K.F. Wakker

TOPEX/Poseidon orbit error assessment

This paper discusses the accuracy of TOPEX/Poseidon orbits computed at Delft University, Section Space Research & Technology (DUT/SSR&T), from several types of tracking data,i.e. SLR, DORIS, and GPS. To quantify the orbit error, three schemes are presented. The first scheme relies on the direct altimeter observations and the covariance of the JGM-2 gravity field. The second scheme is based on crossover difference residuals while the third scheme uses the differences of dynamic orbit solutions with the GPS reduced-dynamic orbit. All three schemes give comparable results and indicate that the radial orbit error of TOPEX/Poseidon is 3–4 cm. From the orbit comparisons with GPS reduced dynamic, both the along-track and cross-track errors of the dynamic orbit solutions were found to be within 10–15 cm.

Ocean tides from harmonic and response analysis on TOPEX/POSEIDON altimetry

With the TOPEX/POSEIDON mission having reached the end of its nominal three-year lifetime, a large number of ocean tides models incorporating TOPEX/POSEIDON altimetry data have been released. Because the major part of these models is based on the two classical analysis methods, i.e. harmonic and response analysis, it is interesting to compare and interpret the results of these two methods. Clearly, this requires that the same data are used and moreover that the data are processed with the same scheme. Therefore, both analysis methods have been implemented and three years of TOPEX/POSEIDON altimeter data have been processed to solve the major diurnal and semi-diurnal constituents of the global ocean tides by harmonic and response analysis. The results of both methods are evaluated from the differences with the most recent Grenoble hydrodynamic model and from the fit with the harmonic constants of a globally-distributed set of tide gauges. It was found that the solutions from the harmonic and response methods differ at the millimetre level and that, according to the tide gauges, the harmonic method leads to slightly more accurate results. Also, results from some experiments with the parameters in the response formalism show that the tidal admittance in both the diurnal and semi-diurnal band can be adequately described with a lag interval of two days and a number of lags of three.

GEOSAT and ERS-1 radar altimetry over the North Atlantic

Abstract ERS-1 (35-day repeat) and GEOSAT (17-day repeat) altimetric measurements over the North Atlantic have been processed to study the mean sea surface and the sea surface currents. This paper presents some details on the processing techniques applied and on the results obtained. The large-scale semi-permanent circulation is determined from a least squares parameter adjustment method in which a number of gravity field coefficients and a low order and -degree dynamic ocean topography model are solved for simultaneously. After radial orbit error reduction by crossover difference residuals minimization, the mesoscale eddy circulation is obtained from analyzing the temporal variation of the local sea surface. In addition, mean wavenumber spectra have been computed for two areas in the North Atlantic, and some Gulfstream eddy characteristics, such as translation and rotation velocity, have been determined.

Dynamic and non-dynamic ERS-1 radial orbit improvement from ERS-1/TOPEX dual-satellite altimetry

Abstract Dual-satellite altimeter crossover differences between ERS-1 and TOPEX/Poseidon have been included as supplementary tracking data in ERS-1 orbit computations from SLR and single-satellite crossover differences. It was found that including the dual-satellite crossover differences slightly improves the ERS-1 radial orbit accuracy of about 12 cm for orbits computed with the JGM-2 gravity field and also leads to a better ‘centering’ of the ERS-1 orbit in the terrestrial reference frame defined for TOPEX/Poseidon. In addition to this dynamic orbit improvement technique, a non-dynamic technique has been investigated that removes the larger part of the ERS-1 radial orbit error from the dual-satellite crossover difference residuals. For ERS-1 orbits computed with the GEM-T2 gravity field, it was found that the non-dynamic technique could improve the radial orbit accuracy from 140 cm to the same level of accuracy as the ERS-1 JGM-2 orbits.

