Objectives The ionosphere-free (IF) model and the undifferenced and uncombined (UDUC) model are the two most commonly used functional models in precise point positioning (PPP). In the UDUC model, the ionospheric error is often described as random walk parameter , and the power spectral density (PSD) in the process of random walk becomes the main factor determining the positioning performance of PPP. The method of determining the PSD by the empirical value can not show the small scale variation of the ionosphere.

Methods Based on the UDUC model, the time correlation information of the ionosphere is analyzed. When the difference time interval of the ionosphere is small, the observation noise is large and it will submerge the changes of the ionosphere.Hence,we use the smooth denoising method to weaken the influence of the observation noise, determine the ionospheric PSD in real time, and reasonably constrain the ionospheric delay parameters in the UDUC model, so as to improve the positioning performance.

Results The experiment was carried out through 10 d BeiDou satellite navigation system (BDS) observations come from 12 stations under different ionospheric models. The results show that compared with the traditional ionospheric-free model, the convergence time of the proposed method is shortened by 8.2%, the horizontal direction accuracy is equivalent, and the vertical direction positioning accuracy is improved by about 31%. Compared with the empirical value PSD method,the convergence time of the proposed method is shortened by about 9.7%, the horizontal direction accuracy is equivalent, and the vertical direction positioning accuracy is improved by about 31%.

Conclusions We recommend that BDS users adopt our proposed method when using UDUC model, which can effectively shorten the convergence time and improve the positioning accuracy to a certain extent.