No abstract

This paper demonstrates the use of polynomial chaos expansions (PCEs) for the nonlinear, non-Gaussian propagation of orbit state uncertainty. Using linear expansions in tensor-products of univariate orthogonal polynomial bases, PCEs approximate the stochastic solution of the ordinary differential equation describing the propagated orbit, and include information on covariance, higher moments, and the spatial density of possible solutions. Results presented in this paper use non-intrusive, i.e., sampling-based, methods in combination with either least-squares regression or pseudo-spectral collocation to estimate the PCE coefficients at any future point in time. Such methods allow for the utilization of existing orbit propagators. Samples based on Sun-synchronous and Molniya orbit scenarios are propagated for up to ten days using two-body and higher-fidelity force models. Tests demonstrate that the presented methods require the propagation of orders of magnitude fewer samples than Monte Carlo techniques, and provide an approximation of the a posteriori probability density function that achieves the desired accuracy. Results also show that Poincaré-based PCEs require fewer samples to achieve a given accuracy than Cartesian-based solutions. In terms of pdf accuracy, the PCE-based solutions represent an improvement over the linear propagation and unscented transformation techniques.

No abstract

The SEASAT satellite, launched on June 27, 1978, carried a radar altimeter designed to measure the altitude of the satellite above the ocean surface, the surface wave height, and the ocean-surface backscatter coetficient from which wind speed can be inferred. Postlaunch engineering assessment indicated that the SEASAT altimeter met the performance specification for 10-cm precision (noise) in the altitude measurements. However, to determine the accuracy of this measurement as well as the accuracy of the wave height and wind speed measurements a significant calibration, validation, and model development effort was required. This summary describes the instrument, atmospheric, and geophysical effects which influence the radar altimeter measurement accuracies and the attendant correction models adopted for the altimeter geophysical data record. Also summarized are the activities of the SEASAT Altimeter/Precision Orbit Determination Experiment Team directed towards the validation and improvement of these models, as well as the investigations required to assess the accuracy of the altimeter measurement and the computed satellite altitude ephemeris. Finally, an accuracy assessment is made for the various altimeter measurement corrections which are included on the altimeter geophysical data record. INTRODUCTIONThe development of satellite altimetry techniques for the remote sensing of ocean surface topography is one of the fundamental objectives of the NASA Ocean Processes Program. The requirements for NASA's satellite altimetry program were formulated at the 1969 Williamstown Conference on Solid Earth and Ocean Physics [Kaula et al., 1970]. Since this conference, satellite altimetry has evolved through the Skylab [McGoogan et al., 1974], GEeS 3 [Stanley, 1979], and SEASAT missions to the extent that it can dramatically improve the way we perform many future oceanographic measurements. Characteristics unique to satellite altimetry are (1) the high accuracy with which surface topography, wave height, and wind speed can be measured and (2) the ability to collect these measurements globally over the time interval of a few days [Apel, 1980]. The satellite served as a stable platform from which the altimeter measured the distance from the antenna feed point to the instantaneous electromagnetic mean sea level. The SEASAT altimeter tracked the position of the sea surface by using a closed loop microprocessor range tracker and an automatic gain control feedback loop. For a description of the altimeter design, see MacArthur [1978]. The geophysical measurements obtained from the returned altimeter pulse are (1) altitude above the ocean surface, which is related to ocean surface topography, (2) ocean surface significant wave height, and (3) ocean surface backscatter coefficient, which is related to the wind speed. Given an independent determination of the satellite position from the orbit determination system, the ocean surface topography can be inferred from the altimeter height measurement. The oceanographic phenomena which influe...

We have conducted an extensive investigation of orbit determination strategies for the Geosat ExactRepeat Mission (ERM). The goal of our studies is to establish optimum geodetic parameters and procedures for the computation of the most accurate Geosat orbits possible and to apply these procedures for the routine computation of Geosat orbits during the ERM for the following purposes: (!) to enhance the value of' the Geosat oceanographic investigations by providing the user community with improved ephemerides, (2) to develop orbit determination techniques for the upcoming altimetric mission TOPEX/POSEIDON, and (3) to assess the radial orbit accuracy obtainable with recently developed gravity models. To this end, ephemerides for the entire first year of the ERM have been computed using the GEODYN II orbit program on the Cyber 205 supercomputer system at the Goddard Space Flight Center. The GEM-T1 gravity solution was used in developing solutions in 25 separate 17-day arcs. Estimated radial orbit errors have been reduced from a level of 3-m rootmean-square (rms) with the operational orbits to about the 85-cm level. Both the operational and precision ephemerides were produced from the same tracking data collected by the U.S. Navy's Operational Network, so most of this improvement is due to improved force and measurement modeling. Recently, a more accurate gravity field, GEM-T2, has become available. Preliminary orbit tests performed with the GEM-T2 gravity model, along with Geosat TRANET-2 Doppler data that have recently been acquired, suggest that radial orbit accuracies of about 35 cm rms can be achieved for Geosat. !. INTRODUCTIONThe U.S. Navy Geodetic Satellite (Geosat) was launched into a retrograde orbit by an Atlas Agena from the Western Test Range on March 12, 1985. It carried a Seasat class radar altimeter and a Doppler beacon. Geosat's primary mission was to provide a dense global altimeter data base for the determination of the marine geoid with a spatial resolution of !5 km. Because the satellite ground tracks were nonrepeating during the primary (geodetic) mission, the altimeter data are classified; thus this phase of the mission was not well suited for determining sea level variability.The long lifetime of the Geosat altimeter and the maneuverability of the spacecraft enabled a secondary mission subsequent to the 18-month primary mission. For this secondary mission, the satellite was maneuvered into a 17nodal-day repeat and frozen orbit [Born et al., 1987]. This orbit, modeled after the 17-day near-repeat orbit for Seasat, is well suited for monitoring the variability of the sea surface. For Geosat the ground track repeats to within 1 km every 17 nodal days. (A nodal day is one revolution of the Earth with respect to the line of nodes of the Geosat orbit.) An exact repeat orbit allows for the direct computation of sea level variability by examining an ensemble of repeating ground tracks. No reference geoid is necessary, since the geoid height is common to the repeating tracks. "Frozen" implies that becau...