Range-rate Data Research Articles

An Approach for a Faster GPS Tracking Extended Kalman Filter

GPS is capable of providing 100 m level accuracy for a great number of users worldwide. In GPS, range and range-rate data can be used with satellite position and velocity to compute user position and velocity using an extended Kalman filter (EKF). However, the EKF is computationally intensive, leading to difficulties in broadband real-time applications. Hence, it is necessary to resort to techniques to improve EKF speed. Therefore, in this paper, the EKF matrices are analyzed in detail, exploiting the sparsity and structure of the EKF matrices to reduce the number of computations. A typical trajectory is simulated, and a comparison of the computation speed of sequential implementations of EKF, both with and without the proposed reduction of computations, is reported. Further, an algorithm is developed to obtain an initial estimate of user position and velocity which is used to initialize the state vector of the EKF algorithm.

Precision orbit determination for TOPEX/Poseidon using TDRSS doppler tracking data

Precision orbit determination on the TOPEX/Poseidon (T/P) altimeter satellite is now being routinely achieved with sub-5cm radial and sub-15 cm total positioning accuracy using state-of-the-art modeling with precision tracking provided by a combination of: (a) global Satellite Laser Ranging (SLR) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), or (b) the Global Positioning System (GPS) Constellation which provides pseudo-range and carrier phase observations. The geostationary Tracking and Data Relay Satellite System (TDRSS) satellites are providing the operational tracking and communication support for this mission. The TDRSS Doppler data are of high precision (0.3 mm/s nominal noise levels). Unlike other satellite missions supported operationally by TDRSS, T/P has high quality independent tracking which enables absolute orbit accuracy assessments. In addition, the T/P satellite provides extensive geometry for positioning a satellite at geostationary altitude, and thus the TDRSS-T/P data provides an excellent means for determining the TDRS orbits. Arc lengths of 7 and 10 days with varying degrees of T/P spacecraft attitude complexity are studied. Sub-meter T/P total positioning error is achieved when using the TDRSS range-rate data, with radial orbit errors of 10.6 cm and 15.5 cm RMS for the two arcs studied. Current limitations in the TDRSS precision orbit determination capability include mismodeling of numerous TDRSS satellite-specific dynamic and electronic effects, and in the inadequate treatment of the propagation delay and bending arising from the wet troposphere and ionosphere.

Flight Test Evaluation of Precision-Code Differential GPS for Terminal Approach and Landing

A flight test evaluation conducted at the NASA Ames Research Center of precision-code differential GPS for terminal approach and landing is described. Differential corrections to satellite range and range-rate measurements are computed in a stationary ground reference system, uplinked to the test aircraft, and employed to correct corresponding airborne satellite data. Differentially corrected range and range-rate data, combined with inertial data, are then utilized with satellite position and velocity to compute aircraft position and velocity employing an eight-state extended Kalman filter.

The GEM‐T2 Gravitational Model

GEM‐T2 is the latest in a series of Goddard Earth models of the terrestrial gravitational field. It is the second in a planned sequence of gravity models designed to improve both the modeling capabilities for determining the TOPEX/Poseidon satellite's radial position to an accuracy of 10‐cm RMS and for defining the long‐wavelength geoid to support many oceanographic and geophysical applications. GEM‐T2 includes more than 6OU coefficients above degree 36, the limit for GEM‐T1, and provides a dynamically determined model of the major tidal components which contains 90 terms. Like GEM‐T1, it was produced entirely from satellite tracking data. GEM‐T2 however, now uses nearly twice as many satellites (31 versus 17), contains 3 times the number of observations (2.4 million), and has twice the number of data arcs (1130). GEM‐T2 utilizes laser tracking from 11 satellites, Doppler data from four satellites, two‐ and three‐way range rate data from Landsat‐1, satellite‐to‐satellite tracking data between the geosynchronous ATS 6 and GEOS 3, and optical observations on 20 different orbits. This observation set effectively exhausts the inclination distribution available for gravitational field development from our historical data base. The recovery of the higher degree and order coefficients in GEM‐T2 was made possible through the application of a constrained least squares technique using the known spectrum of the Earth's gravity field as a priori information. The error calibration of the model was performed concurrently with its generation by comparing the complete model against test solutions which omit each individually identifiable data set in turn. The differences between the solutions isolate the contribution of a given data set, and the magnitudes of these differences are compared for consistency against their expected values from the respective solution covariances. The process yields near optimal data weights and assures that the model will be both self‐consistent and well calibrated. GEM‐T2 has benefitted by its application as demonstrated through comparisons using independently derived gravity anomalies from altimelry. Results for the GEM‐T2 error calibration indicate significant improvement over previous satellite‐only GEM models. The accuracy assessment of the lower degree and order coefficients of GEM‐T2 shows that their uncertainties have been reduced by 20% compared to GEM‐T1. The commission error of the geoid has been reduced from 160 cm for GEM‐T1 to 130 cm for GEM‐T2 for the 36 × 36 portion of the field. The orbital accuracies achieved using GEM‐T2 are likewise improved. This is especially true for the Starlette and GEOS 3 orbits where higher‐order resonance terms not present in GEM‐T1 (e.g., terms with m = 42,43) are now well represented in GEM‐T2. The improvement in orbital accuracy of GEM‐T2 over GEM‐T1 extends across all orbit inclinations. This confirms our conclusion that GEM‐T2 offers a significant advance in knowledge of the Earth's gravity field.

