A COMPARISON BETWEEN SURFACE FITTING AND ORDINARY LEAST SQUARES PREDICTION TECHNIQUES

Abstract

The basic activities of surveying and geodesy are acquiring data from field observations. However, field activities are usually time consuming and therefore expensive. Mathematical models are usually cheaply adapted to densify more data required for a particular objective. Such models should be formulated in a correct manner such that the predicted quantities satisfy their required purpose. In all cases, functions with specified properties must be used. This study aims to: 1) Obtaining empirical covariance functions that can be successfully used in least squares prediction. 2) Obtaining functions (polynomials) that can be used to develop a practical surface. Empirical covariance functions have been prepared from known and expected data and have been tested in the interpolation. The main conclusions of the study are as follows: 1) Both models i.e. surface fitting and least squares prediction give results of the same precision for flat areas. 2) For areas up to 3x3 km2 contour plants of interval of 0.25m can be produced provided six data points, evenly distributed.