FLP-Aided GNSS RTK Positioning: A Means of Supporting Smartphone High-Precision Positioning in Dynamic Urban Environments

  • NAVIGATION: Journal of the Institute of Navigation
  • March 2026,
  • 73
  • navi.730;
  • DOI: https://doi.org/10.33012/navi.730

Abstract

The demand for precise and reliable location data has driven interest in achieving high-accuracy global navigation satellite system (GNSS) positioning with smartphones. However, unaccounted-for code modeling errors, such as multipath, hinder successful carrier-phase ambiguity resolution, especially in dynamic urban environments. This study proposes a new integration method combining GNSS carrier-phase measurements with fused location provider (FLP) positions to mitigate these errors. We investigate the performance of FLP-aided positioning in (a) a single-epoch real-time kinematic (RTK) scenario in which the model parameters are assumed to be unlinked in time and (b) a multi-epoch RTK scenario in which only a subset of the parameters, i.e., the carrier-phase ambiguities, are assumed to be constant over time. The analysis is based on experimental data sets obtained via a Google Pixel 5 smartphone tracking dual-frequency multi-GNSS signals, including L1 + L5 Global Positioning System, E1 + E5a Galileo, and B1 BeiDou Navigation Satellite System code- and carrier-phase observations. Despite severe code multipath, the proposed integration achieves centimeter-level accuracy in over 96% of ambiguity-fixed positioning solutions.

Keywords

1 INTRODUCTION

Real-time kinematic (RTK) positioning has revolutionized high-precision satellite navigation, providing instantaneous centimeter-level solutions, thus overcoming the limitations of standard single-receiver positioning by global navigation satellite systems (GNSSs). The role of RTK has become increasingly prominent in recent years, as a growing demand for precise and reliable positioning information has been witnessed across a wide variety of location-based applications, ranging from pedestrian navigation to commercial applications such as smart transportation and logistics (Amatetti et al., 2022; Nakaaki et al., 2019; Omae et al., 2006). However, the outstanding performance of RTK relies heavily on the resolution of ambiguous cycles (ambiguities) that are present between the carrier-phase measurements of the involved GNSS receivers (Teunissen, 1995). In turn, fast and successful carrier-phase ambiguity resolution requires the provision of auxiliary data, such as GNSS pseudorange (code) measurements, so as to help estimate the so-called “float” ambiguity solutions. Provided that the precision of the float ambiguities leads to a sufficiently large integer ambiguity resolution (IAR) success rate, the float ambiguities are then mapped to their correct integers, recovering the ultra-precise GNSS phase measurements and thereby enabling one to obtain fast centimeter-level positioning solutions.

In view of the dependency of RTK performance on accurate code measurements, extending the applicability of RTK to low-cost GNSS sensors, such as smartphones, remains a challenging task. This difficulty arises because the relatively poor GNSS antenna of low-cost sensors often fails to mitigate the adverse effect of code modeling errors such as signal multipath (Maqsood et al., 2013; Mohamadi et al., 2025). As a consequence, research on the acquisition of precise and reliable positioning solutions from smartphones has been ongoing since 2016, when Google announced that GNSS raw data (code and phase measurements) can be collected from Android Nougat and later operating systems. Accordingly, Humphreys et al. (2016) analyzed smartphone data sets and identified anomalies in such GNSS measurements; they concluded that while most of the anomalies can be identified and remedied, the presence of local multipath hampers high-accuracy smartphone positioning. The effect of multipath becomes more severe in urban environments owing to limited satellite visibility and the presence of large buildings. Subsequent research has shown that smartphones can achieve high-precision positioning under certain conditions. In this respect, Realini et al. (2017) used the goGPS software to process double-differenced (DD) phase observations of Global Positioning System (GPS) L1 signals and concluded that decimeter-level solutions can be realized when the antenna is stationary without the need for carrier-phase IAR. Chen et al. (2019) studied the performance of precise point positioning on a stationary Xiaomi Mi8 device and obtained sub-meter horizontal root mean squared errors (RMSEs) within 30 s. Li and Geng (2019) connected a Nexus 9 device to an external antenna and reported three-dimensional (3D) positioning errors of less than 0.5 m. Darugna et al. (2019) demonstrated that one can largely eliminate multipath by connecting smartphones to a choke-ring survey-grade antenna, leading to centimeter-level positioning even when the antennas are in motion. Liu et al. (2019) implemented an algorithm for RTK combined with an inertial measurement unit (IMU) for Mi8 smartphones and tested the algorithm via a kinematic experiment in suburban areas. The authors obtained meter-level horizontal RMSEs for two trial drives.

In addition to the identification of code multipath, several other studies have demonstrated that smartphone code measurements are also noisier by approximately one order of magnitude when compared with their counterparts collected by geodetic receivers (Paziewski et al., 2021). To compute the noise levels of such low-cost GNSS data, Odolinski and Teunissen (2019) employed the least-squares variance component estimation procedure (Amiri Simkooei, 2007; Teunissen & Amiri-Simkooei, 2008) and conducted a comprehensive assessment of smartphone RTK positioning. The authors showed that the usage of low-cost patch antennas can sometimes double the magnitude of GNSS code standard deviations, hindering successful near-real-time IAR.

To overcome the adverse effects of code modeling errors and high noise levels, particularly in GNSS-challenged environments, one may integrate GNSS with “auxiliary” sensing devices such as lidar and inertial navigation systems (see, e.g., the work by Zhang et al. (2022)). Positioning solutions obtained by such sensors may replace noisy and often multipath-affected code measurements so as to increase the probability of correctly mapping the carrier-phase float ambiguities to their integers, thereby considerably improving the RTK positioning performance in urban environments. The present contribution provides a study on the potential of a lesser-known auxiliary service to aid the performance of smartphone RTK, the Google fused location provider (FLP) service (see the work by Google Developers (2020)). In marked contrast to the aforementioned complementary sensory data, the FLP-derived positioning solution should not be viewed as a complement to the GNSS code data. Instead, it should be regarded as a multipath-mitigated version of the code-derived solution. Therefore, we propose the integration of GNSS carrier-phase measurements with FLP-derived positioning solutions to increase the carrier-phase ambiguity success rate. This proposal relies on the assumption that the FLP-derived solution is largely multipath-mitigated as compared with its GNSS-only code-derived counterpart. To quantify the role of FLP in RTK, we analyze the rover positioning performance under several models of RTK, ranging from single-epoch GNSS-only to multi-epoch FLP-aided RTK. The underlying analysis is conducted on the basis of experimental data sets collected from survey-grade GNSS receivers and smartphones.

