Abstract: GNSS positioning accuracy is affected by pseudo-range measuring error, atmospheric time-delay error, satellite atomic clock error and satellite orbit error, et al. Traditionally, the DOP and UERE parameters are used to estimate positioning error. However, several assumptions are needed in the derivation process of precision representation formula, thus it is actually an approximate estimating formula. In addition, the satellite orbit error of various error sources belongs to three-dimensional error, which requires coordinate transformation and experience parameter model to switch to UERE. Therefore, the paper proposes using matrix perturbation mathematical theory to study the influence of satellite orbit error on positioning accuracy; and describes equation form by conditional number using spectral norm. The simulation result demonstrates that this method can reflect the influence directly without transformation of orbit coordinate and UERE error so that it is more direct and precise to assess the influence of satellite orbit error on positioning accuracy.