On optimal estimation of gravity from gravity gradients at aircraft altitude

Publisher Website
Google Scholar
Abstract
Least squares collocation in physical geodesy is now a standard technique for estimating gravity‐related quantities from discrete observations in a limited region. It is an optimal method because estimation errors due to measurement noise and the discreteness and finite extent of observations are minimized. However, for large observation sets, the computational problem of collocation (i.e., the problem of solving a large, possibly ill‐conditioned, linear system of equations) is also well known and is very clearly illustrated with airborne gravity gradiometry. Natural alternatives to rigorous least squares collocation are therefore examined and are categorized as being either nonoptimal, suboptimal, or virtually optimal. All choices of estimation method are directed at reducing the computational requirements with an awareness of the desired estimation accuracy. An example of a nonoptimal procedure is the use of integral formulas of the Stokes or Vening‐Meinesz type; suboptimal estimation is exemplified by frequency domain collocation; and a case of virtual optimality is the approximate collocation estimator obtained with a few iterations of the conjugate gradient method used to invert the autocovariance matrix.

This publication has 23 references indexed in Scilit: