GNSS measurements are recognized as a key technique for ionosphere monitoring. Such a goal is typically realized with datasets from global or regional networks of permanent stations, which provide, e.g., vertical total electron content maps. Despite the unquestioned role of such an approach, it still suffers from an irregular distribution of on-ground monitoring sites, limiting the precision of GNSS-based ionospheric products. A solution addressing this issue is to adopt dual-frequency measurements from low-cost devices, particularly those provided by GNSS chipsets embedded in modern smartphones. These ubiquitous devices can, theoretically, lead to the extreme densification of ionospheric information; however, their widespread use must be preceded by a detailed analysis of data properties and quality.This still-open issue motivated us to investigate the applicability of ionosphere monitoring using a geometry-free linear combination (GF LC) series built of smartphone-acquired GNSS phase data. In the experiment, we used two smartphones: Google Pixel 7 and Xiaomi 15T Pro, which provide multi-system dual-frequency measurements. The smartphone results were validated against those provided by a high-grade receiver - Trimble Alloy. The dataset comprised GPS, Galileo, and BDS observations collected during three 8-hour sessions. We analysed the completeness and quality of the data, including the noise level, the number of cycle slips, and the consistency and accuracy of smartphone GF LC time series in comparison to the benchmark values. While the analysis confirmed the applicability of smartphone measurements for ionospheric studies, it also revealed the poorer quality of all analysed characteristics. Furthermore, we observe a substantial performance discrepancy between the tested mobile devices, which may pose a problem for their combined utilization.

Seismic torsion is a key parameter to quantify earthquake-induced ground rotations. However, survey-grade rotational seismometers are prohibitively expensive for large-scale deployment, while the MicroElectromechanical Systems (MEMS) gyroscopes lack sufficient precision to measure the seismic rotational motions, especially torsion. We employ a 3-meter baseline dual-antenna GNSS to assist the MEMS gyroscope by providing absolute torsional constraints that suppress integration drift, thereby enhancing the precision and reliability of measurements. We verify the feasibility of the combined solution for torsional measurement and present the systematic assessment of its short-term accuracy. The combined solution achieves a static measurement standard deviation better than 0.086 mrad within 30 s, improving precision by at least 21% over the MEMS-only solution. In the dynamic experiment, the combined solution suppresses integration drift without relying on high-pass filtering, thereby enabling faithful reconstruction of the complete dynamic torsional signal, including its permanent offset. The RMS error within 200 s is 1.105 mrad, significantly lower than the 7.307 mrad obtained with MEMS alone. Furthermore, combined torsion estimation is introduced to enhance torsional observability in six-degree-of-freedom seismogeodesy. The quantitative results can provide critical guidance for designing cost-effective rotational seismology monitoring networks.

Real-time precise point positioning with ambiguity resolution (PPP-AR) is considered a valuable positioning tool applicable in various fields. Limited by the precision and stability of real-time satellite products and observation streams, it is challenging to continuously and correctly resolve the ambiguity, resulting in positioning fragmentation in real-time PPP-AR. Therefore, inspired by the best integer equivariant (BIE) method, we proposed an integer ambiguity clustering estimator (IACE) for improving real-time PPP-AR performance. IACE performs hierarchical agglomerative clustering (HAC) based on ambiguity correlations, enabling a direct approximation of the final candidate through intra- and inter-cluster enumeration. It further introduces the constraints of the fixed ambiguities into the filter with cascading weights, aimed at resisting the influence of potentially incorrect ambiguity resolution. We selected 115 multi-GNSS stations worldwide and carried out 22 days of continuous real-time PPP-AR. It is found that IACE improves the computational efficiency across various ambiguity dimensions compared to classic partial ambiguity resolution (PAR) and BIE, while improving the positioning precision over the float solution by 26.1%, 10.4%, and 5.6% in the east, north, and up components, respectively, overall comparable to the PAR and BIE. Regarding the entire position time series, the IACE-induced jumping rate is 0.04%, while PAR and BIE are 0.37% and 0.28%, respectively. This indicates that IACE effectively resists positioning jumps in the ambiguity-fixed solutions. Moreover, IACE exhibits lower displacement wanders across the time scale of 1 to 104 s compared to the other strategies, showing overall superior positioning capability.

