According to the precise ephemeris has only provided satellite position that is discrete not any time, so propose that make use of interpolation method to calculate satellite position at any time. The essay take advantage of IGS precise ephemeris data to calculate satellite position at some time by using Lagrange interpolation, Newton interpolation, Hermite interpolation, Cubic spline interpolation method, Chebyshev fitting method respectively, which has a deeply analysis in the precision of five interpolations. The results show that the precision of Cubic spline interpolation method is the worst, the precision of Chebyshev fitting is better than Hermite interpolation method. Lagrange interpolation and Newton interpolation are better than other methods in precision. Newton interpolation method has the advantages of high speed and high precision. Therefore, Newton interpolation method has a certain scientific significance and practical value to get the position of the satellite quickly and accurately.

Real-Time Precise Orbit Determination (RTPOD) of Low Earth Orbit (LEO) satellites relies primarily on onboard GNSS observations and may suffer from degraded performance when observation geometry weakens or tracking conditions deteriorate within satellite formations. To enhance the robustness and accuracy of RTPOD under such conditions, a cooperative Extended Kalman Filter (EKF) framework that fuses onboard GNSS and inter-satellite link (ISL) range measurements is established, integrated with an iterative Detection, Identification, and Adaptation (DIA) quality control algorithm. By introducing high-precision ISL range measurements, the strategy increases observation redundancy, improves the effective observation geometry, and provides strong relative position constraints among LEO satellites. This constraint strengthens solution stability and convergence, while simultaneously enhancing the sensitivity of the DIA-based quality control to observation outliers. The proposed strategy is validated in a simulated real-time environment using Centre National d’Etudes Spatiales (CNES) real-time products and onboard observations of the GRACE-FO mission. The results demonstrate comprehensive performance enhancements for both satellites over the experimental period. For the GRACE-D satellite, which suffers from about 17% data loss and a cycle slip ratio several times higher than that of GRACE-C, the mean orbit accuracy improves by 39% (from 13.1 cm to 8.0 cm), and the average convergence time is shortened by 44.3%. In comparison, the GRACE-C satellite achieves a 4.2% mean accuracy refinement and a 1.3% reduction in convergence time. These findings reveal a cooperative stabilization mechanism, where the high-precision spatiotemporal reference is transferred from the robust node to the degraded node via inter-satellite range measurements. This study demonstrates the effectiveness of the proposed method in enhancing the robustness and stability of formation orbit determination and provides algorithmic validation for future RTPOD of LEO satellite formations or large-scale constellations.

With the application and promotion of space geodesy, the popularization of remote sensing technology, and the development of artificial intelligence, a more accurate and stable Terrestrial Reference Frame (TRF) has become more urgent. For example, sea level change detection, crustal deformation monitoring, and driverless cars, among others, require the accuracy of the terrestrial reference frame to be better than 1 mm in positioning and 0.1 mm/a in velocity, respectively. However, the current frequently used ITRF2014 and ITRF2020 do not satisfy such requirements. Therefore, this paper analyzes the coordinate residual time series data of linear TRFs and finds there are still some unlabeled jumps and time-dependent periodic signals, especially in the GNSS coordinate residuals, which can lead to incorrect station epoch coordinates and velocities, further affecting the accuracy and stability of the TRF. The unlabeled jumps could be detected by the sequential t-test analysis of regime shifts (STARS) combined with the generalized extreme Studentized deviate (GESD) algorithms introduced in our earlier paper. These nonlinear time-dependent periodic signals could be modeled better by singular spectrum analysis (SSA) with respect to least squares fitting; the fitting period is no longer composed of semi-annual and annual items, as with ITRF2014. The periods of continuous coordinate residual time series data longer than 5 years are obtained by FFT. The results show that there are no period signals for individual SLR/VLBI sites, and there are still other period terms, such as 34 weeks, 20.8 weeks and 17.3 weeks, in addition to semi-annual and annual items for some GNSS sites. Moreover, after SSA corrections, the re-calculated TRF and the corresponding EOP could be obtained, based on data from the Chinese Earth Rotation and Reference System Service (CERS) TRF and the Earth Orientation Parameter (EOPs) multi-technique determination software package (CERS TRF&EOP V2.0) developed by the Shanghai Astronomical Observatory (SHAO). Their accuracy could be evaluated with respect to the ITRF2014 and the IERS 14 C04, respectively. The results show that the accuracy and stability of the newly established a nonlinear TRF and EOP based on SSA have been greatly improved and better than a linear TRF and EOP. SSA is better than least squares fitting, especially for those coordinate residual time series with varying amplitude and phase. For GPS, comparing with the ITRF2014, the station coordinate accuracy of 10.8% is better than 1 mm, and the station velocity accuracy of 4.4% is better than 0.1 mm/year. There are 3.1% VLBI stations, for which coordinate accuracy is better than 1 mm and velocity accuracy is better than 0.1 mm/year. However, there are no stations with coordinates and velocities better than 1 mm and 0.1 mm/year for the SLR and DORIS. The WRMS values of polar motion x, polar motion y, LOD, and UT1-UTC are reduced by 2.4%, 3.2%, 2.7%, and 0.96%, respectively. The EOP’s accuracy in SOL-B, in addition to LOD, is better than that of the JPL.