The industry mainly uses the technology of carrier smoothing pseudo-range to output smoothed pseudo-range，e.g. Hatch filter, which further reduces the influence of multipath and thermal noise, so as to improve the positioning accuracy. Since the ionosphere has opposite effects on the measured values of the carrier and the pseudo-range, the smoothed pseudo-range will contain the error introduced by the ionospheric delay, which will affect the positioning accuracy and even endanger the safety of life. Therefore, it is important and necessary to study the influence of ionosphere on carrier smooth pseudo-range. By adding the ionospheric time gradient model and multipath model, the output error of smoothing filter is analyzed theoretically, and the above analysis results are simulated and verified, so as to provide the theoretical basis under the scenarios of the ionospheric time gradient monitoring threshold selection, the appropriate filter time constant selection, etc.