Evaluation of JGM 2 geopotential errors from Geosat, TOPEX/Poseidon and ERS-1 crossover altimetry

World-ocean distribution of the crossover altimetry data from Geosat, TOPEX/Poseidon (T/P) and the ERS 1 missions have provided strong independent evidence that NASA's/CSR's JGM 2 geopotential model (70 × 70 in spherical harmonics) yields accurate radial ephemerides for these satellites. In testing the sea height crossover differences found from altimetry and JGM 2 orbits for these satellites, we have used the sea height differences themselves (of ascending minus descending passes averaged at each location over many exact repeat cycles) and the Lumped Latitude Coefficients (LLC) derived from them. For Geosat we find the geopotential-induced LLC errors (exclusive of non-gravitational and initial state discrepancies) mostly below 6 cm, for TOPEX the corresponding errors are usually below 2 cm, and for ERS 1 (35-day cycle) they are generally below 5 cm. In addition, we have found that these observations agree well overall with predictions of accuracy derived from the JGM 2 variance-covariance matrix; the corresponding projected LLC errors for Geosat, T/P, and ERS 1 are usually between 1 and 4 cm, 1 – 2 cm, and 1 – 4 cm, respectively (they depend on the filtering of long-periodic perturbations and on the order of the LLC). This agreement is especially impressive for ERS 1 since no data of any kind from this mission was used in forming JGM 2.

The observed crossover differences for Geosat, T/P and ERS 1 are 8, 3, and 11 cm (rms), respectively. These observations also agree well with prediction of accuracy derived from the JGM 2 variance-covariance matrix; the corresponding projected crossover errors for Geosat and T/P are 8 cm and 2.3 cm, respectively. The precision of our mean difference observations is about 3 cm for Geosat (approx. 24,000 observations), 1.5 cm for T/P (approx. 6,000 observations) and 5 cm for ERS 1 (approx. 44,000 observations). Thus, these “global” independent data should provide a valuable new source for improving geopotential models. Our results show the need for further correction of the low order JGM 2 geopotential as well as certain resonant orders for all 3 satellites.     

SPOT-2 and TOPEX/Poseidon precise orbit determination from DORIS doppler tracking

The French earth observation satellite SPOT-2 has served as a testbed for precise orbit determination from DORIS doppler tracking in anticipation of the TOPEX/Poseidon mission. Using the most up-to-data gravity field model, JGM-2, a radial orbit accuracy of about 2–9 cm was achieved, with an rms of fit of the tracking data of about 0.64 mm/s. Furthermore, it was found that the coordinates of the ground stations can be determined with an accuracy of the order of 2–5 cm after removal of common rotations, and translations.

Using a slightly different model for atmospheric drag, but the same gravity model, precise orbits of TOPEX/Poseidon from DORIS tracking data were determined with a radial orbit accuracy of the order of 4–5 cm, which is far within the 13 cm mission requirement. This conclusion is based on the analysis of 1-day overlap of successive 11-day orbits, and the comparisons with orbits computed from satellite laser tracking (SLR) and from the combination of SLR and DORIS tracking. Results indicate a consistency between the different orbits of 1–4 cm, 4–20 cm, and 6–13 cm in the radial, cross-track, and along-track directions, respectively. The residual rms is about 4–5 cm for SLR data and 0.56 mm/s for DORIS tracking. These numbers are roughly twice as large as the system noise levels, reflecting the fact that there are still some modeling errors left.     

Improving the low orbit satellite tracking ability using nonlinear model predictive controller and Genetic Algorithm

The satellite motion on the reference orbit (RO) with less energy consumption has always persuaded researchers to design optimal control systems. The nonlinear nature and time-varying equations of motion make this quest more challenging. The present study proposes a novel control system for satellite motion on the RO by considering a comprehensive model of its dynamics in orbit and a Nonlinear Model Predictive Controller (NMPC). The NMPC calculates the sub-optimal control inputs of satellite motion reference on the elliptic orbit by minimizing a convex cost function at each stage. Moreover, all weighting parameters of the cost function are optimized by the Genetic Algorithm (GA) to produce less perturbation and guarantee the best NMPC performance. Finally, the implemented NMPC has been compared to a Linear MPC (LMPC). The results show that not only can the NMPC resist against larger errors and perturbations, but it can also compensate for those errors by returning the satellite to its main orbit and maintaining it.