To realize the continuous monitoring of foundation displacement and the prediction of final settlement of long-span bridges based on Beidou navigation satellite system (BDS), the influences of various errors should be eliminated in the collection process of satellite signals. This paper proposes a method to eliminate the multipath errors in BDS signals using stationary wavelet transform. The method simplifies random noises to Gaussian white noises, and combines the determinant criterion of noises and empirical mode decomposition (EMD) method to reduce the random noises in the signal based on autocorrelation function. In order to meet the observation accuracy for foundation displacement of long-span bridges, the measured BDS data and the settlement data obtained by precise levelling were defined by hyperbolic model. Based on the measured data during the construction process and the modelled settlement data, the non-linear relationship of the data was established by BP neural network to realize real-time correction of measured BDS data. The foundation pile of a rail-cum-road bridge under construction was taken as an example, which is over 1 km in length. The BDS data was collected, the bad points were eliminated, and the lost data was compensated by linear interpolation. The real-time measured data of the long-span bridge at foundation pile was denoised and corrected by the proposed method. Results show that compared with the precise levelling results, the proposed method had high precision, which could meet the requirements of continuous monitoring and final settlement prediction of bridge towers of long-span bridges.