This article is organized as follows. In Section 2, we briefly review FLP and its diverse sensory sources. We illustrate how the precision of FLP-derived positioning solutions can reduce the ambiguity dilution of precision (ADOP). In Section 3, both the single- and multi-epoch RTK models are discussed, followed by their FLP-aided versions utilizing FLP location information. Section 4 is devoted to the experiment and its associated data sets, where we highlight a specialized Android app that has been developed with the objective of obtaining accurate FLP solutions. In Section 5, we conduct a comparative study to evaluate the positioning performance of single- and multi-epoch FLP-aided RTK models. For this study, data sets of a Google Pixel 5 (GP5) device and a survey-grade Topcon HiPer VR receiver are processed, and the performances of the corresponding ambiguity-resolved positioning solutions are assessed. In both cases, a permanent Norway GNSS station (equipped with a Trimble NETR9 receiver) serves as the base station. Finally, we provide a summary with concluding remarks in Section 6.

2 FLP TO REDUCE THE ADOP

In addition to standard point positioning, which is realized by GNSS code measurements, smartphones may also take advantage of several other location-based information services to obtain accurate positioning solutions. Location-based technologies such as internet Wi-Fi (Zou et al., 2017), wireless networks (Szilvasi et al., 2012), terrestrial cellular networks (Shamaei & Kassas, 2019), and 3D building models (Groves et al., 2012) can support smartphone positioning. Groves et al. (2012) showed how 3D building models can help detect non-line-of-sight GNSS signals, thus largely avoiding multipath-affected code measurements in the positioning estimation process. As a result, Google has developed an application programming interface for smartphone positioning, the FLP service, to mitigate the adverse effect of GNSS code modeling errors. This location-based service integrates GNSS code data with diverse sensory sources, including 3D mapping-aided GNSS (Groves et al., 2012), to deliver accurate location information. The FLP uses a machine-learning model that leverages 3D building models and other data sources to compute GNSS locations by analyzing a grid of potential locations and measuring the discrepancies between the expected and actual ranges at each grid point. The model identifies which combinations of residuals correspond to the receiver position through a vast amount of training data.

Although the FLP service is commonly used in smartphone single-point positioning, its role in improving the carrier-phase ambiguity resolution strength and, therefore, in enhancing smartphone RTK baseline positioning has not been studied. To provide insight into such a role, one may establish an explicit link between the precision of the FLP-derived positioning solution and the IAR performance. To do so, we commence with the concept of ADOP (Teunissen, 1997). From ADOP, one can infer the probability of correctly resolving the carrier-phase ambiguities, the so-called ambiguity success rate. Smaller ADOP values correspond to a higher upper bound of the ambiguity success rate. For ADOP values smaller than 0.12 cycles, the stated upper bound always remains higher than 99.9%. The ADOP of the single-epoch RTK model can be expressed as follows (Odijk & Teunissen, 2008):

ADOP=2m1m−1σϕλ(1+σp2σϕ2)32f(m−1)1

where f and m denote the numbers of frequencies and satellites commonly tracked by the involved GNSS receivers, respectively. The geometric average of the carrier-phase wavelengths on f frequencies is given by λ. The standard deviations of “undifferenced” phase and code measurements are denoted as σϕ and σp, respectively.

As Equation (1) indicates, the ADOP is largely driven by the variance ratio (σp2/σϕ2). For current GNSS receivers, the stated ratio is large, as the precision of code measurements is often two orders of magnitude worse than that of its carrier-phase counterparts. This increase in both the number of frequencies f and the number of satellites m can reduce ADOP values. Now, we assume that the FLP-derived positioning solution replaces its GNSS-only code-derived version. We also assume that the precision of this FLP-derived solution is smaller than that of the code-derived solution by a factor of γ. Under these assumptions, the corresponding ADOP would decrease, indicating that carrier-phase IAR can indeed benefit from the provision of the FLP-derived positioning solution. Hereafter, we refer to the scalar γ as the “reduction factor.” By definition, γ is larger than one. Let ADOPFLP denote the ADOP of the FLP-aided single-epoch RTK model. The ratio of the RTK ADOP to ADOPFLP can then be shown to read as follows:

ADOPADOPFLP=(σp2+σϕ2σp2+γ2σϕ2)32f(m−1)γ3f(m−1)≈γ3f(m−1)2

The approximation follows as the magnitude of the code variance σp2 is much larger than the phase variance σϕ2. According to Equation (2), ADOPFLP becomes monotonically smaller than the RTK ADOP as the reduction factor increases. However, the rate of this ADOP decrease depends on the numbers of frequencies f and satellites m. For the dual-frequency case (f = 2), Figure 1 presents RTK ADOP values (left) as well as the corresponding ADOP ratios (right) as expressed in Equation (2). As shown, the RTK ADOP for low-cost receivers with code standard deviations larger than 2 m requires more than nine commonly tracked satellites to reach a value below 0.12 cycles (dashed line). In contrast, the ADOP reduction becomes more pronounced when fewer commonly tracked satellites are present. This result highlights the importance of aiding GNSS with complementary sensors for improving the IAR performance in GNSS-challenged environments where a limited number of satellites are tracked. Thus, in the following, we present FLP-aided RTK models and study their IAR performance.

(Left) ADOP values from Equation (1) for the single-epoch, dual-frequency RTK model for different values of the code standard deviation σp (meters) as a function of the number of satellites m; (right) ADOP ratios from Equation (2) for different numbers of satellites m as a function of the reduction factor γ The phase standard deviation is set to σϕ = 0.006m. The dashed line indicates the ADOP value of 0.12 cycles.
FIGURE 1

(Left) ADOP values from Equation (1) for the single-epoch, dual-frequency RTK model for different values of the code standard deviation σp (meters) as a function of the number of satellites m; (right) ADOP ratios from Equation (2) for different numbers of satellites m as a function of the reduction factor γ

The phase standard deviation is set to σϕ = 0.006m. The dashed line indicates the ADOP value of 0.12 cycles.

