Assessment of stochastic models for GPS measurements with different types of receivers

The stochastic model plays an important role in parameter estimation. The optimal estimator in the sense of least squares can only be obtained by using the correct stochastic model and consequently guarantees the precise positioning in GPS applications. In this contribution, the GPS measurements, collected by different types of geodetic dual-frequency receiver pairs on ultra-short baselines with a sampling interval of 1 s, are used to address their stochastic models, which include the variances of all observation types, the relationship between the observation accuracy and its elevation angle, the time correlation, as well as the correlation between observation types. The results show that the commonly used stochastic model with the assumption that all the raw GPS measurements are independent with the same variance does not meet the need for precise positioning and the elevation-dependent weight model cannot work well for different receiver and observation types. The time correlation and cross correlation are significant as well. It is therefore concluded that the stochastic model is much associated with the receiver and observation types and should be specified for the receiver and observation types.