Inter-frequency clock bias (IFCB) products are crucial for GPS L1/L5 and BDS-2 B1/B2 precise point positioning with ambiguity resolution (PPP-AR). The computationally efficient epoch-differenced IFCBs are not adequately precise for PPP-AR, while generating precise IFCB products from the undifferenced uncombined network requires several hours. In this study, we proposed a strategy to fast and precisely estimate IFCB products with the carrier-range network solution. The epoch-differenced model was employed to estimate a priori IFCB products, instead of the undifferenced uncombined network solution. Then the IFCBs are re-estimated with carrier ranges, which come from PPP, reducing tens of thousands of ambiguity parameters and speeding up network solutions. GPS and BDS-2 multi-frequency data from 372 stations over 31 d in 2024 were archived for the IFCB estimation and performance evaluation. When 250 stations were used to estimate IFCB products, the processing only took 88 min. Compared with the undifferenced uncombined model, the proposed strategy saved 56.4% of the computational time. The root mean square (RMS) of the differences between estimated IFCBs and the benchmark IFCBs (i.e. GPS L1/L2 and L1/L5 clock offset differences) was 0.07 ns, matching the RMS of IFCBs from undifferenced uncombined network solution. For BDS-2, the RMS difference amounted to 0.02 ns. When these carrier-range IFCBs were used in PPP-AR instead of epoch-differenced IFCBs, the RMS of positioning errors for GPS L1/L5 static PPP-AR solutions improved from 7.0, 5.7, 15.6 mm to 2.7, 2.9, and 8.9 mm in the east, north and up directions, respectively, which is comparable to using IFCBs from undifferenced uncombined network solution. The mean narrow-lane ambiguity fixing rate improved by 20.6% for GPS and 9.9% for BDS-2. Therefore, this strategy enhances efficiency while guaranteeing the precision of the IFCBs, and can offer a rapid and precise IFCB product to support GPS L1/L5 and BDS-2 B1/B2 PPP-AR.

Galileo satellites modulate pseudorandom code series for both the pilot (Q) and mixed (X) channels, which however undergo separate demodulation processes by different GNSS receivers (e.g., Septentrio receivers accept the pilot channel only whereas Javad the mixed channel only). It is usually assumed that the Galileo code biases on both channels are close to each other, and then all Galileo stations can be safely used to estimate satellite clock offsets and code/phase biases, regardless of their demodulation channels. In this study, we aligned the code biases on the pilot and mixed channels by estimating intra-frequency differential code biases (DCB), and examined whether this alignment could improve the performance of precise point positioning (PPP). We performed a series of satellite clock offset estimations, phase bias estimations and PPP assessments for Galileo using data from 230 stations from days 300 to 365 in 2023. Our analysis uncovered that the ignored DCBs could introduce systematic biases of up to 0.1 m in satellite clock offsets and up to 0.49 cycles in satellite phase biases. Using the aligned code bias products, the unified satellite clock offsets and phase biases across pilot and mixed channels can be estimated. The differences of pilot and mixed satellite clock offsets were reduced to within 0.03 m, while the UPD differences were reduced to an average of 0.02 cycles. With these modified precise products, the static PPP-AR wide-lane ambiguity fixing rates increased from 79.28

We assess the performance of the self-developed receiver coupling dual-frequency low-cost GNSS chipset and IMU MEMS sensor. The system also comprises software dedicated to vibration monitoring based on relative kinematic positioning in a post-processing mode. The observation assessment reveals high accuracy of low-cost GNSS and MEMS accelerometer data. The Septentrio Mosaic X5 chipset exhibits competitive to high-grade receivers' phase observation noise, outperformance in code noise level and observation auto-correlation at a level that may be neglected even in high-rate applications. The evaluation of the MEMS accelerometer data proves that the sensor accuracy is adequate for vibration monitoring. With the shake table experiment, we examine the performance of vibration recovery. An advantage of the coupled solution over a GNSS-only one is documented with a 15 % reduction of the amplitude error. The backward smoothing of coupled solutions drives the next 20 % error drop. Finally, the high performance of the coupled solution based on low-cost GNSS & accelerometer is confirmed by a mean amplitude error of 0.4 mm. The frequency analyses indicate that both coupled and singlesensor solutions precisely detect the vibration frequencies; however, they also confirm the outperformance of the former over the latter. The power spectra of the recovered displacement time series accentuate the benefits of GNSS + accelerometer fusion and backward filtering for reducing displacement noise.

