Comparison Analysis of Different Representations of Uncombined PPP Model on Smartphone Positioning Performance

Farzaneh Zangenehnejad and Yang Gao

Abstract: Over the last few years, many smartphones have been equipped with global navigation satellite system (GNSS) technology allowing the users to use their own devices for the positioning purposes and navigation. Currently there are several hundreds of smartphone models on the market capable of providing the raw GNSS data. Early smartphones only provided single-frequency and mostly GPS only observations. In 2017, the Samsung S8 and Huawei P10 smartphones were released as the first multi GNSS devices which are able to track carrier-phase measurements. However, in May 2018, the Xiaomi Mi8 equipped with the new Broadcom BCM47755 GNSS chipset was released as the world’s first dual-frequency GNSS smartphone, i.e., L5/E5 for GPS and Galileo, respectively (European GNSS Agency, GSA 2018). It can be regarded as a great millstone in smartphone positioning providing the users with the opportunity to make ionospheric-free linear combination between observations of two frequencies to eliminate the ionosphere effect. Precise point positioning (PPP) is an efficient technique to provide real-time precise positioning using precise satellite orbits and satellite clocks provided, e.g., by the International GNSS Service (IGS). Additional correction terms must also be considered in the PPP processing. They include satellite and receiver antenna offsets, carrier phase wind-up, and site displacement effects including solid Earth tides, ocean tide loading and polar motion (Kouba and Héroux 2001, Héroux et al. 2004; Gao and Chen 2005). PPP can be implemented on smartphone observations in both static and kinematic modes. Proper choice of functional model describing the relationships between the observations and the unknowns plays an important role to achieve high-precision precise point positioning (PPP). Therefore, further considerations are required to investigate the performance of different PPP functional models applied to the GNSS smartphones. This contribution aims to comprehensively compare the mathematical expressions of estimable parameters of the uncombined PPP models, namely, UPPP1, UPPP2 and UPPP3. Using multiple datasets gathered from the smartphones, we will evaluate the performance of the three UPPP representations in various aspects, including the statistical reliability (both internal and external reliabilities) and their positioning performances. The three UPPP forms are defined as follows: • UPPP Form 1: Estimating separate receiver clocks for each frequency. The unknowns here are the receiver position, the receiver clock error on each frequency, the real-valued carrier-phase ambiguity terms on each frequency, the tropospheric delay and the slant ionospheric delay on the L1 frequency. • UPPP Form 2: Estimating one receiver clock and one receiver differential code bias (DCB). The unknowns here are the receiver position, the receiver clock error, the real-valued carrier-phase ambiguity terms, the zenith wet delay, the slant ionospheric delay on the L1 frequency and the receiver differential code bias between L1 and L5 frequency. • UPPP Form 3: Estimating one receiver clock and one receiver DCB (another representation). In this form of UPPP model, the receiver DCB can be assimilated into the slant ionospheric delay. The unknowns here are the receiver position, the receiver clock error, the real-valued carrier-phase ambiguity terms on each frequency, the biased-slant ionospheric delay (biased with DCB) and the tropospheric delay. One important point about this form is that the receiver DCB will be assimilated into the slant ionospheric delay. When no external ionosphere information is available, there is no need to estimate an additional parameter for the receiver DCB. However, when an external ionosphere information is available to be added as the weighted constraints, we still need to estimate DCB separately. In this contribution, the Global Ionospheric map (GIM) is used if we need to apply the external ionosphere information. We will show that in terms of degree of freedom, they are the same; however, the structure of the design matrix defining the correlation among the unknowns is different in each representation. We first analyze the Minimum Detectable Bias (MDB) for the GPS and Galileo code and carrier-phase observations on both frequencies obtained from the three UPPP models considering a significance level of 0.001 and detection power of 0.80. The external reliability of the three UPPP models is then evaluated by calculating the Total Positioning Error (TPE) using the same significance level and detection power. The results are summarized as follows: (1) For the code observations, we observe nearly identical MDB values for the three UPPP models. It indicates that for noisy smartphone code observations, the choice of different models (representations) has minimal impact on the MDB values. (2) For the phase observations, the UPPP1 model is identified as the worst model in terms of the internal reliability, particularly evident in its performance for the higher C/N0 observations and the higher elevation angle observations. (3) For the code observations, in terms of TPE, the results of UPPP1 and UPPP2 models are almost similar to each other, while they differ from model UPPP3 (UPPP3 is slightly better). However, for the carrier-phase observations, the TPE results indicate that model UPPP1 performs worse than the other two models. The positioning performance of the three UPPP models is then investigated using the observations of a dual-frequency Google Pixel 5 smartphone. The results are summarized as follows: (1) The three mathematical expressions of the UPPP models have almost the same positioning performance in terms of horizontal RMS values and the 50th percentile of the horizontal positioning errors. (2) The UPPP3 model has better performance compared to the other two models in terms of the vertical RMS values. Overall, the UPPP3 form is the preferred choice.
Published in: Proceedings of the ION 2024 Pacific PNT Meeting
April 15 - 18, 2024
Hilton Waikiki Beach
Honolulu, Hawaii
Pages: 356 - 376
Cite this article: Zangenehnejad, Farzaneh, Gao, Yang, "Comparison Analysis of Different Representations of Uncombined PPP Model on Smartphone Positioning Performance," Proceedings of the ION 2024 Pacific PNT Meeting, Honolulu, Hawaii, April 2024, pp. 356-376. https://doi.org/10.33012/2024.19597
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