3 UNDERLYING MODELS

In this section, we discuss the RTK model for both single- and multi-epoch short-baseline measurement setups. Here, the term “short baseline” refers to the distance between the rover and base station for which atmospheric delays can be assumed negligible (e.g., less than 10 km). We then introduce an extension to the model by utilizing the FLP positioning information.

3.1 Single-Epoch RTK

The DD system of GNSS observation equations at epoch t, in its linearized form, can be expressed as follows (Teunissen & Montenbruck, 2017):

E(yt)=Atxt, with yt=[ϕtpt] and At=[AϕtApt]3

where E(⋅) denotes the expectation operator. The observation vector yt contains the DD carrier-phase and code measurements ϕt and pt, respectively. The unknown parameter vector xt=[atT,btT]T contains the DD integer ambiguities at and the 3×1 rover positioning increment vector bt. The unknown parameters are linked to the measurement via the known phase and code design matrices Aϕt=[Λ,Gt] and Apt=[0,Gt], where the geometry matrix Gt is formed by the between-satellite single-differenced rover-to-satellite line-of-sight unit vectors. The f(m−1)×f (m−1) diagonal matrix Λ = Λf ⊗Im−1, with Λf = diag(λ1,…, λf), contains the carrier-phase wavelengths. The symbol ⊗ denotes the matrix Kronecker product.

3.2 Multi-Epoch RTK

The single-epoch RTK model does not make use of the temporal behavior of the unknown parameters xt=[atT,btT]T. However, one can incorporate information about the parameters' temporal behavior into the estimation process in order to increase the model’s strength. For instance, the DD phase ambiguities at are known to remain constant over time unless cycle slips occur. One can also account for the dynamic motion of the GNSS antenna, e.g., via a constant-velocity dynamic model (Zhang et al., 2022). In this study, we do not make use of such additional information and treat the antenna position bt as an unlinked-in-time parameter. In this “fully kinematic” setup, only the DD ambiguities at are treated as time-constant parameters. Accordingly, the multi-epoch version of the RTK model in Equation (3) is as follows:

E(yt−1)=At−1xt−1,0=FT(xt−xt−1), t=2,3,…E(yt)=Atxt4

where FT=[If(m−1),0]. The unknown parameters involved in the above multiepoch formulation can be recursively estimated under a generalized Kalman filter formulation (Teunissen et al., 2021). The advantage of the multi-epoch formulation in Equation (4) over its single-epoch version in Equation (3) is that the float ambiguity solutions become more precise as the number of epochs increases, thus enabling successful IAR. However, unlike its single-epoch version, the model in Equation (4) is not immune to phase cycle slips. Thus, potential cycle slips should be identified and adapted during filtering.

3.3 Single-Epoch FLP-Aided RTK

To avoid unwanted code modeling errors, our earlier single-epoch RTK model can be revised by replacing the FLP-derived positioning solution with the corresponding GNSS-only code-derived solution. Let the increment of this FLP-derived positioning solution at epoch t be given by the 3×1 vector yFLP,t. Accordingly, the single-epoch model in Equation (3) may be modified as follows:

E(ϕt)=AϕtxtE(yFLP,t)=[0,I3]xt5

Note that auxiliary observation vector yFLP,t must support the GNSS carrierphase data ϕt because the DD phase data in E(ϕt)=Λat+Gtbt are fully reserved for the unknown DD ambiguities at, causing the single-epoch system of phase-only observation equations to be under-determined. Therefore, the role of the FLP-derived positioning solution yFLP,t is to help determine the float ambiguities. Once the unknown ambiguities at are successfully resolved, the system of ambiguity-resolved phase observation equations E(ϕt−Λat)=Gtbt can serve to deliver RTK solutions of bt.

3.4 Multi-Epoch FLP-Aided RTK

As with the GNSS-only single-epoch model in Equation (3), the FLP-aided RTK model in Equation (5) is immune to any potential phase cycle slips. However, the IAR performance of the model in Equation (5) relies on the provision of an accurate FLP-derived positioning solution yFLP,t. In the event that FLP fails to provide accurate solutions, successful IAR may be hampered. As with our earlier GNSS-only multi-epoch model in Equation (4), one can further strengthen the FLP-aided model by incorporating the temporal behavior of the ambiguities into the estimation process. This multi-epoch formulation can be realized by imposing the constraints FT(xt−xt−1)(t=2,3…) on the system of observation equations. This results in the following multi-epoch FLP-aided RTK model:

E(yt−1)=At−1xt−1E(yFLP,t−1)=[0,I3]xt−10=FT(xt−xt−1), t=2,3,…E(yt)=AtxtE(yFLP,t)=[0,I3]xt6

Employing the above model is advantageous because if the FLP service delivers inaccurate solutions, the successful IAR may still be realized if the number of epochs is sufficiently large. As with its GNSS-only version, this formulation also requires the identification and adaptation of potential phase cycle slips because the involved DD ambiguities are treated as time-constant parameters.

3.5 IAR Performance of the Four RTK Models

In this subsection, we evaluate the formal performance of the four RTK models discussed above. To assess the performance of these models and predict their IAR performance before any measurements are taken, we must consider the variance matrix of the float ambiguity solutions. This variance matrix allows us to evaluate the formal ambiguity success rate corresponding to the optimal IAR method of integer least-squares (ILS). To achieve this, we make use of the Ps-LAMBDA software (Verhagen et al., 2013).

The corresponding results are presented in Figure 2, which compares the formal ILS success rates for two different configurations of GPS-only(left) and GPS+Galileo (right). The top row of the figure corresponds to single-epoch RTK (Equation (3)) and FLP-aided RTK (Equation (5)) models, whereas the bottom row corresponds to the multi-epoch RTK (Equation (4)) and FLP-aided RTK (Equation (6)) models. To capture the precision of the GNSS data, the phase standard deviation is set to 6 mm, whereas the code standard deviation ranges from 0.2 m to 2 m. The precision improvement in the FLP solution is characterized by the reduction factor γ, which ranges from 1.11 to 2.5. A larger value of γ indicates a more precise FLP solution.