The International GNSS Service (IGS) observable-specific signal bias (OSB) product is essential to all-frequency precise point positioning with ambiguity resolution (PPP-AR). In general, the code bias product generation precedes, rather than proceeds simultaneously with, the phase bias determination, and such a standard two-step estimation strategy could impair PPP-AR on those non-baseline frequency pairs (e.g., GPS L1/L5, Galileo E1/E6, BDS-3 B1C/B2a, etc.). In this study, we developed an approach to enhance the IGS code OSB products, which was interoperable and coupled with all-frequency phase bias determination. With 31 days of multi-GNSS data from about 380 stations in 2024, it was verified that representative IGS differential code bias products could differ remarkably by over 0.4 ns on average on the GPS/BDS-2/3 non-baseline frequency pairs. Once the CAS (Chinese Academy of Sciences) code OSBs were calibrated, however, the mean ambiguity fixing rates rose significantly from 70 to 90

Establishing a regional ionospheric model to provide precise ionospheric products is a prerequisite for rapid real-time kinematic precise point positioning (PPP-RTK). Thus, a stochastic model for these real-time ionospheric products is also crucial. In this study, we use a Wuhan regional network (average inter-station distance of about 30 km) to comparatively analyze four regional ionospheric modeling methods with commonly-used stochastic models: the inverse distance weighting model (IDW), the quasi-four-dimension ionospheric modeling (Q4DIM), the first-order polynomial function model with internal validation (POLY), and the first-order polynomial function model with external validation (POLY-EV). Our results show that, the POLY/POLY-EV model has the smallest ionospheric delay interpolation root mean square (RMS) error, regardless of whether for inside or peripheral stations of the regional network, during both quiet and active ionospheric conditions. For 4024 and 4314 one-hour samples, the PPP-RTK results show that at inside stations, all four models converge to a horizontal precision of 10 cm within two epochs, with the POLY-EV model having the highest horizontal positioning precision (a mean RMS of 0.83 cm). At the peripheral station, PPP-RTK with the POLY/POLY-EV model achieves a horizontal precision of 10 cm within two epochs, while the IDW and Q4DIM models need 4 and 43 epochs, respectively. The horizontal positioning precision of PPP-RTK using the POLY-EV model is the highest, with a mean RMS of 1.59 cm.

3D building maps have been urgently demanded in numerous applications such as urban planning and disaster monitoring. Conventional LiDAR and visual-based 3D building mapping techniques face challenges like high financial cost and human resource consumption for large-scale 3D map construction and update. Recently, global navigation satellite system (GNSS)-based urban mapping has received much attention, owing to the inherent advantages like wide coverage area, high update efficiency, and low cost. However, most of the existing GNSS mapping approaches merely exploit the single feature of signal power, and cannot provide satisfactory mapping accuracy. In this article, an urban building height estimation method based on smartphone GNSS data is developed, resorting to the machine learning-based GNSS line-of-sight (LOS)/non-line-of-sight (NLOS) classifier. The supervised support vector machine (SVM) uses multiple GNSS signal features extracted from raw data to achieve the LOS/NLOS signal classification. The building height, around which the signal LOS/NLOS condition changes drastically, is estimated by applying a logistic function fitting to the signal LOS probability along the altitude direction. The critical building height estimations in conjunction with a priori database of the 2D building boundaries produce the 3D building map. Experimental campaigns under four different building scenarios are performed to evaluate the performance of the proposed method. Experimental results reveal that the proposed smartphone GNSS LOS/NLOS classification-based approach yields an absolute building height estimation error lower than 2.3 m, as against 21.5 m provided by the existing GNSS building mapping algorithm.

The multipath effect is a major Global Navigation Satellite System (GNSS) error source due to its environment-dependent characteristic, which complicates its mitigation process for the high-rate determination of displacements. For instance, Sidereal Filtering (SF) and Multipath Hemispherical Map (MHM) require the observations spanning at least one full cycle of satellite orbit repeat period (e.g., ten days for Galileo navigation satellite system (Galileo) to reproduce the satellite geometry against ground stations. As a consequence, the practicability of SF and MHM is limited due to potential station-surrounding changes over a long period. In this study, we used the overlap-frequency signals on Global Positioning System (GPS) L1/L5, Galileo E1/E5a, and BeiDou-3 Navigation Satellite System (BDS-3) B1C/B2a to construct an interoperable MHM (i.e., MHM_GEC) across constellations to mitigate multipath more efficiently. We thus used 31 days of 1-Hz GPS/Galileo/BDS-3 data at 21 stations in Europe to compare this overlap-frequency MHM with those GNSS-specific MHMs (i.e., MHM_G for GPS, MHM_E for Galileo, and MHM_C for BDS-3), as well as SF. It is confirmed that the multipath effects on overlap-frequency signals are of a high spatial consistency across all GNSS. The mean reduction rate of applying MHM_GEC to GPS, Galileo, and BDS-3 carrier-phase residuals is 25%, 31%, and 28.5%, respectively, which are up to 25 percentage points higher than those of MHM_G, MHM_E, and MHM _C. Furthermore, the MHM_GEC constructed using 5 to 6 days of data can improve the positioning precision by 40%, outperforming the MHM_E, MHM_C, and SF using 10 days of data. Therefore, the interoperable MHM_GEC is more efficient in mitigating multipath effects for high-precision GNSS positioning.

