An Optimal Carrier-Phase Smoothing Code Algorithm for Low-Cost Single-Frequency Receivers

Carrier-phase smoothing code (CPSC) is a code-smoothing technology that uses carrier-phase changes to reduce code noise in Global Navigation Satellite System (GNSS) appliances. Although CPSC performs well in reducing noise and is easy to implement, it is a trade-off between the reduction of noise and the increase of the variation of ionospheric errors. The width of the smoothing window needs to be large to reduce noise. However, a wider smoothing window increases the variation of ionospheric errors. To circumvent this dilemma, the grid ionospheric model (GIM) was used to estimate the variation of ionospheric errors between consecutive epochs, and a noise estimation method is proposed for low-cost single-frequency receivers. Furthermore, an optimal carrier phase smoothing code (OCPSC) algorithm with an adaptive width smoothing window is proposed to reduce the noise of Global Positioning System (GPS) data. We found that the OCPSC is more robust and its positioning performance is better overall for low-cost single-frequency receivers than is the traditional CPSC. In a static mode, when applying the OCPSC algorithm, the positioning accuracy can be improved by 0.15 m (6%) and 0.06 m (6%) in the horizontal and vertical directions, respectively. These improvements are 0.08 (3%) m and 0.06 m (1%) when a kinematic mode is applied. The research presented here demonstrates that the OCPSC algorithm effectively addresses the trade-off between the reduction of noise and the increase of the variation of ionospheric errors. In the OCPSC algorithm, the grid ionospheric model is used to estimate the variation of ionospheric errors between consecutive epochs, and a noise estimation method is used to estimate noise for low-cost single-frequency receivers. The OCPSC algorithm was applied to static and dynamic experiments. All results in this paper show that, compared with traditional CPSC, the OCPSC algorithm provides more-accurate positioning results for low-cost single-frequency receivers. Because future smartphones will integrate GNSS chips, the proposed OCPSC algorithm has great potential to be applied widely to the market of multiconstellation single-frequency Precise Point Positioning with low-cost smartphones.