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NASA NTRS1993

A demonstration of TDRS orbit determination using differential tracking observables from GPS ground receivers

A Global Positioning System (GPS) flight receiver provides a means of precisely determining orbits for satellites in low to moderate altitude orbits. Above 5000 km altitude, however, relatively few GPS satellites are visible. We present a new approach to orbit determination for satellites at higher altitudes. Modification of GPS ground receivers enables a beacon from the orbiter to be tracked simultaneously with GPS data. The orbit accuracy expected from this GPS-like tracking (GLT) technique in principle could be comparable to accuracies of GPS orbits. Present-day GPS orbit quality from a daily semi-automated analysis system at the Jet Propulsion Laboratory is at the 30 - 50 cm level: expected accuracies for orbiters with GLT are calculated to be in the few-meter range for altitudes up to 100000 km. For geosynchronous satellites, however, there are unique challenges due to geometrical limitations and to the lack of strong dynamical signature in tracking data. We examine two approaches for tracking Tracking and Data Relay Satellites (TDRS) geostationary orbiters. One uses GLT with a global network; the other relies on a small `connected element' ground network with a distributed clock for short baseline differential carrier phase (SB Delta Phi). In priciple, both could meet 50-m TDRS operational requirements. However there are practical difficulties with either pure GLT or SB Delta Phi tracking schemes for present-day TDRS satellites. We describe an experiment planned for late 1993 which will combine aspects of both GLT and SB Delta Phi to demonstrate a new approach for tracking TDRS which offers a number of operationally convenient and attractive features. The TDRS demo will in effect ba a proof of concept experiment for both the GLT and SB Delta Phi approaches to tracking spacecraft.

Lichten, Stephen M.↗

NASA NTRS2001

Implementation of Altimetry Data in the GIPSY POD Software Package

Altimetry data has been used extensively to acquire data about characteristics of the Earth, the Moon, and Mars. More recently, the idea of using altimetry for orbit determination has also been explored. This report discusses modifications to JPL's GIPSY/OASIS II software to include altimetry data as an observation type for precise orbit determination. The mathematical foundation of using altimetry for the purpose of orbit determination is presented, along with results.

Stauch, Jason R.↗

NASA NTRS1995

Wakeshield WSF-02 GPS Experiment

Shuttle mission STS-69 was launched on September 7, 1995, 10:09 CDT, carrying the Wake Shield Facility (WSF-02). The WSF-02 spacecraft included a set of payloads provided by the Texas Space Grant Consortium, known as TexasSat. One of the TexasSat payloads was a GPS TurboRogue receiver loaned by the University Corporation for Atmospheric Research. On September 11, the WSF-02 was unberthed from the Endeavour payload bay using the remote manipulator system. The GPS receiver was powered on prior to release and the WSF-02 remained in free-flight for three days before being retrieved on September 14. All WSF-02 GPS data, which includes dual frequency pseudorange and carrier phase, were stored in an on-board recorder for post-flight analysis, but "snap- shots" of data were transmitted for 2-3 minutes at intervals of several hours, when permitted by the telemetry band- widdl The GPS experiment goals were: (1) an evaluation of precision orbit determination in a low altitude environment (400 km) where perturbations due to atmospheric drag and the Earth's gravity field are more pronounced than for higher altitude satellites with high precision orbit requirements, such as TOPEX/POSEIDON; (2) an assessment of relative positioning using the WSF GPS receiver and the Endeavour Collins receiver; and (3) determination of atmospheric temperature profiles using GPS signals passing through the atmosphere. Analysis of snap-shot telemetry data indicate that 24 hours of continuous data were stored on board, which includes high rate (50 Hz) data for atmosphere temperature profiles. Examination of the limited number of real-time navigation solutions show that at least 7 GPS satellites were tracked simultaneously and the on-board clock corrections were at the microsec level, as expected. Furthermore, a dynamical consistency test provided a further validation of the on-board navigation solutions. Complete analysis will be conducted in post-flight using the data recorded on-board.

