Ionospheric delay is one of the main errors in precise orbit determination (POD) of Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) with satellite-borne GPS technique. Effective elimination or reduction of ionospheric delay can improve POD precision. For satellite-borne GPS dualfrequency data, the ionospheric-free linear combination is generally used to eliminate the first-order term, while igoring the influence of higher-order terms. To improve the POD precision of GRACE-FO, this paper presents an effective method to calculate higher-order ionospheric delay of GRACE-FO observation. Dualfrequency GPS receiver observation is used to calculate the total electron content on the signal propagation path. The magnetic field strength is calculated according to international geomagnetic reference field model, and the angle between the GPS signal propagation path and the geomagnetic field is calculated. Finally, the delays of second-order and third-order terms are calculated and introduced into GRACE-FO reduceddynamic POD. The effect of higher-order ionospheric delay on POD of GRACE-FO is analyzed in detail. The results show that the influence of ionospheric higher-order term on satellite-borne GPS observation is in centimeter level. The orbit precision of GRACE-FO can be improved by adding higher-order ionospheric delay, with improvement order of sub-millimeter level.
Haiyang-2C (HY-2C) is a dynamic, marine-monitoring satellite that was launched by China and is equipped with an onboard dual-frequency GPS receiver named HY2_Receiver, which was independently developed in China. HY-2C was successfully launched on 21 September 2020. Its precise orbit is an important factor for scientific research applications, especially for marine altimetry missions. The performance of the HY2_Receiver is assessed based on indicators such as the multipath effect, ionospheric delay, cycle slip and data utilization, and assessments have suggested that the receiver can be used in precise orbit determination (POD) missions involving low-Earth-orbit (LEO) satellites. In this study, satellite-borne GPS data are used for POD with a reduced-dynamic (RD) method. Phase centre offset (PCO) and phase centre variation (PCV) models of the GPS antenna are established during POD, and their influence on the accuracy of orbit determination is analysed. After using the PCO and PCV models in POD, the root mean square (RMS) of the carrier-phase residuals is around 0.008 m and the orbit overlap validation accuracy in each direction reaches approximately 0.01 m. Compared with the precise science orbit (PSO) provided by the Centre National d’Etudes Spatiales (CNES), the RD orbit accuracy of HY-2C in the radial (R) direction reaches 0.01 m. The accuracy of satellite laser ranging (SLR) range validation is better than 0.03 m. Additionally, a new method is proposed to verify the accuracy of the RD orbit of HY-2C by using space-borne Doppler orbitography and radiopositioning integrated by satellite (DORIS) data directly. DORIS data are directly compared to the result calculated using the accurate coordinates of beacons and the RD orbit, and the results indicate that the external validation of HY-2C RD orbit has a range rate accuracy of within 0.0063 m/s.
As the first in-orbit formation satellites equipped with a Laser Ranging Interferometer (LRI) instrument, Gravity Recovery and Climate Experiment Follow-on (GRACE-FO) satellites are designed to evaluate the effective ability of the new LRI ranging system applied to satellite-to-satellite tracking. To evaluate the application of LRI in GRACE-FO, a relative kinematic orbit determination scheme for formation satellites integrating Kalman filters and GPS/LRI is proposed. The observation equation is constructed by combining LRI and spaceborne GPS data, and the intersatellite baselines of GRACE-FO formation satellites are calculated with Kalman filters. The combination of GPS and LRI techniques can limit the influence of GPS observation errors and improve the stability of orbit determination of the GRACE-FO satellites formation. The linearization of the GPS/LRI observation model and the process of the GPS/LRI relative kinematic orbit determination are provided. Relative kinematic orbit determination is verified by actual GPS/LRI data of GRACE-FO-A and GRACE-FO-B satellites. The quality of relative kinematic orbit determination is evaluated by reference orbit check and K-Band Ranging (KBR) check. The result of the reference orbit check indicates that the accuracy of GRACE-FO relative kinematic orbit determination along X, Y, and Z (components of the baseline vector) directions is` better than 2.9 cm. Compared with the relative kinematic orbit determination by GPS only, GPS/LRI improves the accuracy of the relative kinematic orbit determination by approximately 1cm along with X, Y and Z directions, and by about 1.8 cm in 3D directions. The overall accuracy of relative kinematic orbit determination is improved by 25.9%. The result of the KBR check indicates that the accuracy of the intersatellite baseline determination is about +/−10.7 mm.
Cycle slip detection and repair play important roles in the processing of data from dual-frequency GPS receivers onboard low-Earth orbit (LEO) satellites. To detect and repair cycle slips more comprehensively, an enhanced error method (EEM) is proposed. EEM combines single-frequency and narrow-lane carrier phase observations to construct special observations and observation equation groups. These special observations differ across time and satellite (ATS). ATS observations are constructed by three steps. The first step is differencing single-frequency and narrow-lane observations through a time difference (TD). The second step is to select a satellite as a reference satellite and other satellites as nonreference satellites. The third step is to difference the single-frequency TD observations from the reference satellite and the narrow-lane TD observations from the nonreference satellites by a satellite difference. If cycle slips occur at the reference satellite, the correction values for these ATS observations can be significantly enlarged. To process all satellites, the EEM selects each satellite as a reference satellite and builds the corresponding equation group. The EEM solves these observation equation groups according to the weighted least-squares adjustment (LSA) criterion and obtains the correction values; these correction values are then used to construct the χ 2 values corresponding to different equation groups, and the EEM subsequently carries out a chi-square distribution test for these χ 2 . The satellite corresponding to the maximum χ 2 will be marked. Then, the EEM iteratively processes the other satellites. Cycle slips can be estimated by rounding the float solutions of changes in the ambiguities of cycle slip satellites to the nearest integer. The simulation test results show that the EEM can be used to detect special cycle slip pairs such as (1, 1) and (9, 7). The EEM needs only observation data in two adjacent epochs and is still applicable to observation epochs with continuous cycle slips.
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