The global navigation satellite system (GNSS) is a crucial technical tool used for precisely determining the orbit of low earth orbit (LEO) satellites. However, due to the short arc length of spaceborne GNSS observations and the presence of numerous outliers, there is a high rate of misjudgment of cycle slips, which leads to a decrease in orbit determination accuracy. To address this issue, we propose a linear-fit forward and backward moving window averaging (LFBMWA) algorithm and a modified second-order time-difference phase Ionospheric residual (MSTPIR) algorithm to minimize cycle slip misjudgment by suppressing the impact of outliers. Simulation experiments show that the traditional method using FBMWA and STPIR has an 85.53

Multipath remains one of the major challenges in high-precision GNSS positioning. The multipath hemispherical map (MHM) based on satellites’ location repeatability in space is a popular method to mitigate GNSS multipath effects, but its performance depends on the availability of sufficient satellite orbital tracks in the skyplot. For instance, for BDS-3 medium Earth orbiters and Galileo satellites with 7-day and 10-day orbital repeat times, respectively, the skyplot of their orbital tracks will be too sparse to cover the shifting orbital tracks on the succeeding days, if only a few days of observations are used to construct MHMs. In this study, we establish an interoperable MHM using the overlap frequency signals of GPS, Galileo and BDS-3 (i.e., GPS L1/L5, Galileo E1/E5a and BDS-3 B1C/B2a). We compared the performance of GPS/Galileo/BDS-3 MHM (i.e., MP_GEC) and single-constellation MHMs (i.e., MP_G, MP_E and MP_C). The mean reduction rates of the L1/E1/B1C and L5/E5a/B2a carrier-phase residuals for the MP_GEC applied to GPS, Galileo and BDS-3 are 36

The GNSS Precise Point Positioning (PPP) model is usually established in either an ionospheric-free (IF) combined form or an uncombined (UC) form. These formulations can be equivalent in theory but their applications in practice could still perform differently when integrated with external sensors. In this study, we compared the positioning performance of the two PPP models tightly coupled with the Inertial Navigation System (INS) using a high-grade inertial measurement unit (IMU) in real vehicle navigation tests. The ambiguity resolution (AR) was also exploited in the two PPP models after applying the observable specific biases (OSB) to the GNSS raw code and phase measurements. According to the results, under good satellite observability the UC PPP/INS tightly-coupled integration (TCI) significantly outperforms the IF PPP/INS TCI. The UC TCI model with AR could achieve a positioning accuracy of 4.6 and 3.0 cm in the horizontal and vertical directions, which are improved by 37 % and 63 % respectively relative to the IF TCI model. However, in the case of frequent GNSS signal interruptions or poor satellite observation condition, the IF TCI model shows a superior reliability than the UC TCI. Nevertheless, when the ionospheric parameters are properly constrained in the UC TCI model, substantial improvements in terms of convergence and accuracy are obtained. The UC PPP augmented with external precise ionospheric information would greatly increase the cost, and users may select the appropriate PPP model with INS TCI in real applications in accordance with the demanded accuracy level and measuring conditions. (c) 2024 COSPAR. Published by Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

The release of raw Android global navigation satellite system (GNSS) measurements makes high-precision positioning achievable with low-cost smart devices. Affected by low-cost GNSS chips, linearly polarized antennas, and complex observation environments, Android GNSS observations usually contain a large number of outliers, which significantly degrade their positioning precision and reliability. To address this issue, a robust real-time kinematic (RTK) scheme with sliding window-based factor graph optimization (FGO) was developed. The scheme adopts the GNSS carrier-phase sliding window marginalization, models the carrier-phase ambiguity as a random constant, and incorporates multiple robust estimation strategies. Vehicle kinematic positioning validations were carried out in both open-sky and complex urban environments using representative Xiaomi Mi8 and Huawei P40 smartphones. Using the proposed scheme, the root mean square (rms) of the positioning errors in the east, north, and up components in the open-sky environments is 0.18, 0.13, and 0.38 m, respectively. In complex urban environments, the rms of the positioning precisions in the east, north, and up components was as decent as 1.42, 1.97, and 2.63 m, respectively.

