Novel Concepts for Precise Low Earth Orbiter Navigation With GPS
The Global Positioning System (GPS) is widely used for satellite positioning and navigation, and for numerous geolocation activities.
GPS↗
Engineering topics
Thornton, C. L.
Publications and source records attributed to Thornton, C. L..
Satellite Constellations for Atmospheric Sounding with GPS: A Revolution in Atmospheric and Ionospheric Research
Spaceborne Global Positioning System (GPS) atmospheric science is blossoming. Proposed missions require high performance GPS flight receivers with capabilities beyond most space needs. With GPS technology maturing, and lower cost spaceborne receivers, GPS usage is expanding rapidly for space flight projects. Several of these are discussed, such as atmospheric occultation, ionospheric imaging, etc.
Global Positioning System GPS Atmospheric Science ↗
Reduced-dynamic technique for precise orbit determination of low earth satellites
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Wu, S. C.↗
A reduced-dynamic technique for precise orbit determination
Observations of the Global Positioning System (GPS) will enable a reduced-dynamic technique for achieving subdecimeter orbit determination of earth-orbiting satellites. With this technique, information on the transition between satellite states at different observing times is furnished by both a formal dynamic model and observed satellite positional change (which is inferred kinematically from continuous GPS carrier-phase data). The relative weighting of dynamic and kinematic information can be freely varied. Covariance studies show that in situations where observing geometry is poor and the dynamic model is good, the model dominates determination of the state transition; where the dynamic model is poor and the geometry strong, carrier phase governs the determination of the transition. When neither kinematic nor dynamic information is clearly superior, the reduced-dynamic combination of the two can substantially improve the orbit-determination solution. Guidelines are given here for selecting a near-optimal weighting for the reduced-dynamic solution, and sensitivity of solution accuracy to this weighting is examined.
Wu, S. C.↗
Demonstration of the fiducial concept using data from the March 1985 GPS field test
The first field test of NASA's Global Positioning System (GPS) Geodetic Program took place in March of 1985. The principal objective of this test was the demonstration of the feasibility of the fiducial station approach to precise GPS-based geodesy and orbit determination. Other objectives included an assessment of the performance of the several GPS receiver types involved in these field tests and the testing of the GIPSY software for GPS data analysis. In this article, the GIPSY (GPS Inferred Positioning System) software system is described and baseline solutions are examined for consistency with independent measurements made using very long baseline interferometry.
Davidson, J. M.↗
The March 1985 demonstration of the fiducial network concept for GPS geodesy: A preliminary report
The first field tests in preparation for the NASA Global Positioning System (GPS) Caribbean Initiative were conducted in late March and Early April of 1985. The GPS receivers were located at the POLARIS Very Long Base Interferometry (VLBI) stations at Westford, Massachusetts; Richmond, Florida; and Ft. Davis, Texas; and at the Mojave, Owens Valley, and Hat Creek VLBI stations in California. Other mobile receivers were placed near Mammoth Lakes, California; Pt. Mugu, California; Austin, Texas; and Dahlgren, Virginia. These sites were equipped with a combination of GPS receiver types, including SERIES-X, TI-4100 and AFGL dual frequency receivers. The principal objectives of these tests were the demonstration of the fiducial network concept for precise GPS geodesy, the performance assessment of the participating GPS receiver types, and to conduct the first in a series of experiments to monitor ground deformation in the Mammoth Lakes-Long Valley caldera region in California. Other objectives included the testing of the water vapor radiometers for the calibration of GPS data, the development of efficient procedures for planning and coordinating GPS field exercise, the establishment of institutional interfaces for future cooperating ventures, the testing of the GPS Data Analysis Software (GIPSY, for GPS Inferred Positioning SYstem), and the establishment of a set of calibration baselines in California. Preliminary reports of the success of the field tests, including receiver performance and data quality, and on the status of the data analysis software are given.
Davidson, J. M.↗
GPS-based satellite tracking system for precise positioning
NASA is developing a Global Positioning System (GPS) based measurement system to provide precise determination of earth satellite orbits, geodetic baselines, ionospheric electron content, and clock offsets between worldwide tracking sites. The system will employ variations on the differential GPS observing technique and will use a network of nine fixed ground terminals. Satellite applications will require either a GPS flight receiver or an on-board GPS beacon. Operation of the system for all but satellite tracking will begin by 1988. The first major satellite application will be a demonstration of decimeter accuracy in determining the altitude of TOPEX in the early 1990's. By then the system is expected to yield long-baseline accuracies of a few centimeters and instantaneous time synchronization to 1 ns.
Yunck, T. P.↗
Constraints on Pacific plate kinematics and dynamics with global positioning system measurements
A measurement program designed to investigate kinematic and dynamic aspects of plate tectonics in the Pacific region by means of satellite observations is proposed. Accuracy studies are summarized showing that for short baselines (less than 100 km), the measuring accuracy of global positioning system (GPS) receivers can be in the centimeter range. For longer baselines, uncertainty in the orbital ephemerides of the GPS satellites could be a major source of error. Simultaneous observations at widely (about 300 km) separated fiducial stations over the Pacific region, should permit an accuracy in the centimeter range for baselines of up to several thousand kilometers. The optimum performance level is based on the assumption of that fiducial baselines are known a priori to the centimeter range. An example fiducial network for a GPS study of the South Pacific region is described.
Dixon, T. H.↗
GPS-based certification for the microwave landing system
An MLS (microwave landing system) certification system based on the Global Positioning System (GPS) is described. To determine the position history of the flight inspection aircraft during runway approach, signals from the GPS satellites, together with on-board radar altimetry, are used. It is shown that the aircraft position relative to a fixed point on the runway at threshold can be determined to about 30 cm vertically and 1 m horizontally. A requirement of the system is that the GPS receivers be placed on each flight inspection aircraft and at selected ground sites. The effects of different error sources on the determination of aircraft instantaneous position and its dynamics are analyzed.
