Orbit Determination Process Research Articles

The FK5 equinox and equator from combined radar and optical data of the near-earth asteroids

Minor planets optical observations have long been used for the purpose of establishing a Celestial reference frame. Being in existence since the early 1960s modern high-accuracy radar measurements of the so-called near-Earth asteroids (NEAs) have been widely extended to the orbit determination process and predicting of the next apparition of the asteroid. Even few radar measurements, when added to optical ones, significantly improve asteroid's ephemeris and reduce standard deviations of the orbital elements (Yeomans et al., 1987). The idea to connect optical and radar data in the problem of the catalogue zero-point determination has been stated by several scientists (Boiko, 1975). And even the first attempt of the authors (Krivova et al., 1994) with actual optical and radar observations of two NEAs: (4179) Toutatis and (1862) Apollo appears to have considerable promise. It was demonstrated the possibility of obtaining standard deviations of catalogue orientation parameters 1.5–2 times better with radar data included.

Combining the orbits of the IGS Analysis Centers

Currently seven Analysis Centers of the International GPS Service for Geodynamics (IGS) are producing daily precise orbits and the corresponding Earth Orientation Parameters (EOP). These individual products are available at several IGS Data Centers (e.g. CDDIS, IGN, SIO, etc.). During 1993 no official IGS orbits were produced, but the routine orbit comparisons by IGS indicated that, after small orientation and scale alignments, the orbit consistency was approaching the 20 cm level (a coordinate RMS), and that some orbit combination should be possible and feasible. An IGS combined orbit could provide a precise and efficient extension of the IERS Terrestrial Reference Frame (ITRF). Another advantage of such a combined orbit would be reliability and precision. Two schemes of orbit combinations are considered here: (a) the first method consists of a weighted averaging process of the earth-fixed satellite positions as produced by the individual Centers; (b) the second method uses the individual IGS orbit files as pseudo-observations in an orbit determination process, where in addition to the initial conditions, different parameter sets may be estimated. Both orbit combination methods have been tested on the January 1993 orbit data sets (GPS weeks 680 and 681) with an impressive agreement at the 5 cm level (coordinate RMS). The quality of the combined orbits is checked by processing a set of continental baselines in two different regions of the globe using different processing softwares. Both types of combined orbits gave similar baseline repeatability of a few ppb in both regions which compared favorably to the best individual orbits in the region.

Orbit determination and analysis of Meteor 3-01 rocket (1985-100B) at 13th-order resonance

The orbit of the rocket of Meteor 3-01 (1985-100B) has been determined at 95 epochs between 15 October 1990 and 27 September 1993, during which time the orbit was trapped in 13th-order resonance with the Earth’s geopotential. A total of 5865 observations were used in the orbit determination process, most of which were supplied by the U. S. Navy. A large number of British radar observations were also available together with some visual observations. The variations in the orbital inclination, eccentricity and mean motion have been analysed to determine four lumped harmonic coefficients of order 13 and two of order 26. Before this was done all unwanted perturbations were removed from the data. The principal lumped harmonic coefficients determined are accurate to approximately 0.1 mm in geoid height and as such provide the most stringent test available for comprehensive geopotential models at 13th order.

Determination and analysis of the orbit of Meteor 28 (1977-57A) at 154 epochs during 15th-order resonance

The orbit of Meteor 28 (1977-57A) has been determined at 154 epochs between 8 January 1984 and 18 July 1989 during which the orbit was perturbed by 15th-order resonance with the geopotential. In total 9521 observations were used in the orbit determination process, the majority of which were supplied by the U.S. Navy. The remainder were British radar, visual and Hewitt camera observations. The variations in the inclination and eccentricity have been analysed to determine six lumped harmonics of order 15 and four of order 30 with accuracies of between 0.4 and 4.4 cm in geoid height. Since the orbit of Meteor 28 was Sun-synchronous, many sources of perturbation of the orbit (solar gravity, tidal effects, solar radiation pressure and drag) were enhanced by solar resonance. The removal of perturbations from the inclination and eccentricity to isolate the geopotential resonance effects posed a significant challenge in the analysis.

