Abstract: In the global navigation satellite system (GNSS), an accurate positioning error model is important for understanding how the system works. When the pseudorange error of each satellite has an uncorrelated normal distribution with zero-mean and common variance, the positioning error is equal to the standard deviation of pseudorange error multiplied by the geometric precision. However, in practical applications, the pseudorange errors may differ in variance due to the different signal propagation paths. Especially when the signals are affected by multipath effects or ionospheric scintillation, the pseudorange errors will be significantly different from one another. This paper introduces a theoretical positioning error model of non-uniform pseudorange error based on singular value decomposition (SVD). Using GNSS data at Beijing station and Hong Kong station to analyze the positioning errors affected by multipath effects and ionospheric scintillation, the statistical characteristics of positioning error are consistent with the results given by the positioning error model of non-uniform pseudorange error, proving the correctness and validity of the model.