Formal ILS success rates as a function of the code standard deviation for (left) GPS-only and (right) GPS+Galileo constellations, corresponding to the RTK models in Equations (3)-(6) The top row corresponds to the single-epoch models in Equations (3) and (5), whereas the bottom row corresponds to the multi-epoch models in Equations (4) and (6), evaluated using five epochs. The FLP reduction factor γ = [1.11, 1.25, 1.42, 1.66, 2.00, 2.50] is applied to the code standard deviation.
FIGURE 2

Formal ILS success rates as a function of the code standard deviation for (left) GPS-only and (right) GPS+Galileo constellations, corresponding to the RTK models in Equations (3)-(6)

The top row corresponds to the single-epoch models in Equations (3) and (5), whereas the bottom row corresponds to the multi-epoch models in Equations (4) and (6), evaluated using five epochs. The FLP reduction factor γ = [1.11, 1.25, 1.42, 1.66, 2.00, 2.50] is applied to the code standard deviation.

Figure 2 clearly demonstrates that the ILS success rate increases as the FLP solution becomes more precise (i.e., as γ increases). This highlights the enhanced performance of the RTK models when a more precise FLP solution is employed. The figure also indicates that integrating both the GPS and Galileo constellations results in higher success rates as compared with the GPS-only configuration. Incorporating multi-epoch data into the RTK and FLP-aided RTK models further improves the IAR performance. These formal results underscore the effectiveness of the FLP-aided multi-epoch and multi-GNSS models in obtaining precise positioning solution. In Section 5, we examine the performance of this model via real-world data sets.

The results in Figure 2 illustrate that while FLP-aided RTK can enhance ambiguity resolution, its effectiveness depends on the precision of the FLP-derived positioning solution. If the FLP precision is sufficiently high (i.e., γ > 1.25), the FLP solution provides a constraint that improves ambiguity resolution and enhances fixed solution availability. However, when the FLP precision is too low (i.e., γ < 1.1), the aiding effect of the FLP solution becomes negligible, and the ambiguity resolution performance does not significantly improve. Nonetheless, FLP serves as a multipath-mitigated positioning solution, which can be particularly beneficial in urban environments where stand-alone GNSS suffers from severe multipath effects and signal blockage. In such cases, the integration of multi-GNSS and multi-epoch RTK filtering further mitigates residual errors, improving the stability and accuracy of smartphone-based RTK positioning.

The sensitivity of the FLP-aided RTK model to FLP quality is governed by the reduction factor γ, which quantifies the improvement in precision of the FLP solution compared with the GNSS-only code-derived solution. As shown in Figure 2, a higher γ leads to a sharper improvement in the IAR success rate. However, when the FLP solution is imprecise (e.g., γ ≈ 1.0), its contribution to ambiguity resolution becomes negligible. In such cases, the model behaves similarly to the standard RTK formulation. Notably, the inclusion of an imprecise FLP solution can potentially degrade the positioning performance when the variance matrix of the FLP solution is not correctly specified. In this study, we set the values of the FLP variance matrix empirically. As an alternative, a more detailed investigation using variance component estimation methods can be employed to rigorously set this variance matrix.

4 EXPERIMENTAL SETUP

Static data sets were utilized to assess the proposed single- and multi-epoch FLP-aided RTK methods. These data sets were collected from GNSS receivers of different grades located in a dynamic urban canyon near the Gløshaugen campus of the Norwegian University of Science and Technology. Table 1 and Figure 3 show the antenna setup used to assess the phase and code observation of the GNSS satellites. In this study, low-cost mobile phone GP5 and high-cost survey-grade Topcon HiPer VR receivers and antennas were deployed in the urban canyon, and results were compared with those obtained via a station equipped with a survey-grade Trimble NETR9 receiver from Norway’s HxGN SmartNet network. The objective was to evaluate the performance of GNSS receivers with different grades, including those with superior antenna quality and higher cost, in comparison to smartphones equipped with FLP-aided models. It should be noted that the Topcon HiPer VR and Trimble NETR9 receivers do not have FLP capabilities but are capable of receiving signals with higher quality owing to their advanced antenna design. We utilized TRON, a permanent RTK base station within Norway’s HxGN SmartNet network, as our reference station. The GP5 smartphone is capable of tracking dual-frequency GPS L1 + L5, Galileo E1 + E5a, and BeiDou Navigation Satellite System (BDS) B1 code and phase observations. The smartphone logs the observations through Geo++ RINEX Logger version 2.1.6.

Baseline TRON-GS01 and TRON-GS02 located in Trondheim, Norway: (left) TRON station; (middle) baseline configuration (Map data © 2023 Google); (right) GS01 and GS02 stations
FIGURE 3

Baseline TRON-GS01 and TRON-GS02 located in Trondheim, Norway: (left) TRON station; (middle) baseline configuration (Map data © 2023 Google); (right) GS01 and GS02 stations

View this table:
TABLE 1 Site Identity, Receivers, and GNSS Signals Used in This Study

This study evaluates the role of FLP-aided RTK in environments where multipath significantly affects GNSS ambiguity resolution, as FLP—through its multi-sensor fusion approach—is generally less sensitive to such effects. Conducting open-sky tests, where multipath is minimal, would not fully demonstrate the advantages of FLP. Additionally, while kinematic RTK testing would further validate the real-world applicability of FLP, collecting data and establishing an accurate ground-truth reference in kinematic scenarios present challenges, particularly for a smartphone-based GNSS. However, we fully acknowledge that kinematic validation is essential for mobile applications such as intelligent transportation systems and level-4 autonomous driving, where real-time, high-precision positioning under motion is critical. As a result, kinematic evaluation is planned as future work, where high-precision reference systems will be integrated for further assessment. These systems may include tightly coupled GNSS/IMU integration or visual-inertial odometry, enabling reliable benchmarking of FLP-aided RTK performance in dynamic conditions.

The test environment was inherently dynamic owing to continuous changes such as moving vehicles, pedestrians, and urban obstructions. These factors introduce variations in multipath effects and GNSS signal conditions, making the environment representative of real-world urban navigation scenarios. Because FLP is designed to mitigate multipath, evaluating its performance under these dynamic conditions provides insights in smartphone-based RTK positioning.