Schutz, B. E.↗

NASA NTRS1995

TAOS Orbit Determination Results Using Global Positioning Satellites

Orbit determination results for the Air Force Phillips Laboratory's Technology for Autonomous Operational Survivability (TAOS) satellite using a Rockwell AST V Global Positioning System (GPS) receiver are presented in this paper. Under a cooperative effort, GPS orbit determination technology developed at Jet Propulsion Laboratory (JPL) has been transferred to the U.S. Air Force. JPL's post processing differential GPS software MIRAGE [1] was modified to perform precise orbit determination for the TAOS satellite. Reconstructed TAOS position accuracies of 10 meters (3 sigma) are the objective. With four days of data, three-dimensional positions of less than 3 meters (1 sigma) have been achieved with overlapping orbit determination spans. Orbit determination results are also compared with those of the on-board GPS receiver's navigation solutions and with the Air Force's Satellite Control Network SGLS processing.

TAOS↗

NASA NTRS1995

An Analysis of the TOPEX/Poseidon Operational Orbit: Observed Variations and Why

Launched in August 1992, TOPEX/Poseidon began and continues a very successful global study of the earth's ocean circulation using a combination of dual-frequency radar altimetry and precision orbit determination (POD). POD results are utilized here to reconstruct the operational orbit history in terms of precise classical mean elements. Elaborations of various facets related to mean elements is discussed.

TOPEX↗

NASA NTRS1988

A demonstration of sub-meter GPS orbit determination and high precision user positioning

It was demonstrated that the submeter GPS (Global Positioning System) orbits can be determined using multiday arc solutions with the current GPS constellation subset visible for about 8 h each day from North America. Submeter orbit accuracy was shown through orbit repeatability and orbit prediction. North American baselines of 1000-2000 km length can be estimated simultaneously with the GPS orbits to an accuracy of better than 1.5 parts in 108 (3 cm over 2000 km distance) with a daily precision of two parts in 108 or better. The most reliable baseline solutions are obtained using the same type of receivers and antennas at each end of the baseline. Baselines greater than 1000 km distance from Florida to sites in the Caribbean region have also been determined with daily precision of 1-4 parts in 108. The Caribbean sites are located well outside the fiducial tracking network and the region of optimal GPS common visibility. Thus, these results further demonstrate the robustness of the multiday arc GPS orbit solutions.

Bertiger, Willy I.↗

NASA NTRS2002

Intial orbit determination results for Jason-1: towards a 1-cm orbit

The U.S/France Jason-1 oceanographic mission is carrying state-of-the-art radiometric tracking systems (GPS and Doris) to support precise orbit determination (POD) requirements. The performance of the systems is strongly reflected in the early POD results. Results of both internal and external (e.g., satellite laser ranging) comparisons support that the 2.5 cm radial Rh4S requirement is being readily met, and provide reasons for optimism that 1 cm can be achieved. We discuss the POD strategy underlying these orbits, as well as the challenging issues that bear on the understanding and characterization of an orbit solution at the l-cm level. We also describe a system for producing science quality orbits in near real time in order to support emerging applications in operational oceanography.

Jason-1 oceanography orbits real time↗

NASA NTRS1990

Towards GPS orbit accuracy of tens of centimeters

In this paper, CASA Uno orbit results are presented utilizing data from four continents. Refinements in orbit modeling, combined with the availability of a worldwide tracking network and the dense distribution of tracking sites in North and South America, have improved orbit determination precision to about 60 cm (per component) for four of the seven GPS satellites tracked in CASA Uno. The orbit results are consistent with California baseline repeatabilities, which are at the few mm level in horizontal and length, and 1-2 cm in the vertical. Baseline comparisons with VLBI provide a measure of orbit accuracy, showing sub-cm agreement in length and 1.5 cm agreement in the horizontal.

