Local gravity disturbance estimation from multiple-high-single-low satellite-to-satellite tracking

The idea of satellite-to-satellite tracking in the high-low mode has received renewed attention in light of the uncertain future of NASA's proposed low-low mission, Geopotential Research Mission (GRM). The principal disadvantage with a high-low system is the increased time interval required to obtain global coverage since the intersatellite visibility is often obscured by Earth. The U.S. Air Force has begun to investigate high-low satellite-to-satellite tracking between the Global Positioning System (GPS) of satellites (high component) and NASA's Space Transportation System (STS), the shuttle (low component). Because the GPS satellites form, or will form, a constellation enabling continuous three-dimensional tracking of a low-altitude orbiter, there will be no data gaps due to lack of intervisibility. Furthermore, all three components of the gravitation vector are estimable at altitude, a given grid of which gives a stronger estimate of gravity on Earth's surface than a similar grid of line-of-sight gravitation components. The proposed Air Force mission is STAGE (Shuttle-GPS Tracking for Anomalous Gravitation Estimation) and is designed for local gravity field determinations since the shuttle will likely not achieve polar orbits. The motivation for STAGE was the feasibility to obtain reasonable accuracies with absolutely minimal cost. Instead of simulating drag-free orbits, STAGE uses direct measurements of the nongravitational forces obtained by an inertial package onboard the shuttle. The sort of accuracies that would be achievable from STAGE vis-a-vis other satellite tracking missions such as GRM and European Space Agency's POPSAT-GRM are analyzed

Satellite-to-satellite tracking experiment for global gravity field mapping

The satellite-to-satellite (STS) tracking concept for estimating gravitational parameters offers an attractive means to improve on regional and global gravity models in areas where data availability is limited. The extent to which the STS tracking measurements can be effectively utilized in global field models depends primarily on the satellite's altitude, number of satellites, and their orbit constellation. The estimation accuracy of the gravity field recovery also depends on the measurement accuracy of the sensors employed in the STS tracking concept. A comparison of the obtainable accuracies in the gravity field recovery using various STS tracking concepts was presented by Jekeli. The results of a feasibility study for a specific realization of the STS high-low tracking concept are summarized. In this realization, the high altitude satellites are the GPS satellites, and the low orbit satellite is the space shuttle. The GPS satellite constellation consists of 18 satellites in 6 orbital planes inclined at 55 deg. The shuttle orbit is at approximately 300 km, with an inclination of 30 deg. This specific configuration of high-low satellites for measuring perturbation in the gravity field is named the Air Foce STAGE (Shuttle GPS Tracking for Anomalous Gravitation Estimation) mission. The STAGE mission objective is to estimate the perturbations in gravity vector at the shuttle altitude to an accuracy of 1 mgal or better. Recent simulation studies have confirmed that the 1 mgal accuracy objective is near optimum for the STAGE mission

Very accurate upward continuation to low heights in a test of non-Newtonian theory

Recently, gravity measurements were made on a tall, very stable television transmitting tower in order to detect a non-Newtonian gravitational force. This experiment required the upward continuation of gravity from the Earth's surface to points as high as only 600 m above ground. The upward continuation was based on a set of gravity anomalies in the vicinity of the tower whose data distribution exhibits essential circular symmetry and appropriate radial attenuation. Two methods were applied to perform the upward continuation - least-squares solution of a local harmonic expansion and least-squares collocation. Both methods yield comparable results, and have estimated accuracies on the order of 50 microGal or better (1 microGal = 10(exp -8) m/sq s). This order of accuracy is commensurate with the tower gravity measurments (which have an estimated accuracy of 20 microGal), and enabled a definitive detection of non-Newtonian gravity. As expected, such precise upward continuations require very dense data near the tower. Less expected was the requirement of data (though sparse) up to 220 km away from the tower (in the case that only an ellipsoidal reference gravity is applied)

