Statistical Analysis of Moving-Base Gravimetry and Gravity Gradiometry
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Date
2003-09
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Ohio State University. Division of Geodetic Science
Abstract
Moving-base gravimetry systems require multiple sensors to extract the gravitational signal – an
accelerometer (or gravimeter), or a set of mutually orthogonal accelerometers that sense the action
forces on the vehicle; a suite of gyroscopes (or a stabilized platform) that provides proper
orientation for the accelerometers; and a geometric (kinematic) positioning system (e.g., GPS)
from which the kinematic acceleration may be derived, and that also provides geospatial
referencing of the signals. The error in the recovered gravitational signal depends on the individual
sensor errors, but also on the coupling of the sensor errors to the actual acceleration environment
of the system. The error analysis is fairly well known and documented in the literature and agrees
largely with experimental and operational results. This report reviews the analysis in detail and
extends it to moving-base gravity gradiometry. In the latter case the system comprises a set of
gradiometers (or differential accelerometers), a suite of gyros for orientation (stabilization), and a
geospatial referencing system (GPS). The errors in the recovered gravitational gradients depend
on the sensor errors, but also on the coupling of these errors to the angular rate environment of the
system. The analyses specifically target airborne systems used for gravity and gravity gradient
mapping. While the orientation bias error is especially detrimental to airborne gravimetry, it is the
random noise in the gyro angular rate that contributes most to airborne gradiometry, as it couples
with the total angular rate. The analysis shows that a gradiometer with 1 E/ √Hz sensitivity will
not be adversely compromised (at medium and high frequencies) if the required gyros have bias
repeatability of 0.0015 °/hr and sensitivity of 0.01 °/hr/ √Hz ≈ 0 .00015 °/ √hr , and if the
orientation bias is 0.06 °. The latter numbers all reflect an order of magnitude lower than
commensurate gradient error effects of 1 E/ √Hz . This report also provides detailed models for
the various error sources, as well as for the accelerations and angular rates of the aircraft and for
the gravitational signal to wavelengths as short as 1 m.
Description
Technical Report prepared for National Imagery and Mapping Agency. Contract No. NMA202-98-1-1110. OSURF Project No. 736145.