use them in a second step as pseudo-observations for gravity field determination. The drawback of not directly using the original GPS measurements is, however, that kinematic positions are correlated due to the ambiguities in the GPS carrier phase observations, which in principle requires covariance information be taken into account over several epochs. The impact of covariance information on orbit reconstruction and gravity field recovery was studied by Jäggi et al. (2011a) to eventually compare GPS-only gravity field recovery from CHAMP, GRACE, and GOCE (Jäggi et al., 2011b).
The 1-sec kinematic positions of the GOCE satellite were used to generate gravity field solutions up to degree and order 120. Figure 1 shows geoid height differences of bi-monthly solutions covering November–December of the years 2009, 2010, 2011, 2012 with respect to ITG-GRACE2010. A Gaussian filter with a radius of 300km is adopted to focus on the long- to medium-wavelength part of the differences. Figure 1 clearly reveals that all four bi-monthly solutions are prone to systematic errors centered along the geomagnetic equator. Barely visible in 2009, the size of the systematic errors is increasing over the years with a maximum impact on the bi-monthly solution from 2011, where maximum geoid height differences reach peak values of 20 cm. Due to their systematic nature the errors are not reduced by accumulating longer data series but become more pronounced.
In order to better confine the origin for the systematic errors around the geomagnetic equator the ionosphere-free GPS carrier phase residuals of the orbit determination may be averaged at the ionosphere piercing point of the corresponding observation directions. Figure 2 (left) shows the averaged residuals for of the November–December period of the year 2011 when modeling the higher order ionospheric (HOI) correction terms as recommended by the IERS 2010 conventions. Since the systematics are still clearly visible, they are not caused by the HOI terms or, more precisely, that they cannot be eliminated or significantly reduced by the current HOI model implementation.
Jäggi et al. (2015) related the systematic errors to large ionosphere changes, which may be extracted by analyzing epoch differences of the geometry-free linear combination Figure 2 (right) shows for the November–December period of the year 2011 that the systematics can be largely eliminated by discarding measurements with ionosphere changes larger than 5 cm/s. Despite the exclusion of all observations related to large ionosphere changes, this merely corresponds to 94.4% of the total set of available GPS observations. On average 93.8% of the kinematic positions can still be determined, which implies a small reduction of about 6.2% for the set of kinematic positions used for gravity field recovery. For the time span of days 300–365 in the years 2009, 2010, and the 2012, the reduction is even significantly smaller, amounting to 0.1%, 0.2%, and, 3.7%, respectively. A clear reduction of the systematic errors was also observed in gravity field solutions by Jäggi et al. (2015) when using the improved set of kinematic positions.
Jäggi, A., Prange, L., Hugentobler, U. (2011a): Impact of covariance information of kinematic positions on orbit reconstruction and gravity field recovery. Advances in Space Research, 47(9): 1472-1479, doi: 10.1016/j.asr.2010.12.009.
Jäggi, A., Bock, H., Prange, L., Meyer, U., Beutler, G. (2011b). GPS-only gravity field recovery with GOCE, CHAMP, and GRACE. Advances in Space Research, 47(6): 1020-1028, doi: 10.1016/j.asr.2010.11.008.
Jäggi, A., Bock, H., Meyer, U., Beutler, G.,van den Ijssel, J. (2015): GOCE: assessment of GPS-only gravity field determination. Journal of Geodesy, 89(1): 33-48, doi: 10.1007/s00190-014-0759-z.