Seasat precise orbit computation and altimeter data processing

Abstract This paper presents an overview of the research performed by the Orbital Mechanics Section of Delft University of Technology on the precise orbit computation of Seasat and the processing of the satellites altimeter measurements. After a general description of the Seasat tracking and orbit characteristics, the applications of the altimeter data for geophysical and oceanographic investigations and as tracking data are addressed. Subsequently, the accuracy of orbit determination achieved by processing laser range data only or laser ranges in combination with altimeter height cross-over differences is discussed, and the identification of the radial orbit error from altimeter height residual profiles is described. The geographical correlation of the radial orbit error is analysed and the development of a tailored gravity model is addressed. Finally, the elimination of the residual radial orbit error is discussed and an example is given of the computation of a mean sea surface.

Analysis of radial orbit errors of ERS-1, and the development of super-tailored gravity models

Abstract The altimetry mission of the future ESA remote sensing satellite ERS-1 requires very accurate orbit solutions, of which in particular the radial position component should have an accuracy of approximately 10 cm. This paper presents some investigations into the possibility of reducing the radial position error due to the earths gravity field, which is by far the largest contributing error source. With a detailed harmonic analysis of the ERS-1 orbit a number of gravity field model terms are identified which produce the major radial orbit perturbations. These dominant terms are adjusted in a least-squares orbit determination and parameter estimation procedure using actual SEASAT laser tracking observations and altimeter height measurements. The initial gravity model is the NASA GEM-L2 model derived from satellite tracking data only, with an emphasis on LAGEOS data. The resulting super-tailored model yields a significantly improved radial accuracy relative to GEM-L2, but fails to reach the accuracy of the SEASAT-tailored model PGS-S4. Finally, the SEASAT altimeter residuals and the residuals of the cross-over differences are analyzed in the frequency domain by applying a special filtering technique which separates the major radial orbit error and geoid error contributions.

Gravity field model adjustment from ERS-1 and TOPEX altimetry and SLR tracking using an analytical orbit perturbation theory

Abstract The JGM-2 gravity field model has been adjusted using 70 days of ERS-1 and 19 10-day repeat cycles of TOPEX/Poseidon SLR and single satellite altimeter crossover differences. In addition, dual satellite altimeter crossover differences between ERS-1 and TOPEX for the selected 70-day period of ERS-1 and TOPEX repeat cycle 18 have been used in the JGM-2 model adjustment. In the computation of the normal equations, use was made of the analytical Lagrange linear perturbation theory. The single satellite altimeter crossover difference rms was brought down from 15.2 to 14.1 cm for ERS-1 and from 10.6 to 10.5 cm for TOPEX. The dual satellite altimeter crossover difference rms was reduced from 17.7 to 16.9 cm. Furthermore, the weighted rms of fit of SLR measurements was brought down from 16.0 to 14.4 cm for ERS-1, and from 5.4 to 5.0 cm for TOPEX/Poseidon.

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

Abstract 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.

APPLICATION OF SATELLITE ALTIMETER DATA TO ORBIT ERROR CORRECTION AND GRAVITY MODEL ADJUSTMENT

Abstract The full exploitation of the oceanographical information contained in altimeter height observations made during altimetry missions of the past (SEASAT), present (GEOSAT) and future (ERS-1, TOPEX/Poseidon), requires very accurate satellite orbits. Although the dynamic models involved in the orbit computation are of steadily increasing accuracy, the strived-for accuracy of 10 cm of the radial position component may not be achieved for all these missions in the near future. Several techniques have been devised to apply altimeter or cross-over data to satellite orbit correction and gravity model adjustment. This paper will address two methods which are currently being developed at Delft University of Technology (DUT). Using analytical theory, a gravity model may be adjusted with a limited number of laser range and cross-over difference observations by applying constraint matrices. This technique was successfully applied to tune the GEM-T1 model. With the same theory a new method of orbit error correction used by the so-called cross-over minimization technique for restricted areas has been devised, which allows the recovery of the eliminated orbit error, and the combination of these errors from several areas into a global error model.

Kalman filter orbit improvement from Kootwijk laser range observations

Abstract Modern satellite ranging lasers emit short pulses at a low beam divergence and therefore require accurate satellite position predictions. To reach these accuracies the application of a Kalman filter orbit improvement technique has been investigated. Using laser observations acquired at only one groundstation the filter scheme provides real-time satellite position prediction updates, and also yields better predictions for subsequent passes over that station.