NASA Logo

NTRS

NTRS - NASA Technical Reports Server

Back to Results
Reducing Errors by Use of Redundancy in Gravity MeasurementsA methodology for improving gravity-gradient measurement data exploits the constraints imposed upon the components of the gravity-gradient tensor by the conditions of integrability needed for reconstruction of the gravitational potential. These constraints are derived from the basic equation for the gravitational potential and from mathematical identities that apply to the gravitational potential and its partial derivatives with respect to spatial coordinates. Consider the gravitational potential in a Cartesian coordinate system {x1,x2,x3}. If one measures all the components of the gravity-gradient tensor at all points of interest within a region of space in which one seeks to characterize the gravitational field, one obtains redundant information. One could utilize the constraints to select a minimum (that is, nonredundant) set of measurements from which the gravitational potential could be reconstructed. Alternatively, one could exploit the redundancy to reduce errors from noisy measurements. A convenient example is that of the selection of a minimum set of measurements to characterize the gravitational field at n3 points (where n is an integer) in a cube. Without the benefit of such a selection, it would be necessary to make 9n3 measurements because the gravitygradient tensor has 9 components at each point. The problem of utilizing the redundancy to reduce errors in noisy measurements is an optimization problem: Given a set of noisy values of the components of the gravity-gradient tensor at the measurement points, one seeks a set of corrected values - a set that is optimum in that it minimizes some measure of error (e.g., the sum of squares of the differences between the corrected and noisy measurement values) while taking account of the fact that the constraints must apply to the exact values. The problem as thus posed leads to a vector equation that can be solved to obtain the corrected values.
Document ID
20110016841
Acquisition Source
Jet Propulsion Laboratory
Document Type
Other - NASA Tech Brief
Authors
Kulikov, Igor
(California Inst. of Tech. Pasadena, CA, United States)
Zak, Michail
(California Inst. of Tech. Pasadena, CA, United States)
Date Acquired
August 25, 2013
Publication Date
June 1, 2004
Publication Information
Publication: NASA Tech Briefs, June 2004
Subject Category
Man/System Technology And Life Support
Report/Patent Number
NPO-30536
Distribution Limits
Public
Copyright
Public Use Permitted.
No Preview Available