Precise orbit determination and analysis from satellite altimetry and laser ranging

For optimum utilization of satellite-borne instrumentation, it is necessary to know precisely the orbital position of the spacecraft. The aim of this thesis is therefore two-fold - firstly to derive precise orbits with particular emphasis placed on the altimetric satellite SEASAT and secondly, to utilize the precise orbits, to improve upon atmospheric density determinations for satellite drag modelling purposes. Part one of the thesis, on precise orbit determinations, is particularly concerned with the tracking data - satellite laser ranging, altimetry and crossover height differences - and how this data can be used to analyse errors in the orbit, the geoid and sea-surface topography. The outcome of this analysis is the determination of a low degree and order model for sea surface topography. Part two, on the other hand, mainly concentrates on using the laser data to analyse and improve upon current atmospheric density models. In particular, the modelling of density changes associated with geomagnetic disturbances comes under scrutiny in this section. By introducing persistence modelling of a geomagnetic event and solving for certain geomagnetic parameters, a new density model is derived which performs significantly better than the state-of-the-art models over periods of severe geomagnetic storms at SEASAT heights. This is independently verified by application of the derived model to STARLETTE orbit determinations.

Resonance studies of artificial earth satellites

Orbit determination from artificial satellite observations is a key process in obtaining information about the Earth and its environment. A study of the perturbations experienced by these satellites enables knowledge to be gained of the upper atmosphere, the gravity field, ocean tides, solid-Earth tides and solar radiation. The gravity field is expressed as a double infinite series of associated Legendre functions (tesseral harmonics). In contemporary global gravity field models the overall geoid is well determined. An independent check on these gravity field harmonics of a particular order may be made by analysis of satellites that pass through resonance of that order. For such satellites the perturbations of the orbital elements close to resonance are analysed to derive lumped harmonic coefficients. The orbital parameters of 1984-106A have been determined at 43 epochs, during which time the satellite was close to 14th order resonance. Analysis of the inclination and eccentricity yielded 6 lumped harmonic coefficients of order 14 whilst analysis of the mean motion yielded additional pairs of lumped harmonics of orders 14, 28 and 42, with the 14th order harmonics superseding those obtained from analysis of the inclination. This thesis concentrates in detail on the theoretical changes of a near-circular satellite orbit perturbed by the Earth's gravity field under the influence of minimal air-drag whilst in resonance with the Earth. The satellite 1984-106A experienced the interesting property of being temporarily trapped with respect to a secondary resonance parameter due to the low air-drag in 1987. This prompted the theoretical investigation of such a phenomenon. Expressions obtained for the resonance parameter led to the determination of 8 lumped harmonic coefficients, coincidental to those already obtained. All the derived lumped harmonic values arc used to test the accuracy of contemporary gravity field models and the underlying theory in this thesis.

Satellite borne radar altimetry : empirical orbit refinement and ocean signal recovery techniques

Measurements of the sea surface obtained by satellite borne radar altimetry are irregularly spaced and contaminated with various modelling and correction errors. The largest source of uncertainty for low Earth orbiting satellites such as ERS-1 and Geosat may be attributed to orbital modelling errors. The empirical correction of such errors is investigated by examination of single and dual satellite crossovers, with a view to identifying the extent of any signal aliasing: either by removal of long wavelength ocean signals or introduction of additional error signals. From these studies, it was concluded that sinusoidal approximation of the dominant one cycle per revolution orbit error over arc lengths of 11,500 km did not remove a significant mesoscale ocean signal. The use of TOPEX/Poseidon dual crossovers with ERS-1 was shown to substantially improve the radial accuracy of ERS-1, except for some absorption of small TOPEX/Poseidon errors. The extraction of marine geoid information is of great interest to the oceanographic community and was the subject of the second half of this thesis. Firstly through determination of regional mean sea surfaces using Geosat data, it was demonstrated that a dataset with 70cm orbit error contamination could produce a marine geoid map which compares to better than 12cm with an accurate regional high resolution gravimetric geoid. This study was then developed into Optimal Fourier Transform Interpolation, a technique capable of analysing complete altimeter datasets for the determination of consistent global high resolution geoid maps. This method exploits the regular nature of ascending and descending data subsets thus making possible the application of fast Fourier transform algorithms. Quantitative assessment of this method was limited by the lack of global ground truth gravity data, but qualitative results indicate good signal recovery from a single 35-day cycle.