INS/GPS Vector Gravimetry Along Roads in Western Montana

This project is supported under a contract with the National Geospatial-Intelligence Agency, contract no. NMA- NMA401-02-1-2005; and this report serves as an Interim Technical Report for the project.This document reports on a comprehensive look at the data collected by the GPSVan (OSU, Center for Mapping) in western Montana in April and June of 2005. The data consist of inertial measurement unit (IMU) data, extracted from high-accuracy inertial navigation systems, and differential GPS data that are combined to estimate the (3-D) gravity vector along the roadways traveled by the vehicle. The key to the evaluation of these tests and to their deemed success was the repeated runs of the traverses, rather than the existing control data in the region. The fairly dense network of gravity data provided only some overall corroboration of the accuracy in the vertical components of the estimates. The deflection of the vertical (DOV) data and other independent sources of computed DOV’s provided barely some long-wavelength confirmation of our estimates, while the repeatability of the traverses verified fine detail in the recovered horizontal components. However, this precision was not consistent and large errors remain in the horizontal components. The single largest detriment to our estimates was the inaccuracy in the kinematic GPS positioning solution. Due to road overpasses and other obstructions, the GPS solution was often degraded significantly due to the inability to solve for the cycle ambiguity. This had a direct and demonstrable effect on the gravity estimation. When all systems were working at peak performance, we showed better than mgal repeatability in the down component of the gravity disturbance and standard deviation of 2-3 mgal with respect to the interpolated control data. No attempt was made in this first analysis to solve for biases and linear trends, nor to take advantage of the multiple traverses to arrive at final along-track gravity disturbance estimates. Three essential conclusions were obtained from our analysis: 1) GPS solutions must be improved, e.g., using INS to help recover the cycle ambiguity after a GPS outage; 2) more direct, along-track control data are necessary, particularly in the horizontal components, to obtain a meaningful assessment of the vector gravimetry capability of the system; and 3) an operational system would clearly benefit from redundancy in instrumentation in order to imitate and take advantage of multiple traverses along each surveyed road. The first chapter summarizes the instrument setup, the survey routes, the data collected, and the control data available. The second chapter briefly reviews the techniques used to obtain the gravity vector estimates, relying heavily on previous publications and reports. Results of applying these techniques to the data are shown in Chapter 3; followed by the concluding chapter with comments and analyses, and an outlook toward further data processing

The Statistical Performance of the Matched Filter for Anomaly Detection Using Gravity Gradients

This document first reviews the theory of detecting a subsurface linear anomaly using the matched filter applied to observations of the gravitational gradient in the presence of a nominal gravitational background field and along tracks crossing the anomaly orthogonally or at an arbitrary angle. The maximum filter output indicates the likely location along the track and, with appropriate statistical assumptions on the background field and measurement noise, it also serves as a test statistic in the probabilistic evaluation of the filter’s performance. Different setups of the Neyman-Pearson statistical hypothesis test yield calculated probabilities of either a miss or a false alarm, respectively. The needed statistics of the maximum filter output are properly obtained using the distribution of order statistics. Through Monte Carlo simulations, we analyzed the ability of the matched filter to identify certain signals in typically correlated gravity fields using observations of elements of the gravity gradient tensor. We also evaluated the reliability of the hypothesis testing and of the associated calculated probabilities of misses and false alarms. We found that the hypothesis test that yields the probability of a miss is more robust than the one for the probability of a false alarm. Moreover, the probability of a miss is somewhat less than the probability of a false alarm under otherwise equal circumstances. Our simulations and statistical analyses confirm that the power of the tests increases as the signal strength increases and as more gradient tensor components per observation point are included. Finally, we found that the statistical methods apply only to single tracks (one-dimensional matched filter) and that the matched filter itself performs poorly for multiple parallel tracks (two-dimensional formulation) crossing a linear anomaly obliquely. Therefore, these methods are most useful, with respect to both the detection and the probability calculation, for single tracks of data crossing a linear anomaly (at arbitrary angle)

Synopsis of early field test results from the gravity gradiometer survey system

Although the amount of data yielded by the initial airborne and surface tests was modest, it was sufficient to demonstrate that the full gravity gradient tensor was successfully measured from moving platforms both in the air and on the surface. The measurements were effectively continuous with spatial along-track resolution limited only by choice of integration lengths taken to reduce noise. The airborne data were less noisy (800 E squared/Hz typical) than were the Gravity Gradiometer Survey System (GGSS) measurements taken at the surface (5000 E squared/Hz typical). Single tracks of surface gravity disturbances recovered from airborne data were accurate to 3 to 4 mgal in each component of gravity when compared to 5 x 5 mean gravity anomalies over a 90 km track. Multitrack processing yielded 2 to 3 mgal when compared to 5 x 5 mean anomalies. Deflection of the vertical recovery over a distance of 150 km was about one arcsecond

Orbital Gravity Gradiometry Beyond GOCE: Mission Concepts

Significant advances in the technologies needed for space-based cryogenic instruments have been made in the last decade, including cryocoolers, spacecraft architectures and cryogenic amplifiers. These enable considerably more complex instruments to be put into orbit for long-duration missions. One such instrument is the Superconducting Gravity Gradiometer (SGG) developed by Paik, et al. A magnetically levitated version is under consideration for a follow-on mission to GRACE (Gravity Recovery and Climate Experiment) and GOCE (Gravity field and steady-state Ocean Circulation Explorer). With its inherently greater rejection of common mode accelerations and ability to cancel the coupling of angular accelerations into the gradient signal, the SGG can achieve [an accuracy of] 0.01 milli-Eotvos (gravitational gradient of the Earth) divided by the square root of frequency in hertz, with requirements for attitude control that can be met with existing spacecraft. In addition, the use of a cryocooler for cooling the instrument will alleviate the previously severe constraint on mission lifetime imposed by the use of superfluid helium,. enabling mission durations in the 5-10 year range. Studies are underway to determine requirements for orbit (polar versus sun-synchronous), altitude (which affects spacecraft drag), instrument temperature and stability, cryocooler vibration control, and control and readout electronics. These will be used to determine the SGG's sensitivity and ultimate resolution for gravity recovery. This paper will discuss preliminary instrument and spacecraft design, and toplevel mission requirements