Use of an Expert System in Autonomous Orbit Control

Orbital Control (OC) is a vital aspect of every satellite mission. Traditionally, the process of OC and orbit determination (OD) has been very labour intensive. The analysis of the OD solution, the identification of anomalous behaviour and diagnosis of any problems that might occur, are all essentially made by the specialist. There is significant scope for the mundane and routine operations to be automated under software control, and for the experience and knowledge of the experts to be encapsulated in an Expert System. The paper will discuss the role of Expert Systems in OC with an emphasis placed on the practical implications and benefits that such systems can offer. A prototype system, that has been developed to cover the areas of Initial OD of Geosynchronous Transfer Orbits and the routine phase of OD of Geosynchronous Orbits, will be presented.

Visual Binary Orbit Calculation with the Help of a PC: One Possible approach

AbstractIn this work we suggest one possible approach to “computerization” of the process of the visual double star orbit determination. Our computer program, based on the original method (Olević 1989), is interactive which means that the calculator of the orbit makes the final decision about the choice of the best orbit.

Approach for targeting landers and penetrators using orbital opticalnavigation

Onboard orbital optical navigation data is analyzed with the purpose of generating topographic maps for selecting a landing site. It is suggested that a near-real time orbit-determination process be used for solving a large set of parameters including the spacecraft orbit and primary-body gravity field, the rotational properties of the planetary body, the coordinates of surface features, and the camera-pointing and orientation angles of each picture. A batch-sequential formulation of the standard least-squares problem is employed, along with backward smoothing and a square-root formation filter. An experiment in which over 100 images of Phobos are processed to estimate about 2000 parameters is presented, with emphasis on coordinate systems, transforming points on the reference surface to images in the picture, parameter estimation, and cartographic accuracy.

Orbit determination and analysis of Meteor 3 (1970−19A) at 15th-order resonance

The orbit of Meteor 3 (1970−19 A) has been determined at 52 epochs between August 1978 and January 1980 during which the orbit was perturbed by 15th-order resonance with the geopotential. U.S. Navy, together with Hewitt camera, theodolite, kinetheodolite and visual observations were used in the orbit determination process. The variations in the inclination and eccentricity have been analysed to determine six lumped harmonics of order 15 and two of order 30. In the analysis of the eccentricity an air drag model incorporating an oblate atmosphere with a diurnal density variation was used. The variations in the inclination and eccentricity have previously been analysed by King-Hele and Walker (1982, Proc. R. Soc. A379, 247) using orbits determined by the U.S. Naval Research Laboratory. The aim of this work is to find improved values of the lumped harmonics by using more accurately determined orbits.

Mouse embryos cultured in bovine amniotic fluid

Classical Orbit Determination algorithms provide an estimation of the state vector and its associated uncertainty assuming Gaussian processes and linear dynamics. However, a common problem of Orbit Determination processes is the misrepresentation of the Resident Space Object uncertainty through the estimated and predicted covariance. Ultimately, this causes a great impact in the quality and accuracy of Space Surveillance and Tracking products as the covariance is overly optimistic (too small) and the true uncertainty of the object is not properly captured. One of the causes for the unrealism of the covariance is found in the uncertainty of the dynamical and measurement models used to describe the motion of the objects.The aim of this work is to devise a novel methodology to improve the covariance realism of Orbit Determination and Orbit Propagation processes through the classical theory of consider parameters in batch least-squares estimators. The devised methodology uses the theory of consider parameters to add the uncertainty of dynamic and measurement models to the estimated covariance.The magnitude of the consider parameters is weighted using statistical inference techniques, proposing an innovative method to derive its contribution to the covariance. The conceived methodology is suitable for any type of measurement or object, although its primary goal is to correct unrealistic covariance of non-cooperative targets.Among the wide variety of uncertainty sources affecting covariance realism, the influence and effect of two relevant modelling uncertainties, the atmospheric drag force and the range bias, is discussed during this publication. The proposed methodology is first applied to a simulated scenario of tracking measurements, using a Monte Carlo approach. A case involving real radar observations is presented as well, where the uncertainty realism of the Sentinel-3A orbit determination and propagation is assessed and improved. Using the novel methodology of Covariance Determination, covariance realism improvement of a real tracking campaign is achieved and the uncertainty of the atmospheric drag force model quantified.