Thornton, C. L.↗
UDU/T/ covariance factorization for Kalman filtering
There has been strong motivation to produce numerically stable formulations of the Kalman filter algorithms because it has long been known that the original discrete-time Kalman formulas are numerically unreliable. Numerical instability can be avoided by propagating certain factors of the estimate error covariance matrix rather than the covariance matrix itself. This paper documents filter algorithms that correspond to the covariance factorization P = UDU(T), where U is a unit upper triangular matrix and D is diagonal. Emphasis is on computational efficiency and numerical stability, since these properties are of key importance in real-time filter applications. The history of square-root and U-D covariance filters is reviewed. Simple examples are given to illustrate the numerical inadequacy of the Kalman covariance filter algorithms; these examples show how factorization techniques can give improved computational reliability.
Thornton, C. L.↗
Elements of solar sail navigation with application to a Halley's comet rendezvous
The problem of interplanetary navigation of a solar sail spacecraft is examined and found to be analogous to that of solar electric spacecraft. The dominant navigation error sources are shown to be accelerations that are unaccounted for in the description of the vehicle's motion, due to the inability to precisely model the solar radiation pressure. A strategy for navigation in the presence of these accelerations is devised, based on techniques previously developed for solar electric vehicles. An evaluation of the strategy is made for a Halley's comet rendezvous mission, and the results of that evaluation indicate that the strategy gives acceptable performance.
Jacobson, R. A.↗
Filtering and error analysis via the UDU super T covariance factorization
Kalman filter algorithms based on the UDU super T covariance factorization are discussed, with special attention given to algorithm implementation efficiency. A U-D-factored covariance error-analysis algorithm is formulated, and its efficiency and numerical stability are demonstrated in a representative orbit determination problem. The numerical results are compared with those obtained using covariance error-analysis formulas, and the comparison highlights the numerical superiority of the present algorithm. A byproduct of the U-D analysis is a highly efficient algorithm mechanization of the arbitrary gain covariance update formula.
Thornton, C. L.↗
Navigation capability for an ion drive rendezvous with Halley's Comet
Navigation accuracies are presented for a 1985 rendezvous with Halley's Comet using an ion propulsion system. Individual error sources are examined to determine their relative contributions to final delivery errors. The sensitivity of delivery accuracy to stochastic thrust variations is demonstrated by considering a baseline thrust error model and a more benign alternative model. Also studied are the effects of increased comet ephemeris uncertainties and of operational time delays between the orbit determination process and the guidance implementation.
Thornton, C. L.↗
Linear stochastic control using the UDU matrix factorization
The classical LQG stochastic control law is reformulated using the matrix factorization S equals UDU super T. This method yields a statistical guidance analysis algorithm that is numerically superior to the classical solution yet requires negligible additional computation and storage. Moreover, experience with U-D algorithms has shown them to be adaptable and easy to implement on a variety of problems.
Thornton, C. L.↗
Navigation capability for an ion drive rendezvous with Halley's Comet
An analysis has been conducted in connection with plans for a study of Halley's Comet during its 1986 apparition. The use of low-thrust vehicles, utilizing an ion drive system, is being considered for a comet rendezvous mission. A preliminary trajectory for the Halley rendezvous mission calls for launch on June 20, 1982, followed by rendezvous on December 21, 1985. The navigation analysis described focuses on the terminal approach to Halley, the 60-day period preceding rendezvous. Navigation analysis assumptions are examined, taking into account navigation error sources, radio tracking, onboard optical data, earth-based comet observations, and orbit determination and guidance strategies. The preliminary mission design considers a rendezvous at approximately 56,000 km from the comet nucleus (6,000 km outside the dust envelope). Navigation performance is measured in terms of comet-relative position and velocity errors at encounter. Variations to the baseline navigation study provide illustrations concerning the close link between delivery accuracy and stochastic thrust errors.
Thornton, C. L.↗
Gram-Schmidt algorithms for covariance propagation
This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UD(transpose of U), where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and coloured process noise parameters increase mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.
Thornton, C. L.↗
Numerical comparison of Kalman filter algorithms - Orbit determination case study
Numerical characteristics of various Kalman filter algorithms are illustrated with a realistic orbit determination study. The case study of this paper highlights the numerical deficiencies of the conventional and stabilized Kalman algorithms. Computational errors associated with these algorithms are found to be so large as to obscure important mismodeling effects and thus cause misleading estimates of filter accuracy. The positive result of this study is that the U-D covariance factorization algorithm has excellent numerical properties and is computationally efficient, having CPU costs that differ negligibly from the conventional Kalman costs. Accuracies of the U-D filter using single precision arithmetic consistently match the double precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity to variations in the a priori statistics.
Bierman, G. J.↗
Triangular covariance factorizations for
An improved computational form of the discrete Kalman filter is derived using an upper triangular factorization of the error covariance matrix. The covariance P is factored such that P = UDUT where U is unit upper triangular and D is diagonal. Recursions are developed for propagating the U-D covariance factors together with the corresponding state estimate. The resulting algorithm, referred to as the U-D filter, combines the superior numerical precision of square root filtering techniques with an efficiency comparable to that of Kalman's original formula. Moreover, this method is easily implemented and involves no more computer storage than the Kalman algorithm. These characteristics make the U-D method an attractive realtime filtering technique. A new covariance error analysis technique is obtained from an extension of the U-D filter equations. This evaluation method is flexible and efficient and may provide significantly improved numerical results. Cost comparisons show that for a large class of problems the U-D evaluation algorithm is noticeably less expensive than conventional error analysis methods.
Thornton, C. L.↗