Abstract: The Ground Based Augmentation System (GBAS) uses carrier phase smoothing pseudorange differential correction to achieve navigation aided positioning. The smoothing time constant is a key parameter affecting the accuracy of carrier phase smoothing pseudorange. To analyze the effects of ionospheric time gradient and spatial gradient on Hatch filtering under different smoothing times. Based on the analysis of the total error variance of the filtering caused by the ionospheric time-space gradient and multipath effect, the adaptive optimal smoothing time constant is derived. The positioning errors of GBAS static and dynamic environments are tested respectively. The experimental results show that the adaptive optimal smoothing time constant reduces the GBAS pseudorange measurement error, which enhances the positioning accuracy.