Orbit determination strategy and accuracy for a Comet Rendezvous mission

Orbit determination during the postrendezvous phases of the Comet Rendezvous/Asteroid Flyby mission is described. The orbit determination process is discussed, with emphasis placed on optical imaging of landmarks, Doppler tracking, and the effects of nongravitatio nal accelerations. Rotational dynamics are introduced for the cometary nucleus. State estimation errors are given for spacecraft trajectory prediction and cometary nucleus attitude prediction. Estimation errors are also given for physical parameters that describe the cometary nucleus such as moments of inertia and gravity field harmonics. The orbit determination performance in support of science instrument pointing while in orbit about the nucleus is described.

Orbit computation system for “IRS”

This paper discusses the Orbit Computation System and precise orbit determination accuracies of the first operational Indian Remote sensing Satellite(IRS). The analysis presented describes navigational strategy, achievable accuracies in orbit determination and ground location in the processed imagery. A brief description of the scene framing procedure, orbit and scene information computation needed for Ancilary Computer Compatible Tape (ACCT), which would be subsequently used for processing various levels of imageries, is presented. The impetus for such analysis was originated with the need to meet mission objectives, precise orbit keeping and precision annotation in imagery which have put high accuracy requirements on orbit determination and processing. This necessitated improvement of tracking data systems, data handling techniques, improved dynamical models and computational techniques which include trajectory propagation. A brief description of orbit determination process is presented along with the tracking network configured for IRS during acquisition and normal phases. It is demonstrated under operational environment of IRS, that the position can be determined to an accuracy better than 500 meters. The analysis include orbit determination processing in the presence of live satellite data, viz. SPOT and LANDSAT as well as simulated data of IRS.

Preliminary evaluation of Doppler-determined pole positions computed using World Geodetic System 1984

Since 1975, the Defense Mapping Agency (DMA) has been determining polar motion as a byproduct of computing the precise orbits of the Navy Navigation Satellite System (NNSS) satellites. The orbit determination process currently incorporates the NSWC 9Z2 terrestrial reference system and the NWL 10E-1 Earth Gravitational Model (EGM) to degree 28 and order 27. The World Geodetic System 1984 (WGS 84), developed by DMA, will replace the NSWC 9Z2/10E-1 system for NNSS orbit determination. The WGS 84 EGM to degree and order 41 will be utilized. This paper presents the results of two experiments which compared pole positions computed in the two systems. These comparisons indicate that use of WGS 84 improves agreement between pole position values resulting from the Nova-class satellite orbit solutions and the values determined by other modern techniques.

Determination of GPS orbits using double difference carrier phase observations from regional networks

Carrier phase measurements are potentially the most precise observations available from theGPS satellite system, the formal precision being of the order of one centimeter per observation. If the so called double differences are used as the basic observable, the analysis is relatively simple, since satellite- and receiver-clocks may be represented by basic models. We investigate the feasibility of double difference phase observations for orbit determination using the material of the 1985 High Precision Baseline Test, where the coordinates of the so called fiducial points (Haystack, Ft. Davis Richmond and Mojave) are held fixed.TI-4100 andAFGL-receiver observations were used in the same orbit determination process. Although no surface weather data had been available to us, the orbit quality seems to be of the order of0.1 ppm. When we use these orbits to estimate the coordinates of the five “non-fiducial points” Owens Valley, Hat Creek Mammoth Lake, Austin and Dahlgren we get a repeatability of the order of5 cm for latitude and longitude and10 cm for height, if the observations of the first four days of the campaign are compared to those of the second four days. If we use our orbits estimated withTI andAFGL observations to process the Mojave—Owens Valley baseline (length245 km) measured by the twoSERIES-X receivers, we obtain day to day repeatabilities of1.6 cm (0.06 ppm) in length,2 cm (0.08 ppm) in latitude,4 cm (0.16 ppm) in longitude and7 cm (0.29 ppm) in height. Since there are indications that regional networks will be realized in the near future, the results presented here should encourage the realization of regional high precision orbit determination services.