Orbit and altimetric corrections for the ERS satellites through analysis of single and dual satellite crossovers

Due to the failure of PRARE the orbital accuracy of ERS-1 is typically 10-15 cm radially as compared to 3-4cm for TOPEX/Poseidon. To gain the most from these simultaneous datasets it is necessary to improve the orbital accuracy of ERS-1 so that it is commensurate with that of TOPEX/Poseidon. For the integration of these two datasets it is also necessary to determine the altimeter and sea state biases for each of the satellites. Several models for the sea state bias of ERS-1 are considered by analysis of the ERS-1 single satellite crossovers. The model adopted consists of the sea state bias as a percentage of the significant wave height, namely 5.95%. The removal of ERS-1 orbit error and recovery of an ERS-1 - TOPEX/Poseidon relative bias are both achieved by analysis of dual crossover residuals. The gravitational field based radial orbit error is modelled by a finite Fourier expansion series with the dominant frequencies determined by analysis of the JGM-2 co-variance matrix. Periodic and secular terms to model the errors due to atmospheric density, solar radiation pressure and initial state vector mis-modelling are also solved for. Validation of the dataset unification consists of comparing the mean sea surface topographies and annual variabilities derived from both the corrected and uncorrected ERS-1 orbits with those derived from TOPEX/Poseidon. The global and regional geographically fixed/variable orbit errors are also analysed pre and post correction, and a significant reduction is noted. Finally the use of dual/single satellite crossovers and repeat pass data, for the calibration of ERS-2 with respect to ERS-1 and TOPEX/Poseidon is shown by calculating the ERS-1/2 sea state and relative biases.

First year qualifying report: neural networks for extracting wind vectors from satellite scatterometer data

The ERS-1 Satellite was launched in July 1991 by the European Space Agency into a polar orbit at about km800, carrying a C-band scatterometer. A scatterometer measures the amount of radar back scatter generated by small ripples on the ocean surface induced by instantaneous local winds. Operational methods that extract wind vectors from satellite scatterometer data are based on the local inversion of a forward model, mapping scatterometer observations to wind vectors, by the minimisation of a cost function in the scatterometer measurement space.par This report uses mixture density networks, a principled method for modelling conditional probability density functions, to model the joint probability distribution of the wind vectors given the satellite scatterometer measurements in a single cell (the `inverse' problem). The complexity of the mapping and the structure of the conditional probability density function are investigated by varying the number of units in the hidden layer of the multi-layer perceptron and the number of kernels in the Gaussian mixture model of the mixture density network respectively. The optimal model for networks trained per trace has twenty hidden units and four kernels. Further investigation shows that models trained with incidence angle as an input have results comparable to those models trained by trace. A hybrid mixture density network that incorporates geophysical knowledge of the problem confirms other results that the conditional probability distribution is dominantly bimodal.par The wind retrieval results improve on previous work at Aston, but do not match other neural network techniques that use spatial information in the inputs, which is to be expected given the ambiguity of the inverse problem. Current work uses the local inverse model for autonomous ambiguity removal in a principled Bayesian framework. Future directions in which these models may be improved are given.

Global non-dynamic refinement of radial orbit error for altimetric earth satellites

The accuracy of altimetrically derived oceanographic and geophysical information is limited by the precision of the radial component of the satellite ephemeris. A non-dynamic technique is proposed as a method of reducing the global radial orbit error of altimetric satellites. This involves the recovery of each coefficient of an analytically derived radial error correction through a refinement of crossover difference residuals. The crossover data is supplemented by absolute height measurements to permit the retrieval of otherwise unobservable geographically correlated and linearly combined parameters. The feasibility of the radial reduction procedure is established upon application to the three day repeat orbit of SEASAT. The concept of arc aggregates is devised as a means of extending the method to incorporate longer durations, such as the 35 day repeat period of ERS-1. A continuous orbit is effectively created by including the radial misclosure between consecutive long arcs as an infallible observation. The arc aggregate procedure is validated using a combination of three successive SEASAT ephemerides. A complete simulation of the 501 revolution per 35 day repeat orbit of ERS-1 is derived and the recovery of the global radial orbit error over the full repeat period is successfully accomplished. The radial reduction is dependent upon the geographical locations of the supplementary direct height data. Investigations into the respective influences of various sites proposed for the tracking of ERS-1 by ground-based transponders are carried out. The potential effectiveness on the radial orbital accuracy of locating future tracking sites in regions of high latitudinal magnitude is demonstrated.