Lichten, Stephen M.↗

NASA NTRS2012

The Precise Orbit and the Challenge of Long Term Stability

The computation of a precise orbit reference is a fundamental component of the altimetric measurement. Since the dawn of the modern altimeter age, orbit accuracy has been determined by the quality of the GPS, SLR, and DORIS tracking systems, the fidelity of the measurement and force models, and the choice of parameterization for the orbit solutions, and whether a dynamic or a reduced-dynamic strategy is used to calculate the orbits. At the start of the TOPEX mission, the inaccuracies in the modeling of static gravity, dynamic ocean tides, and the nonconservative forces dominated the orbit error budget. Much of the error due to dynamic mismodeling can be compensated by reduced-dynamic tracking techniques depending on the measurement system strength. In the last decade, the launch of the GRACE mission has eliminated the static gravity field as a concern, and the background force models and the terrestrial reference frame have been systematically refined. GPS systems have realized many improvements, including better modeling of the forces on the GPS spacecraft, large increases in the ground tracking network, and improved modeling of the GPS measurements. DORIS systems have achieved improvements through the use of new antennae, more stable monumentation, and of satellite receivers that can track multiple beacons, and as well as through improved modeling of the nonconservative forces. Many of these improvements have been applied in the new reprocessed time series of orbits produced for the ERS satellites, Envisat, TOPEX/Poseidon and the Jason satellites, and as well as for the most recent Cryosat-2 and HY2A. We now face the challenge of maintaining a stable orbit reference for these altimetric satellites. Changes in the time-variable gravity field of the Earth and how these are modelled have been shown to affect the orbit evolution, and the calibration of the altimetric data with tide gauges. The accuracy of the reference frame realizations, and their projection into the future remains a source of error. Other sources of omission error include the geocenter for which no consensus model is as of yet applied. Although progress has been made in nonconservative force modeling through the use of detailed satellite-specific models, radiation pressure modeling, and atmospheric density modeling remain a potential source of orbit error. The longer term influence of variations in the solar and terrestrial radiation fields over annual and solar cycles remains principally untested. Also the long term variation in optical and thermal properties of the space vehicle surfaces would contribute to biases in the orbital frame if ignored. We review the status of altimetric precision orbit determination as exemplified by the recent computations undertaken by the different analysis centers for ERS, Envisat, TOPEX/Poseidon, Jason, Cryosat2 and HY2A, and we provide a perspective on the challenges for future missions such as the Jason-3, SENTINEL-3 and SWOT.

Lemoine, Frank G.↗

NASA NTRS1990

Sensitivity of high-accuracy Tracking and Data Relay Satellite System (TDRSS) user spacecraft orbit determination to tracking schedules

The results of a study to analyze the dependence of TDRSS user spacecraft orbit determination consistencies on varying tracking schedules are presented. In this study, the TDRS-East orbit determination results obtained utilizing Bilateration Ranging Transponder System data were evaluated. Six state parameters, three position and three velocity components and the solar radiation pressure coefficient, are estimated for TDRS-East. It is concluded that, in order to achieve high-precision orbit determination, the tracking coverage should not fall below 10 minutes every two orbits as decreasing it to every four orbits will significantly degrade the accuracy; present state-of-the-art consistency in orbit determination using TDRSS tracking is approximately 15 to 20 meters.