To achieve fixed positioning solutions, we employ the LAMBDA method (Teunissen, 1995) with a partial IAR strategy (Hou et al., 2016) for all four models. When the ambiguities are successfully fixed, the ambiguity-resolved carrier-phase observations enable millimeter- to centimeter-level precision of the baseline. To collect FLP data, we developed a specialized Android app with the objective of obtaining the most precise FLP solution available. The app was designed to run on a wide range of Android devices and to take advantage of the latest positioning technologies available on such devices.

Figure 4 presents the architecture of the developed FLP application, demonstrating adherence to the model-view-controller (MVC) design pattern, a stalwart of structured software engineering. The MVC paradigm facilitates the separation of concerns, streamlining the development and subsequent maintenance of the application. The model component is responsible for managing data and executing business logic. Central to these tasks is the acquisition of location data, which is a fundamental aspect of the FLP application. The model interacts with both the Android location service and the Google FLP to obtain GNSS location updates, as well as handling the storage of these data in the SQLite database. The view component is the graphical user interface through which users interact with the application. This component offers functionalities such as GNSS location acquisition, data storage, interface management, and an optional countdown timer for location tracking over extended periods. The controller acts as the intermediary, processing user inputs from the view component, invoking the relevant modules within the model to perform the necessary operations, and updating the view with the results.

Architecture of the developed FLP application employing the MVC design pattern The architecture delineates the distribution of the application into three interconnected components: a model component that manages data and business logic with location services; a view component that provides a user interface (UI) for interaction and display; and a controller component that orchestrates the flow of data between the model and the view. This structure facilitates streamlined development, security, and maintenance. The application was developed using Java and XML, with data storage handled by an SQLite database, tested and verified on Android 11 and above.
FIGURE 4

Architecture of the developed FLP application employing the MVC design pattern

The architecture delineates the distribution of the application into three interconnected components: a model component that manages data and business logic with location services; a view component that provides a user interface (UI) for interaction and display; and a controller component that orchestrates the flow of data between the model and the view. This structure facilitates streamlined development, security, and maintenance. The application was developed using Java and XML, with data storage handled by an SQLite database, tested and verified on Android 11 and above.

In practice, the user engages with the view component to initiate actions such as location acquisition and data storage. These actions are relayed to the controller, which validates and forwards the instructions to the appropriate modules in the model. For instance, when the “save data” command is issued, the model interacts with the database to save the location data. The model also manages a countdown timer, automating the retrieval and storage of location data at predefined intervals. The application was crafted using Java for the core logic, with extensible markup language (XML) utilized for defining application settings and the user interface. For data persistence, the SQL language is employed within the SQLite database module. The application has been tested on a Pixel 4 emulator running Android 11 (application programming interface 30) and has been confirmed to operate on a GP5 smartphone with Android versions 11 and above. The SQLite database, integrated into the Android ecosystem, stores critical location data, including longitude, latitude, altitude, and timestamp information. These data can be accessed from the smartphone’s download folder, facilitating export via email or direct transfer to a computer.

Figure 5 displays the interface visualization of the FLP application as rendered on a Pixel 4 emulator running Android 11, offering a practical demonstration of the application functionality. Figure 5(a) depicts the FLP application icon on the home screen of the emulator, serving as the entry point for the user. Figure 5(b) illustrates the primary output of the application’s core modules, displaying the collected GNSS location data from the FLP client after the “GET FLP LOCATION” action is initiated. The acquired data are presented in terms of longitude, latitude, and altitude. Simultaneously, to ensure accuracy, the application fetches and displays a basic GNSS location from the Android location service for comparative purposes. Figure 5(c) highlights the user’s ability to store collected location data in the database with the “SAVE LOCATION TO DB” button. Upon successful data storage, a confirmation message is displayed, affirming the completion of the operation. Figure 5(d) introduces the countdown timer functionality, where the user can input a specific duration after which the application will automatically begin the location data collection process. Figure 5(e) displays the active countdown timer, with the remaining time prominently indicated in blue. This automated process ensures that location data are methodically captured and stored without continuous user intervention. Figure 5(f) showcases the “CLEAR” button’s functionality, which clears the displayed location information from the screen. This feature provides the user with a clear indication that a new session of location data collection can be initiated. Additionally, the application facilitates the visualization of saved location data within the phone’s “download” directory, which can be accessed and managed through the software DB Browser for SQLite. This function supports the user’s ability to review and export collected data for further use or analysis.

Interface of the developed FLP application on a Pixel 4 emulator with Android 11: (a) app icon on the home screen, (b) real-time collection of GNSS and FLP location data, (c) feedback upon successful data storage, (d) input interface for the countdown timer, (e) countdown timer during operation, and (f) interface after location data have been cleared These panels collectively exhibit the application capabilities in acquiring, processing, and managing location data for accuracy and efficiency.
FIGURE 5

Interface of the developed FLP application on a Pixel 4 emulator with Android 11: (a) app icon on the home screen, (b) real-time collection of GNSS and FLP location data, (c) feedback upon successful data storage, (d) input interface for the countdown timer, (e) countdown timer during operation, and (f) interface after location data have been cleared These panels collectively exhibit the application capabilities in acquiring, processing, and managing location data for accuracy and efficiency.

The FLP solution used in this study was obtained exclusively from Android-based devices. The Topcon HiPer VR receiver does not utilize FLP data and serves as a reference for comparison purposes.

The FLP-derived positioning solution used in this study is treated as an external aiding source to support RTK ambiguity resolution. However, Google does not provide explicit precision metrics for FLP positions, meaning that their accuracy cannot be directly analyzed. Instead, the effectiveness of FLP aiding is inferred based on observed improvements in RTK performance. FLP information is available at every epoch, ensuring continuous support for RTK processing. However, the accuracy of this information may vary depending on environmental factors such as urban density, multipath conditions, and satellite visibility, which influence the sensor fusion process used to generate FLP positions.

Although the proposed models assume continuous FLP availability, we acknowledge that in practice, FLP outputs may occasionally be delayed or missing owing to device limitations or urban obstructions. In the single-epoch FLP-aided RTK model, when FLP data are unavailable, the model reverts to the conventional GNSS-only RTK formulation using code- and carrier-phase measurements. This fallback makes the solution more sensitive to multipath and typically degrades ambiguity resolution performance. In the multi-epoch FLP-aided RTK model, intermittent FLP outages can be handled via the time-update step of Kalman filtering. When an FLP update is missing at a certain epoch, the filter time-predicts a new FLP solution using the FLP solution of the previous epoch and the dynamic model of the position state. The precision of this time-predicted solution becomes worse as the time gap between epochs increases. Consequently, the corresponding ambiguity resolution performance may temporarily degrade until FLP support resumes. These considerations highlight the importance of robust and continuous FLP availability for maintaining optimal RTK performance.

