Objectives This paper aims to address two issues in the construction of a carrier phase multipath grid model. First, it focuses on resolving the problem of mismatch between constraint conditions and their prior variances during the process of solving grid parameters. Second, it tackles the escalating demand for higher grid resolution as the complexity of the site environment increases. This escalating demand leads to an exponential growth in the number of solving parameters, resulting in a significant decrease in solving efficiency.

Methods A multipath modeling method of global navigation satellite system grid based on improved adaptive moment estimation (Adam) gradient descent is proposed to address the spatial distribution characteristics of static station multipath. The proposed method does not need prior constraints on grid parameters, and can significantly shorten the calculation time of high spatial resolution models and improve modeling efficiency.

Results The results of multipath experiments in complex environments indicate that by increasing the spatial grid resolution from 2° to 0.05°, the calculation parameters increase sharply by 1 556 times, but the calculation time only increase by 0.27 times. The multipath fitting accuracy improves from 73.93% to 82.89% and the horizontal and vertical positioning accuracies increase from 71.6% to 80.9% and from 72.4% to 82.0%, respectiveiy. The experimental results of GPS L1 and BDS B1C interoperability signal multipath show that the same frequency signal multipath has consistent spatial distribution characteristics, and can be applied to joint multipath modeling of interoperability signals.

Conclusions This method can significantly improve the efficiency of high-resolution grid based multipath modeling and can be effectively used for high-precision carrier phase multipath modeling in complex observation environments.