Doll, C. E.↗

NASA NTRS1999

Lunar Prospector Orbit Determination Uncertainties Using the High Resolution Lunar Gravity Models

The Lunar Prospector (LP) mission began on January 6, 1998, when the LP spacecraft was launched from Cape Canaveral, Florida. The objectives of the mission were to determine whether water ice exists at the lunar poles, generate a global compositional map of the lunar surface, detect lunar outgassing, and improve knowledge of the lunar magnetic and gravity fields. Orbit determination of LP performed at the Jet Propulsion Laboratory (JPL) is conducted as part of the principal science investigation of the lunar gravity field. This paper will describe the JPL effort in support of the LP Gravity Investigation. This support includes high precision orbit determination, gravity model validation, and data editing. A description of the mission and its trajectory will be provided first, followed by a discussion of the orbit determination estimation procedure and models. Accuracies will be examined in terms of orbit-to-orbit solution differences, as a function of oblateness model truncation, and inclination in the plane-of-sky. Long term predictions for several gravity fields will be compared to the reconstructed orbits to demonstrate the accuracy of the orbit determination and oblateness fields developed by the Principal Gravity Investigator.

Carranza, Eric↗

NASA NTRS2017

Orbit Determination of the Lunar Reconnaissance Orbiter: Status After Seven Years

The Lunar Reconnaissance Orbiter (LRO) has been orbiting the Moon since 2009, obtaining unique and foundational datasets important to understanding the evolution of the Moon and the Solar System. The high-resolution data acquired by LRO benefit from precise orbit determination (OD), limiting the need for geolocation and co-registration tasks. The initial position knowledge requirement (50 m) was met with radio tracking from ground stations, after combination with LOLA altimetric crossovers. LRO-specific gravity field solutions were determined and allowed radio-only OD to perform at the level of 20 m, although secular inclination changes required frequent updates. The high-accuracy gravity fields from GRAIL, with <10 km spatial resolution, further improved the radio-only orbit reconstruction quality (<10 m). However, orbit reconstruction is in part limited by the 0.3-0.5 mm/s measurement noise level in S-band tracking. One-way tracking through Laser Ranging can supplement the tracking available for OD with 28-Hz ranges with 20-cm single-shot precision, but is available only on the nearside (the lunar hemisphere facing the Earth due to tidal locking). Here, we report on the status of the OD effort since the beginning of the mission, a period spanning more than seven years. We describe modeling improvements and the use of new measurements. In particular, the LOLA altimetric data give accurate, uniform, and independent information about LRO's orbit, with a different sensitivity and geometry which includes coverage over the lunar farside and is not tied to ground-based assets. With SLDEM2015 (a combination of the LOLA topographic profiles and the Kaguya Terrain Camera stereo images), another use of altimetry is possible for OD. We extend the 'direct altimetry' technique developed for the ICESat mission to perform OD and adjust spacecraft position to minimize discrepancies between LOLA tracks and SLDEM2015. Comparisons with the radio-only orbits are used to evaluate this new tracking type, of interest for the OD of future lunar orbiters carrying a laser altimeter. LROC NAC images also provide independent accuracy estimation, through the repeated views taken of anthropogenic features for instance.

Erwan Mazarico↗

NASA NTRS2017

Drag-Free Control and Drag Force Recovery of Small Satellites

Drag-free satellites provide autonomous precision orbit determination, accurately map the static and time varying components of Earth's mass distribution, aid in our understanding of the fundamental force of gravity, and will ultimately open up a new window to our universe through the detection and observation of gravitational waves. At the heart of this technology is a gravitational reference sensor, which (a) contains and shields a free-floating proof mass from all non-gravitational forces, and (b) precisely measures the position of the test mass inside the sensor. Thus, both test mass and spacecraft follow a pure geodesic in spacetime. By tracking the position of a low Earth orbiting drag-free satellite we can directly determine the detailed shape of geodesics and through analysis, the higher order harmonics of the Earths geopotential. This paper explores two different drag-free control systems on small satellites. The first drag-free control system is a continuously compensated single thruster 3-unit CubeSat with a suspension-free spherical proof-mass. A feedback control system commands the thruster and Attitude and Determination Control System to fly the tender spacecraft with respect to the test mass. The spheres position is sensed with a LED-based differential optical shadow sensor, its electric charge controlled by photoemission using UV LEDs, and the spacecraft position is maintained with respect to the sphere using an ion electrospray propulsion system. This configuration is the most fuel-efficient drag-free system possible today. The second drag-free control system is an electro-statically suspended cubical proof-mass that is operated with a low duty cycle, limiting suspension force noise over brief, known time intervals on a small GRACE-II -like satellite. The readout is performed using a laser interferometer, which is immune to the dynamic range limitations of voltage references. This system eliminates the need for a thruster, enabling drag-free control systems for passive satellites. In both cases, the test mass position, GPS tracking data, and commanded actuation, either thrust or suspension system, can be analyzed to estimate the 3-axis drag forces acting on the satellite. The data produces the most precise maps of upper atmospheric drag forces and with additional information, detailed models that describe the dynamics of the upper atmosphere and its impact on all satellites that orbit the Earth. This paper highlights the history, applications, design, laboratory technology development and highly detailed simulation results of each control system.