Smartphone manufacturers often use a duty-cycling technique to reduce power consumption, which involves tracking the carrier phase for short periods and then shutting down tracking for the following periods. This approach results in non-continuous GNSS carrier-phase observations, which can negatively impact the accuracy and reliability of positioning. To address this issue, starting from Android 9 and subsequent versions, a new feature known as “force full GNSS measurements” has been introduced for developers. This feature allows for continuous carrier-phase tracking, thereby increasing the data availability and the continuous nature of phase measurements. However, it is important to note that enabling this feature will increase the power consumption of the smartphone, which may have an impact on battery life. Therefore, during the experiment, we disabled the duty-cycling settings of the smartphones to ensure observation continuity.

The GNSS stochastic model used in this study is based on a sinusoidal satellite elevation weighting strategy with undifferenced standard deviations, capturing the randomness of the GNSS observations. Table 2 presents the specific standard deviations used in the stochastic model, as well as a detailed description of the setup configuration employed in the analysis, acting as a reference for the model. The use of the same code and phase standard deviations for each individual GNSS is an important aspect of the model configuration, ensuring consistency across different data sources and reducing errors in estimated positions. The stated elevation weighting function is applied to address the degradation in GNSS data precision when satellites are tracked at low elevation angles. Thus, the GNSS data with higher elevations are given more weight, as they tend to provide more precise solutions.

View this table:
TABLE 2 Details of Static Data Sets, Wherein TRON is Established as the Reference Station for All Devices The typical values for zenith-referenced standard deviations (STDs) of the undifferenced measurements are set a priori (see, e.g., the work of Amiri-Simkooei and Tiberius (2007) or Zaminpardaz et al. (2017)).

5 NUMERICAL RESULTS

In this section, we conduct a numerical analysis, assessing the performance of the proposed single- and multi-epoch FLP-aided RTK GNSS positioning models and subsequently comparing them with their stand-alone counterparts. In this assessment, our study focuses on two fundamental performance metrics, namely, positioning accuracy and the availability of fixed positions.

  • Positioning accuracy: This metric is evaluated by comparing estimated positions from different methods with reference positions obtained from a total station. The RMSE is used as the metric to measure this difference. The RMSE is calculated as the square root of the mean of the squared differences between the estimated values and the truth values, providing an estimate of the variability or dispersion of errors in the estimated values compared with the ground-truth coordinates. Thus, smaller RMSE values indicate more accurate positioning solutions.

  • Percentage of fixed positions with an RMSE smaller than 10 cm: This parameter quantifies the “availability” of fixed-positioning methods. The formula for calculating the availability of fixed positions is as follows:

Availability of fixed positions=#solutions with an RMSE less than 10cmTotal number of positions ×100%7

In this study, a fixed solution refers to positions with an RMSE smaller than 10 cm. The choice of 10 cm as a threshold is based on its relevance to level-4 autonomous robotic applications, where precise localization is essential for safe and efficient operation. The ground-truth positions were determined by using a total station, ensuring an accurate reference for RMSE calculations.

We evaluate the positioning performance of the GP5 mobile phone, which is a low-cost device, and the Topcon HiPer VR survey-grade receiver, which is a high-cost device, by utilizing FLP-aided models and comparing them with conventional RTK GNSS positioning methods. Furthermore, we compare the positioning performance of GP5 and Topcon HiPer VR receivers and antennas deployed in an urban canyon with that of a permanent station equipped with a survey-grade Trimble NETR9 receiver from Norway’s HxGN SmartNet network. This comparison will enable us to assess the positioning performance of receivers with different grades, including those with superior antenna quality and higher cost, in comparison to smartphones equipped with FLP-aided models.

Table 3 provides a comprehensive comparison of single- and multi-epoch RTK and FLP-aided RTK techniques employing GP5, Topcon HiPer VR, and Trimble NETR9 instruments. The comparison takes into account positioning accuracy and fixed solution availability. The table presents positioning accuracy data for the east, north, and up directions, as well as the availability for each device and method. The observations were collected over 63, 60, and 120 min for GP5, Topcon HiPer VR, and Trimble NETR9, respectively, utilizing GPS L1 + L5 + Galileo E1 + E5a + BDS B1 signals.

View this table:
TABLE 3 Positioning Accuracy and Availability Corresponding to the RTK Models Using Different Devices This table presents the positioning accuracy (in east [E], north [N], and up [U] directions) and availability of single- and multi-epoch RTK and FLP-aided RTK methods, using Trimble NETR9, Topcon HiPer VR, and GP5. The data for each device were collected for 63, 80, and 60 min, respectively, as indicated in Table 2. GPS L1 + L5 + Galileo E1 + E5a + BDS B1 observations were utilized in these models.

The results demonstrate that the Trimble NETR9 performs the best in terms of the availability of fixed positions among the three receivers tested, achieving 100% availability in both single- and multi-epoch RTK methods. This superior performance is due to the fact that Trimble NETR9 is a survey-grade receiver located in an open-sky environment. In contrast, the Topcon HiPer VR has a lower availability in the single-epoch RTK scenario because of the impact of multipath caused by the urban canyon environment. However, the FLP-aided model can improve the availability of the Topcon HiPer VR in the single-epoch RTK mode. The lowest availability was observed for the GP5 receiver for both single- and multi-epoch RTK, as it is a lower-cost receiver. However, in the multi-epoch FLP-aided RTK scenario, GP5 provides an availability comparable to that of the Topcon HiPer VR. This finding indicates that the FLP-aided model can improve the availability of GP5 to a certain extent, making it comparable to that of a high-cost receiver. In addition to availability, this study evaluated the accuracy of fixed positions. The results show that all three receivers consistently achieve centimeter-level accuracy in all three dimensions using both single- and multi-epoch RTK methods.