Navigation and Guidance Problems of Japanese Space VLBI Satellite - VSOP

The Institute of Space and Astronautical Science (ISAS) of Japan is planning to launch a space VLBI (Very Long Baseline Interferometory) satellite called VSOP (VLBI Space Observatory Programme) in 1995. The weight of this VSOP is about 800kg, carrying a gigantic parabolla antenna, 10m in diameter, and its trajectory is1,000 km in perigee and 20,000 km in apogee.Simultaneously combined with many ground radio observatories over the world, this satellite will receive signals from various radio sources such as quasars and radio galaxies. When these observed data are transmitted to the ground in 64 MHz wide band-width channel, they are correlated with the ground observations, yielding precise maps representing internal structures of such radio sources.Navigation and guidance problems of this VSOP will be discussed in this paper. Particullary the attitude control problem that requires one hundredth degree in pointing of the antenna imposes severe restriction on the guidance system, because of flexible structures of the large antenna and solar cell paddles.(Fig.1)Also the clock synchronization, i.e. maintaining precise time-tags on the observed data by the satellite, synchronized with the very stable atomic clocks such as hydrogen masers on the ground, will become a crucial, technological problem. For this purpose, a beacon carrying precise clock information will be transmitted to the satellite and it will be returned to the ground. Later, these signals are calibrated using informations of the trajectory, troposphere, ionosphere, etc., in order to detect exact timing on the spacecraft. Hence very accurate orbit determnation of the spacecraft is required. In order to augment the radiometric data such as range and range-rate data, the GPS(Global Positioning System) receiver may be placed on-board

Preliminary orbit determination using satellite-to-satellite limited range and range-rate data

A method is presented for the problem of preliminary orbit determination by use of limited range and/or range-rate data with random initial guesses. This method, based on observation function minimization techniques, is essentially a deterministic process. The problem considered consists of an unknown geocentric satellite observed by either one or two tracking satellites using minimum measurement data sets for the determination of the unknown satellite's orbital elements. Additional data, in excess of the minimum data, are used to identify spurious solutions. The feasibility of achieving satisfactory orbit determination has been explored by simulation studies. It is found that using two observers to track the unknown satellite produces faster convergence even with poor initial guesses. Numerical examples show that computational time can be reduced about ten to thirty percent over that using only one observer.

Locating and determining the orientation of underwater research equipment: Acoustic range and range rate data

A formulation is presented for evaluating the performance of acoustic data systems to determine the location and orientation of underwater research apparatus. The variables to describe the position of the underwater research apparatus are referenced to a surface ship, and represent the straight-line distance from the stern of the ship to a point on the apparatus ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</tex> ), the angular distance down from the sea surface ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Phi</tex> ), and the angular distance from the direction of motion of the ship ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Theta</tex> ). The three orientation variables on the apparatus are the angle between the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z'</tex> axes ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</tex> ), the angle between the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x'</tex> axes in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x'-y'</tex> plane ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Omega</tex> ), and the angle which locates the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x'</tex> axis in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x'-y'</tex> plane ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega</tex> ). A simple model for the sound velocity variation with depth is included in the range data analysis, while the Doppler data are shown not to need that further complication in the analysis. An error model is constructed and applied to three geometries which represent common underwater research devices. Accuracy goals for possible applications of these devices are discussed, and performance requirements for an acoustic system which would meet the goals are derived.

VHF Tracking Transponder Onboard Bhaskara II

This paper presents the system design, hardware realization and inorbit performance of VHF Tracking Transponder onboard BHASKARA II. The system as a prime payload is being used for transponding the tracking data for the satellite. The range and range rate data obtained from the satellite is used for the orbital parameter updating and orbit prediction for the satellite.

New filter for radar use and its microprocessor realization†

A new digital filter is presented for use in radar systems to extract smoothed range and range rate data from noisy range data. The performance of a real-time micro-processor realization of the filter is discussed, and comparisons are provided with fillers that have been previously reported.

On the recovery of geopotential coefficients using satellite-to-satellite range-rate data on a sphere

If satellite range-rate information is given continuously on an extra terrestrial sphere (S), the spherical harmonic coefficients of the gravitational potential of the Earth can be determined by direct integration of the data. An exact solution is given in the case when circular satellite orbits crosses S in all directions. A simpler acquisition of the data is achieved when the observations are restricted to polar satellite orbits. However, in this case the solutions become more complex due to attenuation. A solution to order sin Δ, where Δ is the separation angle of the two satellites, is given for the zonal harmonics. For tesseral hamonics a zero-order solution is derived. Corrections are given for observations out of S.