Small Satellites↗

NASA NTRS1990

The application of Encke's method to long arc orbit determination solutions

The Laser Geodynamics Satellite (LAGEOS) was launched on May 4, 1976 to provide geophysical measurements by means of laser ranging techniques. To date, over twelve years of laser range measurements have been collected from various tracking stations located around the world. Laser range measurements to LAGEOS have contributed to studies of earth rotation, plate tectonics, global baseline, and the gravity field as well as many other areas. Some of these studies are based upon the determination of a single, continuous orbit for LAGEOS for time spans on the order of several years. Current studies at the University of Texas Center for Space Research include the precision orbit determination of LAGEOS for arc lengths of up to 12.8 years which represents over 31,000 orbital revolutions. These long arc studies have led to the implementation of Encke's method to improve the convergence of the batch filter while reducing numerical integration errors. While the technique has been successfully applied to arc lengths of up to 12.8 years, the results presented focus on the solution of a six-year arc.

Lundberg, J. B.↗

NASA NTRS2011

Time Variable Gravity modeling for Precise Orbits Across the TOPEX/Poseidon, Jason-l and Jason-2 Missions

Modeling of the Time Variable Gravity (TVG) is believed to constitute one of the the largest remaining source of orbit error for altimeter satellite POD. The GSFC operational TVG model consists of forward modeling the atmospheric gravity using ECMWF 6-hour pressure data, a GRACE derived 20x20 annual field to account for changes in the hydrology and ocean water mass, and linear rates for C20, C30, C40, based on 17 years of SLR data analysis (IERS 2003) using the EIGEN-GL04S1 (a GRACE+Lageos-based geopotential solution). Although the GSFC Operational model can be applied from 1987, there may be long-term variations not captured by these linear models, and more importantly the linear models may not be consistent with more recent surface mass trends due to global climate change, We have evaluated the impact of TVG in two different wavs: (1) by using the more recent EIGEN-6S gravity model developed by the GFZ/GRGS tearm, which consists of annual, semi-annual and secular changes in the coefficients to 50x50 determined over 8(?) years of GRACE+Lageos+GOCE data (2003-200?): (2) Application of 4x4 solutions developed from a multi satellite SLR+DORIS solution based on GGM03S that span the period from 1993 to 2011. We have evaluated the recently released EIGEN6s static and time-varying gravity field for Jason-2 (J2). Jason-I (J1), and TOPEX/Posiedon (TP) Precise Orbit Determination (POD) spanning 1993-2011. Although EIGEN6s shows significant improvement for J2POD spanning 2008 - 2011, it also shows significant degradation for TP POD from 1992. The GSFC 4x4 time SLR+DORIS-based series spans 1993 to mid 2011, and shows promise for POD. We evaluate the performance of the different TVG models based on analysis of tracking data residuals use of independent data such as altimeter crossovers, and through analysis of differences with internally-generated and externally generated orbits.

