Various techniques and procedures for refining ERS-1 orbits

The satellite ERS-1 was launched in July 1991 in a period of high solar activity. Sparse laser tracking and the failure of the experimental microwave system (PRARE) compounded the orbital errors which resulted from mismodelling of atmospheric density and hence surface forces. Three attempts are presented here to try and refine the coarse laser orbits of ERS-1, made prior to the availability of the full altimetric dataset. The results of the first attempt indicate that by geometrically modelling the satellite shape some improvement in orbital precision may be made for any satellite; especially one where no area tables already exist. The second and third refinement attempts are based on the introduction of data from some second satellite; in these examples SPOT-2 and TOPEX/Poseidon are employed. With SPOT-2 the method makes use of the orbital similarities to produce along-track corrections for the more fully tracked SPOT-2. Transferring these corrections to ERS-1 produces improvements in the precise orbits thus determined. With TOPEX/Poseidon the greater altitude results in a more precise orbit (gravity field and atmospheric errors are of less importance). Thus, by computing height differences at crossover points of the TOPEX/Poseidon and ERS-1 ground tracks the poorer orbit of ERS-1 may be improved by the addition of derived radial corrections. In the positive light of all three results several potential modification are suggested and some further avenues of investigation indicated.

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.

Application of ERS-1 and Topex/Poseidon altimetry using precise orbits

The work described in this thesis concerns the application of radar altimetry, collected from the ERS-1 and TOPEX/POSEIDON missions, to precise satellite orbits computed at Aston University. The data is analysed in a long arc fashion to determine range biases, time tag biases, sea surface topographies and to assess the radial accuracy of the generated orbits through crossover analysis. A sea surface variability study is carried out for the North Sea using repeat altimeter profiles from ERS-1 and TOPEX/POSEIDON in order to verify two local U.K. models for ocean tide and storm surge effects. An on-side technique over the English Channel is performed to compute the ERS-1, TOPEX and POSEIDON altimeter range biases by using a combination of altimetry, precise orbits determined by short arc methods, tide gauge data, GPS measurements, geoid, ocean tide and storm surge models. The remaining part of the thesis presents some techniques for the short arc correction of long arc orbits. Validation of this model is achieved by way of comparison with actual SEASAT short arcs. Simulations are performed for the ERS-1 microwave tracking system, PRARE, using the range data to determine time dependent orbit corrections. Finally, a brief chapter is devoted to the recovery of errors in station coordinates by the use of multiple short arcs.

Approximating differentiable relationships between delay embedded dynamical systems with radical basis functions

This thesis is about the study of relationships between experimental dynamical systems. The basic approach is to fit radial basis function maps between time delay embeddings of manifolds. We have shown that under certain conditions these maps are generically diffeomorphisms, and can be analysed to determine whether or not the manifolds in question are diffeomorphically related to each other. If not, a study of the distribution of errors may provide information about the lack of equivalence between the two. The method has applications wherever two or more sensors are used to measure a single system, or where a single sensor can respond on more than one time scale: their respective time series can be tested to determine whether or not they are coupled, and to what degree. One application which we have explored is the determination of a minimum embedding dimension for dynamical system reconstruction. In this special case the diffeomorphism in question is closely related to the predictor for the time series itself. Linear transformations of delay embedded manifolds can also be shown to have nonlinear inverses under the right conditions, and we have used radial basis functions to approximate these inverse maps in a variety of contexts. This method is particularly useful when the linear transformation corresponds to the delay embedding of a finite impulse response filtered time series. One application of fitting an inverse to this linear map is the detection of periodic orbits in chaotic attractors, using suitably tuned filters. This method has also been used to separate signals with known bandwidths from deterministic noise, by tuning a filter to stop the signal and then recovering the chaos with the nonlinear inverse. The method may have applications to the cancellation of noise generated by mechanical or electrical systems. In the course of this research a sophisticated piece of software has been developed. The program allows the construction of a hierarchy of delay embeddings from scalar and multi-valued time series. The embedded objects can be analysed graphically, and radial basis function maps can be fitted between them asynchronously, in parallel, on a multi-processor machine. In addition to a graphical user interface, the program can be driven by a batch mode command language, incorporating the concept of parallel and sequential instruction groups and enabling complex sequences of experiments to be performed in parallel in a resource-efficient manner.

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.

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.

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.

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.

An investigation of the pressaccidic spike potential

A large negative spike potential, which is closely related to the onset of saccadic eyemovements, can be recorded from electrodes adjacent to the orbits. This potential, thepresaccadic spike potential, has often been regarded as an artefact related to eyemovement recordings and little work has been performed to establish its normal waveformand parameters. A positive spike potential, exactly coincident with the frontal negativespike, has also been recorded from electrodes positioned over the posterior scalp andthere has been some debate regarding any possible relationship between the twopotentials. The frontal spike potential has been associated with motor unit activity in theextraocular muscles prior to the saccade. This thesis investigates both the large anteriorand smaller posterior spike potentials and relates these recordings to the saccadic eyemovements associated with them. The anterior spike potential has been recorded from normal subjects to ascertain its normallatency and amplitude parameters for both horizontal and vertical saccades. A relationshipbetween saccade size and spike potential amplitude is described, the spike potentialamplitude reducing with smaller saccades. The potential amplitude also reduces withadvancing age. Studying the topographical distribution of the spike potential across thescalp shows the posterior spike activity may arise from potential spread of the larger frontalspike potential. Spike potential recordings from subjects with anomalous eye movements further implicate the extraocular muscles and their innervation in the generation of the spike potential. These recordings indicate that the spike potential may have some use as a clinical recording from patients with disease conditions affecting either their extraocular muscles or the innervational pathways to these muscles. Further recordings of the potential are necessary, however, to determine the exact nature of the changes which may occur with such conditions.