Gravitational spectra from direct measurements

A simple rapid method is described for determining the spectrum of a surface field (in spherical harmonics) from harmonic analysis of direct (in situ) measurements along great circle arcs. The method is shown to give excellent overall trends (smoothed spectra) to very high degree from even a few short arcs of satellite data. Three examples are taken with perfect measurements of satellite tracking over a planet made up of hundreds of point masses using (1) altimetric heights from a low‐orbiting spacecraft, (2) velocity (range rate) residuals between a low and a high satellite in circular orbits, and (3) range rate data between a station at infinity and a satellite in a highly eccentric orbit. In particular, the smoothed spectrum of the earth's gravitational field is determined to about degree 400(50‐km half wavelength) from 1° × 1° gravimetry and the equivalent of 11 revolutions of Geos 3 and Skylab altimetry. This measurement shows there is about 46 cm of geoid height (rms worldwide) remaining in the field beyond degree 180.

Platform Location and Data Collection by Satellite Systems the EOLE Experiment

A technical description of the EOLE location and data collection system with 480 constant level balloons released in the Southern Hemisphere is presented : the EOLE satellite contacts successively each platform, acquires and stores range and range rate data allowing computation of the location of each transponder and meteorological data measured by the plat form sensors. This information is stored on board and then read out by telemetry upon reception of a command from ground stations. The experiment itself is described and the main technical results are analyzed ; the ultimate location accuracy of the EOLE System was found to be of the order of 300 meters for fixed platforms but, some difficulties concerning the Location of drifting balloons were encountered due to the necessity of compensating the Doppler shift for platform motion. The main scientific results are briefly presented as well as some post-EOLE experiments. Future developments of this type of location and data collection system are described as a conclusion.

Electrooptical processing for radio astronomy

A recent report of the first computer-generated radio-derived photographs of the Whirlpool Galaxy will no doubt provide impetus for additional radio photography of astronomical events. Electro-optical techniques, developed in the past decade for obtaining high resolution range, range-rate, and angular target data with array radars, may be highly suitable for generating visible images of astronomical events. The electrooptical processor can furnish continuously and unambiguously, in the form of an optical image, the distribution of radio emission present in the entire effective scan sector of an array without the necessity of electronic steering.

The ATS-F/NIMBUS-E Tracking Experiment

In this paper the objective of the ATS-F/NIMBUS-E Tracking Experiment, the first of such kind, is presented. Specifically, this experiment has a two-fold purpose: First, to gain experience in the practical use of satellite-to-satellite range and range rate data for very accurate orbit determination (this was its original intent); and second, to evaluate the real usefulness of such a technique for geodetic studies despite the fact that the 1000 km NIMBUS orbit is not ideally suited for such a purpose.The accuracies of the tracking systems of the satellite-to-satellite and satellite-to-ground link (ATS-F to the Rosman, N.C. ground station) will be ~ 0.035 cm/s in range rate and ~ 1 m in range – utilizing a 10 s integration time. With these values one obtains, based upon performed error analyses, orbit height errors in the order of 0.1 to 0.3 m for the near earth orbiting NIMBUS spacecraft. This experiment will therefore hopefully prove to be a significant first step for future Earth applications spacecraft carrying altimeters systems for measuring ocean height variations.In addition, laser corner reflectors placed on board the ATS-F will make a total independent position determination of this spacecraft to approximately 15 m to 30 m possible, assuming that the location errors of four laser tracking stations used to determine the orbit are about 3 m or 5 m in each component respectively, with laser ranging system noise errors of 1.2 m and bias errors of 0.15 m. A small position error of the ATS-F, the ‘orbiting tracking station’ is essential in order to make full usage of the small satellite-to-satellite tracking errors mentioned.For purpose of geodetic studies, one of the final goals, range rate variations of 0.1 cm/s or less corresponding to surface gravity anomaly of 20 mgal or less (over a half-width of 100 km on the Earth surface), will have to be measured during a time interval of approximately, say, 30–60 s. These values are within the range of the planned tracking systems accuracies for ATS-F and NIMBUS-E.

Algorithm to compute tropospheric refraction effects on range measurements

A two-quartic tropospheric refractivity profile for correcting satellite data has been modeled by Hopfield [1969, 197O]. Her model is theoretically based on a troposphere with constant lapse rate of temperature. It treats the “dry” and “wet” components of the tropospheric refractivity N separately and represents each as a fourth-degree function of height above the geoid. Expressions are given to compute the contributions to both range and range rate data.

CAS Message Format

The collision avoidance system (CAS) defined by the ATA provides for the exchange of range, range-rate, and altitude data, as well as the less significant items of altitude rate and north-south and east-west velocity vector data. This paper discusses the CAS message format and presents data (based on McDonnell-Douglas in-flight experience with its EROS system) on the accuracy of gathering the CAS data.