On the Orbit Determination Problem

Various important aspects of the satellite orbit determination problem are critically discussed with a view to emphasizing the importance of a wise choice of suitable system models, coordinates sets, and estimators. We describe several aspects of the orbit determination process and also review much of the available literature on the application of Kalman-filter type algorithms to the problem of near-Earth, geosynchronous, and deep-space mission type orbit determination. Some features of on-board orbit determination are also addressed. It is believed that this review with a touch of tutorial will enable engineers and scientists to arrive at an orbit determination methodology (ODM) that will have attributes of good numerical stability, efficiency, and precision in orbit estimation.

Comparison of NAVSTAR satellite L band ionospheric calibrations with Faraday rotation measurements

Using the Faraday rotation technique, the Deep Space Network of the Jet Propulsion Laboratory (JPL) monitors ionospheric total electron content (TEC) at its three complexes at Goldstone, California, Canberra, Australia, and Madrid, Spain, to correct data used in the orbit determination process for ionospheric effects. With the number of earth satellites suitable for Faraday rotation measurements steadily decreasing, JPL is investigating other ways to determine ionospheric TEC. One promising method has been developed by MacDoran and Spitzmesser. This method exploits the coherent P code modulation of the two L band signals (1575.42 and 1227.60 MHz) transmitted by satellites of the NAVSTAR Global Positioning System (GPS), but does not require knowledge of the code. It has been named SLIC, for satellite L band ionospheric calibration. With the full complement of 18 GPS satellites in operation in 1987, continuous ionospheric sampling in at least four directions will be feasible with SLIC. In this paper, TEC data measured at Goldstone using SLIC are compared with the results of mapping Goldstone Faraday TEC to the five GPS satellite lines of sight. The results of the two methods are in reasonable agreement.

Comparative studies of atmospheric density models used for earth satellite orbit estimation

The results of a comparative orbit determination study of four global atmospheric density models (modified Harris-Priester, Jacchia-Roberts, Mass Spectrometer/Incoherent Scatter, and Simple Exponential Model) are presented. The primary objective of this study was quantitative evaluation of the definitive orbit determination consistency and accuracy obtained using these models as measured by the maximum position differences that occur during solution overlap periods. A secondary objective was comparison of propagated ephemerides with definitive orbit solutions in order to evaluate predictive accuracies. The results indicate that, for satellites above 300 km, all four atmospheric density models produce comparable orbit determination accuracies when an atmospheric drag scaling factor and the satellite state vector are estimated during the orbit determination process.

The determination of the satellite orbit of Mariner 9

This paper presents a comprehensive analysis of the Mars orbital phase of the Mariner 9 trajectory as determined from Earth based radio data. Both the method and accuracy of the orbit determination process are reviewed. Analysis is presented to show the effects of Mars gravity model and node in the plane of the sky errors on the accuracy of orbit determination. In addition the long term evolution of the orbit from insertion through the first 500 revolutions is presented, and decomposed into effects from the Mars garvity field,n-body perturbations, and solar radiation pressure. Since the orbit period is nearly commensurable with the Mars rotational period, the orbit experiences significant resonance perturbations. The primary perturbation is in-track with a maximum amplitude of 1000 km and a wavelength of 39 spacecraft revolutions.

An empirically derived lunar gravity field

A new method has been devised to determine spherical harmonic coefficients of the lunar gravity field. This method uses a two-step data reduction and estimation process. The first step applies a weighted least-squares empirical orbit determination process to Doppler tracking data to estimate long-period Kepler elements and rates. In the second step, lunar gravity coefficients are determined using another weighted least-squares processor which fits the long-period Lagrange perturbation equations to the estimated Keplerian rates. This method has been applied to tracking data from the Lunar Orbiter missions. A gravity potential of degree and order four is presented and error sources discussed. Plots of lunar equipotential surfaces are shown. Gravity field results are applied to various physical properties of the Moon such as moments and products of inertia. This gravity field has been investigated using data from several Apollo missions. Solutions from these data, in all cases except that of Apollo 15, result in improved orbit predictions as compared to those using other fields. All solutions indicate that the field models are still imcomplete.