Estimation of Analytical Covariance Parameters using the Marquardt-Lavenberg Algorithm

Abstract

Gravity prediction for filling of gravity voids is an essential task in countries with sparse gravity data. The least squares collocation (LSC) has been a preferred prediction tool for geodesists over the years for predicting gravity values at unsampled locations. However, the accuracy of the LSC depends on the covariance function used and by extension the method of estimating the parameters of such analytical covariance function. This study presents a novel approach for the estimation of analytical covariance parameters by implementation of the Marqurdt-Lavenberg (ML) algorithm in a non-linear programming (NLP) optimization approach. The suitability of the ML algorithm for estimating the essential parameters of a covariance matrix is tested within a 1 degree by 1 degree grid within Ondo state (typifying a sparse data region). Results obtained when analyzed by Leave out (LO) validation show that the ML algorithm is efficient for estimating essential covariance parameters with a RMSE 1.196mgals. Furthermore, statistical analysis of the result indicate that there exists a very strong correlation (near perfect relationship) with a Pearson correlation value of 0.93 between the predicted values and the known gravity values of the LO points. It is therefore concluded that the ML method is a reliable method for estimating covariance parameters for geodetic application even in regions with sparse gravity data