Comparison of the Stochastic Models for Double-Differenced GPS Measurements

Double-differenced GPS carrier phase measurements are commonly used in GPS precise positioning applications and processed with algorithms based on the least-squares (LS) principle. In order to apply the LS principle, one needs to define properly both the functional and stochastic models. Whilst the functional model for precise GPS positioning is sufficiently well known, realistic stochastic modeling is still a difficult task to accomplish in practice. Incorrect stochastic models for double-differenced GPS measurements will lead to unreliable estimates for ambiguity resolution and, eventually, it will bias positioning results. The common assumption when we construct the stochastic model is that all raw GPS measurements are independent and have the same variances. In fact, this is not realistic, since due to varying noise levels measurements obtained from different GPS satellites cannot have the same accuracy. A realistic stochastic modeling should be able to capture the ordinary noises in the observables. In order to specify a realistic stochastic model for precise relative GPS positioning applications, in this paper the performance of three stochastic models namely the commonly used model or the standard model, the outer product of residual data vector model and Minimum Norm Quadratic Unbiased Estimation (MINQUE) are examined and effects of each the proposed model on statistic for ambiguity search and positioning accuracy are compared. The results indicate that the MINQUE model tends to perform better than the other models. Using the MINQUE model, the reliability of the ambiguity resolution and the statistics of the baseline components can be improved. It may suggest that the MINQUE model, which is based on modern statistical theory, is capable of capturing the ordinary noises.