Zelensky, Nikita P.↗

NASA NTRS2011

Combined Weekly Coordinate Solutions from SLR and DORIS

In International Terrestrial Reference Frame (ITRF) 2005 and ITRF2008, the approach for the construction of solutions by the IERS has been for individual analysis centers of each technique to process geodetic tracking data, and for each technique to develop a solution (or contribution) that is integrated into the final ITRF solution by careful combination of the technique solutions. The connections between the geodetic networks are realized by the application of local ties. In an alternate approach, we may assure processing homogeneity by creating normal equations for different techniques with the same orbit determination software, using identically derived algorithms. Another derivative of this approach is to realize the ties between the techniques using satellites tracked with multiple techniques; in effect tieing the networks together using satellite dynamics. In this solution, we develop a time series and a set of cumulative solutions from Satellite Laser Ranging (SLR) & Doppler Orbitography and Radio-positioning Integrated by Satellite (DORIS) based on homogeneous processing with the NASA GEODYN precise orbit determination suite of programs, where we jointly combine weekly the SLR data to Lageos1, Lageos2, Starlette, and Stella with the DORIS data from SPOT2-SPOT5, as well as satellites that utilize both techniques (TOPEX/Poseidon, Envisat, Jason-2). We discuss the modeling that is applied including upgrades implemented since the submission of the GSC ITRF2008 contributions for IDS. Firstly, we compare the SLR-only solutions comprising four geodetic satellites with the standard approach of utilizing only Lageos1 & Lageos2. Secondly, we evaluate the impact on the DORIS coordinates of the joint analysis with the SLR data.

Lemoine, F.↗

NASA NTRS1988

Sub-meter GPS orbit determination and high precision user positioning - A demonstration

High-accuracy orbit solutions have been obtained for GPS satellites, and submeter orbit accuracy is demonstrated for two well-tracked satellites. Orbit accuracy was tested based upon orbit repeatability from independent data sets, orbit prediction, ground baseline determination, and formal errors. Baselines of up to 2000 km in North America found with the GPS orbits show a daily repeatability of 0.3-1.5 parts in 10 to the 8th, and are found to agree well with VLBI solutions at the level of 0.3-3 parts in 10 to the 8th. Baselines were also determined between Florida and sites in the Caribbean region over 1000 km away, with a daily repeatability of 1-4 parts in 10 to the 8th.

Lichten, Stephen M.↗

NASA NTRS2015

Hubble Space Telescope Astrometry of the Procyon System

The nearby star Procyon is a visual binary containing the F5 IV-V subgiant Procyon A, orbited in a 40.84-year period by the faint DQZ white dwarf (WD) Procyon B. Using images obtained over two decades with the Hubble Space Telescope, and historical measurements back to the 19th century, we have determined precise orbital elements. Combined with measurements of the parallax and the motion of the A component, these elements yield dynamical masses of 1.478 plus or minus 0.012M and 0.592 plus or minus 0.006M for A and B, respectively. The mass of Procyon A agrees well with theoretical predictions based on asteroseismology and its temperature and luminosity. Use of a standard core-overshoot model agrees best for a surprisingly high amount of core overshoot. Under these modeling assumptions, Procyon A's age is approximately 2.7 Gyr. Procyon B's location in the H-R diagram is in excellent agreement with theoretical cooling tracks for WDs of its dynamical mass. Its position in the mass-radius plane is also consistent with theory, assuming a carbon-oxygen core and a helium-dominated atmosphere. Its progenitor's mass was 1.9-2.2M, depending on its amount of core overshoot. Several astrophysical puzzles remain. In the progenitor system, the stars at periastron were separated by only approximately AU, which might have led to tidal interactions and even mass transfer; yet there is no direct evidence that these have occurred. Moreover the orbital eccentricity has remained high (approximately 0.40). The mass of Procyon B is somewhat lower than anticipated from the initial-to-final-mass relation seen in open clusters. The presence of heavy elements in its atmosphere requires ongoing accretion, but the place of origin is uncertain.

PROCYON↗