Regarding the accuracy of the float positioning solutions, the Trimble NETR9 has an RMSE of 0.230 m (east), 0.228 m (north), and 0.518 m (up) in single-epoch RTK mode. In multi-epoch RTK mode, the RMSE values are 0.037 m (east), 0.053 m (north), and 0.085 m (up). In contrast, the Topcon HiPer VR exhibits higher RMSE values in float solutions across all directions in both single- and multi-epoch scenarios. This result is expected because of the influence of multipath effects in the urban canyon test site compared with the low multipath environment in which the Trimble NETR9 is located. The RMSE values of float solutions are also worse for the FLP-aided RTK methods compared with conventional methods.

In the case of the low-cost receiver, GP5, poor float solution accuracy is observed in both single- and multi-epoch RTK modes. In single-epoch RTK mode, the RMSE values for the east, north, and up components are 8.696 m, 5.105 m, and 26.654 m, respectively. These inaccuracies are attributed to the low-cost antenna of the smartphone and the impact of multipath in the test site’s environment. However, the study reveals that the FLP-aided model significantly improves the float solution accuracy of GP5 in multi-epoch RTK scenarios. The RMSE values for the east, north, and up components are improved to 0.163 m, 0.869 m, and 0.252 m, respectively, making the accuracy comparable to that of higher-cost receivers.

Although differences in positioning accuracy along the north and east directions may be influenced by GNSS satellite geometry, multipath effects, and environmental factors, this study primarily focuses on evaluating the feasibility of achieving sub-10-cm accuracy rather than analyzing directional error distributions. Because the percentage of correctly fixed solutions (i.e., those with RMSE < 10 cm) is the key performance indicator, further investigation into the north-east accuracy discrepancy was not conducted.

Table 3 compares the performance of Trimble NETR9, Topcon HiPer VR, and GP5 receivers in single- and multi-epoch RTK and FLP-aided RTK modes, indicating their ability to provide accurate and available positioning solutions using different signals. Trimble NETR9 demonstrates the highest availability and accuracy, whereas Topcon HiPer VR faces limitations in availability owing to urban canyon environments. GP5 shows lower availability but can benefit from the FLP-aided model. Despite the accuracy limitations of GP5, the FLP-aided model shows greatly improved accuracy in multi-epoch RTK scenarios, making it comparable to higher-cost receivers.

In the event that no signal tracking failures or multiple phase cycle slips occur, the Kalman filter underlying the multi-epoch GNSS models can run without the need to be re-initialized throughout the experiment. In practice, however, the filter may sometimes needs to re-initialized so as to avoid the adverse effect of modeling errors in the positioning estimates. To address this issue and gain further insights into the impact of filter re-initialization on positioning performance, an additional scenario was investigated. In this scenario, the Kalman filter is re-initialized at different time intervals, including every 10 s, 30 s, 1 min, 5 min, 10 min, 15 min, and 30 min. Each time that the Kalman filter is re-initialized, it makes use of the current available measurements to reset the state and covariance matrices. Table 4 presents the effect of Kalman filter re-initialization on the availability of fixed positions in the multi-epoch RTK and FLP-aided RTK methods. The table displays the percentage of fixed positions with a re-initialized Kalman filter at different time intervals for the GP5 and Topcon HiPer VR devices. For the GP5, in the multi-epoch RTK method, the availability of fixed positions gradually increases with longer re-initialization intervals. For a re-initialization interval of 10 s, only 1% of positions are fixed, whereas the percentage increases to 2% for a re-initialization interval of 30 s. The availability further improves to 4% for 1 min, 19% for 5 min, 36% for 10 min, 43% for 15 min, and 56% for 30 min. In the multi-epoch FLP-aided RTK method, the availability of fixed positions is higher than that of the multi-epoch RTK method. The availability starts at 16% for a re-initialization interval of 10 s and gradually increases to 18% for 30 s, 22% for 1 min, 32% for 5 min, 45% for 10 min, 48% for 15 min, and 63% for 30 min .

View this table:
TABLE 4 Effects of Kalman Filter Re-initialization on Availability of Fixed Positions for Multi-Epoch RTK and FLP-Aided RTK Methods The percentage of fixed positions is shown for different Kalman filter re-initialization intervals for GP5 and Topcon HiPer VR devices in multi-epoch RTK and FLP-aided RTK methods.

For the Topcon HiPer VR device, both the multi-epoch RTK and multi-epoch FLP-aided RTK methods exhibit a significantly higher availability of fixed positions. In the multi-epoch RTK method, the availability is consistently high, starting at 99.9% for a re-initialization interval of 10 s and reaching 100% for intervals of 1 min and longer. Similarly, in the multi-epoch FLP-aided RTK method, the availability remains consistently high at 99.97% or higher for all re-initialization intervals.

The findings of this study emphasize the positive correlation between longer re-initialization intervals and improved availability of fixed positions. Additionally, the FLP-aided RTK method consistently outperforms the standard RTK method in terms of fixed position availability across all re-initialization intervals.

Figure 6 presents a comparison of the code multipath combination (CMC) (Nahavandchi & Joodaki, 2010) between different receivers in different environments. The receivers examined include the GP5 (low-cost receiver) and the Topcon HiPer VR (survey-grade receiver) in a dynamic urban canyon test environment, as well as the Trimble NETR9 (survey-grade receiver) in a low-multipath permanent station environment. The plot displays the CMC values on the y-axis against the epochs on the x-axis, revealing variations in CMC values among the receivers. The GP5 shows the highest sensitivity to multipath interference, attributed to its low-cost nature and the presence of multiple paths in the test environment. Conversely, the Trimble NETR9 demonstrates the lowest CMC value, as expected for a survey-grade receiver in a low-multipath permanent station environment. Notably, the Topcon HiPer VR, despite being a survey-grade receiver, exhibits higher multipath interference than the the other survey-grade receiver, indicated by its larger CMC value, reflecting a greater multipath effect in the test environment relative to the permanent station environment. These findings underscore the influence of receiver quality and testing environment on the severity of multipath effects.

