Performance of Smartphone BDS-3/GPS/Galileo Multi-Frequency Ionosphere-Free Precise Code Positioning

Abstract

The continuously improving performance of mass-market global navigation satellite system (GNSS) chipsets is enabling the prospect of high-precision GNSS positioning for smartphones. Nevertheless, a substantial portion of Android smartphones lack the capability to access raw carrier phase observations. Therefore, this paper introduces a precise code positioning (PCP) method, which utilizes Doppler-smoothed pseudo-range and inter-satellite single-difference methods. For the first time, the results of a quality investigation involving BDS-3 B1C/B2a/B1I, GPS L1/L5, and Galileo E1/E5a observed using smartphones are presented. The results indicated that Xiaomi 11 Lite (Mi11) exhibited a superior satellite data decoding performance compared to Huawei P40 (HP40), but it lagged behind HP40 in terms of satellite tracking. In the static open-sky scenario, the carrier-to-noise ratio (CNR) values were mostly above 25 dB-Hz. Additionally, for B1C/B1I/L1/E1, they were approximately 8 dB-Hz higher than those for B2a/L5/E5a. Second, various PCP models were developed to address ionospheric delay. These models include the IF-P models, which combine traditional dual-frequency IF pseudo-ranges with single-frequency ionosphere-corrected pseudo-ranges using precise ionospheric products, and IFUC models, which rely solely on single-frequency ionosphere-corrected pseudo-ranges. Finally, static and dynamic tests were conducted using datasets collected from various real-world scenarios. The static tests demonstrated that the PCP models could achieve sub-meter-level accuracy in the east (E) and north (N) directions, while achieving meter-level accuracy in the upward (U) direction. Numerically, the root mean square error (RMSE) improvement percentages were approximately 93.8%, 75%, and 82.8% for HP40 in the E, N, and U directions, respectively, in both open-sky and complex scenarios compared to single-point positioning (SPP). In the open-sky scenario, Mi11 showed an average increase of about 85.6%, 87%, and 16% in the E, N, and U directions, respectively, compared to SPP. In complex scenarios, Mi11 exhibited an average increase of roughly 68%, 75.9%, and 90% in the E, N, and U directions, respectively, compared to SPP. Dynamic tests showed that the PCP models only provided an improvement of approximately 10% in the horizontal plane or U direction compared to SPP. The triple-frequency IFUC (IFUC123) model outperforms others due to its lower noise and utilization of multi-frequency pseudo-ranges. The PCP models can enhance smartphone positioning accuracy.