Helmert variance component estimation for mixed additive and multiplicative random error model

Abstract

Abstract With the development of surveying and mapping science, the object of measurement adjustment has been extended from a single observation of the same kind in the past to different precisions of the same kind, or different kinds of observations. There are additive and multiplicative errors related to electronic instrument measurements, which affect the quality of the adjustment results. A single additive error model is difficult to meet the accuracy requirements, so a mixed additive and multiplicative random error model (MAMREM) is needed. Aiming at the problem of inaccurate MAMREM stochastic model, this paper proposes Helmert Variance Component Estimation (VCE) to determine the weight matrix in different types of observations under MAMREM. In this paper, the formula and iterative algorithm of Helmert variance component estimation applied to MAMREM are derived, and the weights of different kinds of observations in the adjustment process are estimated. In order to verify the effectiveness of the method, the digital elevation model experiment and the side network experiment are used to verify the method. The results prove the effectiveness of the method.