Alternative Geometric Determination of Altazimuthal‐Distance Covariance Matrices

Abstract

Conventional equations for determining the variance‐covariance matrix of vertical angles, geodetic azimuths and distances are based on the standard law of propagation of covariance using the Jacobian matrix of the corresponding functional relationships. A conceptually simpler geometric approach exclusively dependent on the notion of rotation matrices is presented here. The method completely avoids the cumbersome requirement of taking partial derivatives of non‐linear expressions. As an added advantage the method contributes to clarify several points related to dimensional transformations between linear and angular units.