Drag coefficients with applications to satellite orbits

In the last twenty or so years the results of theory and experiment have produced much information on the characteristics of gas-surface interactions relevant to a satellite in hyperthermal free-molecular flow. This thesis contains reviews of the rarefied gas dynamics applicable to satellites and has attempted to compare existing models of gas-surface interaction with contemporary knowledge of such systems. It is shown that a more natural approach would be to characterise the gas-surface interaction using the normal and tangential momentum accommodation coefficients, igma' and igma respectively, specifically in the form igma = constant , igma' = igma'0 -igma'1sec i where i is the angle subtended between the incident flow and the surface normal and igma,igma'0 and igma'1 are constants. Adopting these relationships, the effects of atmospheric lift on inclination, i, and atmospheric drag on the semi-major axis, a, and eccentricity, e, have been investigated. Applications to ANS-1 (1974-70A) show that the observed perturbation in i can be ascribed primarily to non-zero igma'1 whilst perturbations in a and e produce constraint equations between the three parameters. The numerical results seem to imply that a good theoretical orbit is achieved despite a much lower drag coefficient than anticipated by earlier theories.

Satellite laser ranging and the ETALON Geodetic satellites

The technique of Satellite Laser Ranging is today a mature, important tool with applications in many area of geodynamics, geodesy and satellite dynamics. A global network of some 40 stations regularly obtains range observations with sub-cm precision to more than twelve orbiting spacecraft. At such levels of precision it is important to minimise potential sources of range bias in the observations, and part of the thesis is a study of subtle effects caused by the extended nature of the arrays of retro-reflectors on the satellites. We develop models that give a precise correction of the range measurements to the centres of mass of the geodetic satellites Lageos and Etalon, appropriate to a variety of different ranging systems, and use the Etalon values, which were not determined during pre-launch tests, in an extended orbital analysis. We have fitted continuous 2.5 year orbits to range observations of the Etalons from the global network of stations, and analysed the results by mapping the range residuals from these orbits into equivalent corrections to orbital elements over short time intervals. From these residuals we have detected and studied large un-modelled along-track accelerations associated with periods during which the satellites are undergoing eclipse by the Earth's shadow. We also find that the eccentricity residuals are significantly different for the two satellites, with Etalon-2 undergoing a year-long eccentricity anomaly similar in character to that experienced at intervals by Lageos-1. The nodal residuals show that the satellites define a very stable reference frame for Earth rotation determination, with very little drift-off during the 2.5 year period. We show that an analysis of more than about eight years of tracking data would be required to derive a significant value for 2. The reference frame defined by the station coordinates derived from the analyses shows very good agreement with that of ITRF93.

Mean sea surface modelling from multi-satellite altimetry utilising frequency domain techniques

A technique is presented for the development of a high precision and resolution Mean Sea Surface (MSS) model. The model utilises Radar altimetric sea surface heights extracted from the geodetic phase of the ESA ERS-1 mission. The methodology uses a modified Le Traon et al. (1995) cubic-spline fit of dual ERS-1 and TOPEX/Poseidon crossovers for the minimisation of radial orbit error. The procedure then uses Fourier domain processing techniques for spectral optimal interpolation of the mean sea surface in order to reduce residual errors within the model. Additionally, a multi-satellite mean sea surface integration technique is investigated to supplement the first model with additional enhanced data from the GEOSAT geodetic mission.The methodology employs a novel technique that combines the Stokes' and Vening-Meinsz' transformations, again in the spectral domain. This allows the presentation of a new enhanced GEOSAT gravity anomaly field.

Combination of altimetry data from different satellite missions

Substantial altimetry datasets collected by different satellites have only become available during the past five years, but the future will bring a variety of new altimetry missions, both parallel and consecutive in time. The characteristics of each produced dataset vary with the different orbital heights and inclinations of the spacecraft, as well as with the technical properties of the radar instrument. An integral analysis of datasets with different properties offers advantages both in terms of data quantity and data quality. This thesis is concerned with the development of the means for such integral analysis, in particular for dynamic solutions in which precise orbits for the satellites are computed simultaneously. The first half of the thesis discusses the theory and numerical implementation of dynamic multi-satellite altimetry analysis. The most important aspect of this analysis is the application of dual satellite altimetry crossover points as a bi-directional tracking data type in simultaneous orbit solutions. The central problem is that the spatial and temporal distributions of the crossovers are in conflict with the time-organised nature of traditional solution methods. Their application to the adjustment of the orbits of both satellites involved in a dual crossover therefore requires several fundamental changes of the classical least-squares prediction/correction methods. The second part of the thesis applies the developed numerical techniques to the problems of precise orbit computation and gravity field adjustment, using the altimetry datasets of ERS-1 and TOPEX/Poseidon. Although the two datasets can be considered less compatible that those of planned future satellite missions, the obtained results adequately illustrate the merits of a simultaneous solution technique. In particular, the geographically correlated orbit error is partially observable from a dataset consisting of crossover differences between two sufficiently different altimetry datasets, while being unobservable from the analysis of altimetry data of both satellites individually. This error signal, which has a substantial gravity-induced component, can be employed advantageously in simultaneous solutions for the two satellites in which also the harmonic coefficients of the gravity field model are estimated.