The availability of raw Android global navigation satellite system (GNSS) data is driving innovation in high-precision positioning using Android smartphones. However, inconsistent pseudorange and phase observations, low dual-frequency data integrity, and unknown receiver-side hardware biases prevent the ambiguity resolution of GNSS precise point positioning (PPP) for smartphones. In this study, we thus provide a comprehensive real-time kinematic precise point positioning (PPP-RTK) strategy. First, carrier phase observations are adjusted to be consistent with the pseudorange observations. Next, rapid single-frequency PPP convergence is achieved by regional atmospheric enhancement. Finally, intersatellite difference ambiguities are formed to eliminate unknown receiver-side hardware biases and combined with the partial ambiguity resolution strategy to achieve ambiguity-fixed centimeter-level smartphone PPP-RTK positioning. The results show that using the proposed PPP-RTK strategy, the root mean square (rms) of ambiguity-fixed solution positioning errors is 0.7, 1.3, and 2.5 cm in the east, north, and upper components, respectively, for a representative Huawei P40 smartphone connected to an external survey-type antenna, and 1.2, 1.5, and 5.8 cm for the P40 smartphone using its embedded antenna in an open-sky environment. And their ambiguity fixing rates all reached more than 98%. In 21 sets of experiments, PPP-RTK for smartphones with external and embedded antennas took an average of 1.0 and 63.5 s, respectively, to converge to an ambiguity-fixed solution with a horizontal positioning error within 5 cm. This provides a way for rapid and high-precision GNSS positioning in stand-alone mode for smartphones, which may facilitate the development and widespread use of smartphone high-precision GNSS positioning.

The increasingly improved performance of mass-market GNSS chipsets is driving smartphone GNSS positioning or velocimetry as a low-cost GNSS solution for high-precision vibration monitoring applications. In this study, the Android GNSS velocity measurement performance of mass-market smartphones was evaluated. Based on the smartphone GNSS data generated by the Geo + + RINEX Logger, we found smartphone anomalous clock variations, as evidenced by the biases between the TDCP-estimated and Doppler-estimated receiver clock drifts, as well as frequent jumps. As a result, the traditional Doppler and TDCP combination method that estimates the receiver TDCP clock drift as the same parameter as the Doppler clock drift is no longer applicable. To solve this problem, we provide two strategies, including inter-satellite differencing and dual clock drift estimation. The results of static and shake table experiments show that the traditional combination method solutions for smartphones contain many outliers, with the root mean square (RMS) of the horizontal velocity measurement errors exceeding 1 m/s. In contrast, using the inter-satellite differencing and dual clock drift estimation strategies, the velocity error RMS are both reduced to less than 1 cm/s. For a representative Huawei P40 smartphone, their static experimental horizontal velocity error RMS is 0.27 and 0.26 cm/s, respectively, and their mean velocity error RMS of six shaking tests are 0.52 and 0.40 cm/s, respectively. In addition, the causes of this anomalous clock variation are further discussed and the noise characteristics of Android multi-constellation multi-frequency Doppler and TDCP observations are analyzed. These results are encouraging and show that we can obtain a few mm/s velocities using inexpensive smartphones or their embedded GNSS chipsets. In this case, there is a cost-effective solution for implementing a dense network of monitoring arrays or developing low-cost monitoring instruments with integrated GNSS.

Global Navigation Satellite System (GNSS) is an important technical tool for building deformation monitoring, but in complex environments such as urban canyons, the GNSS signals received by monitoring stations are susceptible to severe multipath errors, resulting in a significant decrease in positioning precision. The multipath hemispherical map (MHM) model is a common method to mitigate multipath errors in GNSS, but its performance can be compromised by high-frequency multipath errors, outliers, and non-line-of-sight signals caused by nearby obstructions. In this study, an MHM model with geographic cut-off elevation constraints is proposed, which considers signal quality and terrain topography surrounding the station to mask those unsatisfactory signals, and leverages the advantages of the MHM model for mitigating low-frequency multipath. To validate the effectiveness of the proposed method, a GNSS deformation monitoring experiment was carried out in an urban environment. The results show that the root mean square (RMS) values of horizontal and vertical positioning errors for the ambiguity-fixed solution using the proposed method are 0.40 and 0.68 cm, respectively, showing improvements of 65.9% and 63.4% compared to the solution without multipath correction (M0), 43.8% and 37.0% to the solution using traditional MHM model (M1), and 63.2% and 50.0% to the solution using geographic cut-off elevation model (M2), respectively. Correspondingly, the ambiguity fixing rate increased from 84.95%, 95.31% and 98.97% of M0, M1 and M2 solutions to 99.95%. The proposed MHM model with geographic cut-off elevation constraints can improve the positioning precision, and thus would be helpful for GNSS deformation monitoring in complex environments.

