Determination of the geoid from deflections of the vertical using a least-squares surface fitting technique

Abstract

The least-squares surface fitting technique is applied to the problem of determining the geoid from a given set of deflections. A higher order mixed algebraic polynomial is used. The coefficients are computed so as to minimize the sum of the squares of the differences between the polynomial's derivatives in the meridian as well as prime vertical directions and the corresponding deflection components. Astro-geodetic geoids for North America and some selected sub-areas are presented. These are then compared with the U.S. Army Map Service 1967 and the Computer Sciences Corporation/Goddard Space Flight Centre 1972 geoids. The precision of this least-squares technique is discussed and possible refinements are proposed.