An unwritten rule to resolve GNSS ambiguities in precise point positioning (PPP-AR) is that users should follow faithfully the frequency choices and observable combinations mandated by satellite clock and phase bias providers. Switching to other frequencies of measurements requires that the satellite clocks be converted, albeit in a roundabout way, to agree with the new frequencies of code biases. Satellite phase biases, on the other hand, are prescribed conventionally as wide-lane and narrow-lane combinations, which prevents users from resolving other phase combinations in the case of multi-frequency observables. We therefore develop an approach to compute observable-specific phase biases (phase OSBs) in concert with the legacy, but ambiguity-fixed, satellite clocks to enable PPP-AR over any frequency choices and observable combinations at the user end, i.e. , all-frequency PPP-AR. In particular, the phase OSBs on the baseline frequencies ( e.g. , L1/L2 for GPS and E1/E5a for Galileo) are estimated by decoupling the code OSBs pre-aligned with the satellite clocks; then satellite clocks are re-estimated by holding pre-resolved undifferenced ambiguities and phase OSBs on the baseline frequencies; finally, all third-frequency phase OSBs are determined by introducing the ambiguity-fixed satellite clocks above. We used a global network of multi-frequency GPS/Galileo data over a month to verify this approach. In dual-frequency PPP-AR using GPS L1/L2, L1/L5, Galileo E1/E5a, E1/E5b, E1/E5 and E1/E6 signals, over 95% of wide-lane and narrow-lane ambiguity residuals were within ±0.25 and ±0.15 cycles, respectively, after the code and phase OSB corrections on raw GNSS measurements. As a result, the ambiguity fixing rates reached around 95% in all PPP-AR tests, though it was only the satellite clocks aligned with the GPS L1/L2 and Galileo E1/E5a pseudorange that were applied throughout. We stress that the key to computing such phase OSBs for all-frequency PPP-AR is that the code OSBs have the same bias datum as that of the satellite clocks.

The availability of GNSS raw measurements and the improved performance of mass-market GNSS chipsets for tracking multi-constellation dual-frequency signals have facilitated the development of smartphone high-precision GNSS positioning. However, the channel-dependent carrier phase biases within typical smartphone GNSS chipset prevent Android multi-GNSS ambiguity resolution. In this study, the channel-dependent biases were investigated for the Android GLONASS G1, BDS B1I, Galileo E5a and QZSS L1 carrier phase observations. They destroy the integer property of GNSS ambiguities and result in varying GLONASS inter-frequency bias (IFB) rates. As a result, Android multi-GNSS double-difference ambiguity resolution is hindered and the traditional method of correcting for a constant GLONASS IFB rate is no longer applicable. We propose an on-the-fly phase biases correction method, which introduces reliability verification by resolving only the bias-free ambiguities and estimating the phase bias corrections on-the-fly by gain filtering. In this way, GPS/GLONASS/Galileo/BDS/QZSS dual-frequency ambiguities are resolved for a representative Xiaomi Mi 8 smartphone. For a ~ 13 km short baseline, when the smartphone is connected to an external survey-grade antenna, the time to first fix was 50 s and the fixing rate was 99.21% with the root mean square (RMS) of positioning errors of 1.32, 1.48 and 1.92 cm for the east, north and up components, respectively. Compared with dual-frequency GPS and five-constellation GNSS without phase biases correction, the ambiguity-fixing rate was improved by 30.4% and 99.2%, and the positioning accuracy was improved by 93.4% and 41.8%, respectively. In the case of the smartphone’s embedded antenna, the ambiguity-fixing rate of five-constellation GNSS dropped to about 60% due to multipath, but the positioning precision of its ambiguity-fixed solutions was still at centimeter level, which was less than one-tenth of its float solutions. Therefore, the implementation of multi-GNSS ambiguity resolution will further boost the potential of high-precision GNSS positioning for smartphones.