L1 CMC values for (a) GP5 and (b) Topcon HiPer VR corresponding to pseudorandom noise 14 and 30, together with their differences
FIGURE 6

L1 CMC values for (a) GP5 and (b) Topcon HiPer VR corresponding to pseudorandom noise 14 and 30, together with their differences

The positioning errors of the single- and multi-epoch RTK and FLP-aided RTK methods for the GP5 smartphone are depicted in Figure 7. The smartphone is evaluated under a short baseline and upright position configuration, as shown in Figure 3. In Figures 7(a)-(d), the top graph displays scatterplots of the horizontal (north and east) positioning errors, whereas the bottom graph shows the corresponding time series of the vertical (up) positioning errors for a total of 63 min of data, as reported in Table 2. These results were obtained using GPS L1 and L5, Galileo E1 and E5a, and BDS B1 signals.

Positioning errors for (a) single-epoch RTK, (b) single-epoch FLP-aided RTK, (c) multi-epoch RTK, and (d) multi-epoch FLP-aided RTK using the GP5, together with the (e) corresponding number of tracked satellites and position dilution of precision (PDOP) Horizontal (north, east) positioning scatter (top) and corresponding vertical (up) positioning error time series (top) are shown in panels (a)-(d) for 63 min of data (compare with Table 2). In these models, GPS L1 + L5 + Galileo E1 + E5a + BDS B1 observations have been used. A zoomed-in plot is shown to depict the two orders of magnitude when going from incorrectly fixed solutions (red dots) to correctly fixed solutions (green dots), where correctly fixed solutions are defined as positions with an RMSE smaller than 10 cm across all coordinate components (north, east, up).
FIGURE 7

Positioning errors for (a) single-epoch RTK, (b) single-epoch FLP-aided RTK, (c) multi-epoch RTK, and (d) multi-epoch FLP-aided RTK using the GP5, together with the (e) corresponding number of tracked satellites and position dilution of precision (PDOP) Horizontal (north, east) positioning scatter (top) and corresponding vertical (up) positioning error time series (top) are shown in panels (a)-(d) for 63 min of data (compare with Table 2). In these models, GPS L1 + L5 + Galileo E1 + E5a + BDS B1 observations have been used. A zoomed-in plot is shown to depict the two orders of magnitude when going from incorrectly fixed solutions (red dots) to correctly fixed solutions (green dots), where correctly fixed solutions are defined as positions with an RMSE smaller than 10 cm across all coordinate components (north, east, up).

Based on the information presented in Figure 7, the availability for GP5 in both the single- and multi-epoch RTK scenarios is 1% and 79%, respectively. However, when the FLP-aided RTK model is utilized, the availability is significantly improved to 30% and 96% in the single- and multi-epoch scenarios, respectively. This result suggests that the FLP-aided model can enhance the availability of GP5 to a certain degree, rendering it comparable to a higher-cost receiver.

6 CONCLUSIONS

In this study, we proposed a novel methodology that makes use of single- and multi-epoch FLP-aided RTK models, integrating FLP positioning solutions into the RTK estimation process. We compared the proposed integration with traditional stand-alone single- and multi-epoch RTK GNSS positioning using data sets for a low-cost GP5 receiver, a survey-grade Topcon HiPer VR receiver, and a Trimble NETR9 receiver. Our experiments showed that FLP-aided RTK GNSS positioning significantly improves positioning accuracy and the availability of fixed positions on smartphones in dynamic urban environments. Our methodology achieved centimeter-level accuracy with 96% availability, even in the presence of pseudorange multipath on smartphones. The main findings of this paper are summarized as follows:

  • Precision and availability of smartphone positioning: The proposed FLP-aided models are tailored for smartphones with FLP apps. Once the FLP-derived positioning solution is integrated with the GNSS carrier-phase data, the corresponding ambiguity-resolved carrier-phase data lead to fixed solutions, with over 90% of the fixed solutions having an RMSE smaller than 10 cm. These results hold for the experimental data in this paper that were collected under complex environmental conditions.

  • Single-epoch formulation versus FLP integration: As shown in Table 3, switching from the singe-epoch model to the multi-epoch model led to a considerable increase in the availability of smartphone RTK positioning, e.g., from 1% to 79%. In the case of the FLP integration, however, a much smaller availability improvement would be observed if one uses only the single-epoch model, e.g., from 1% to 30%.

  • Multi-epoch formulation with FLP integration: To effectively boost the availability of smartphone RTK positioning, one can utilize the FLP-aided model in addition to employing the multi-epoch formulation. As shown in Table 3, a tremendous improvement in the availability of fixed solutions can be experienced when the FLP-derived solution supports the multi-epoch formulation, e.g., from 1% to 96%.

The results of this study demonstrate that FLP-aided RTK can enhance smartphone-based high-precision positioning in challenging urban environments. This improvement can be particularly beneficial for applications such as pedestrian localization, intelligent transportation systems, and smart city infrastructure monitoring, where multipath effects degrade stand-alone GNSS solutions. By leveraging the FLP solution—which is typically less sensitive to multipath because of its use of multi-sensor fusion and context-aware modeling—the proposed method supports reliable positioning in dynamic urban settings, benefiting services that require accurate and robust localization, including autonomous mobility and augmented reality-based navigation.

Correctly specifying the precision of the FLP solution is crucial in aiding RTK. In this study, we made use of a priori experiments to empirically assess the variance matrix of the FLP solution. However, one can employ variance component estimation methods to rigorously specify such a matrix (Amiri Simkooei, 2007). This is an important topic that merits investigation in future studies.

DATA AVAILABILITY

The permanent station GNSS observations utilized in this study were acquired from the Leica Geo Office’s NRTK Norway Network, accessible at https://no-sbc.nrtk.eu/sbc/spider-business-center. Additionally, International GNSS Service final orbit data were obtained from the Crustal Dynamics Data Information System, available at https://cddis.nasa.gov/archive/gnss/products.

The FLP data collection application used in this study was developed for internal research purposes. While it is not publicly available at this stage, access to the application or related data may be granted upon request. Future work will also explore options for open-source distribution or controlled access to support further research in smartphone-based RTK positioning.

HOW TO CITE THIS ARTICLE:

Mohamadi, A., Nahavandchi, H., & Khodabandeh, A. (2026). FLP-aided GNSS RTK positioning: A means of supporting smartphone high-precision positioning in dynamic urban environments. NAVIGATION, 73. https://doi.org/10.33012/navi.730

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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In this Issue

NAVIGATION: Journal of the Institute of Navigation

NAVIGATION: Journal of the Institute of Navigation

Vol. 73

January 2, 2026

Table of Contents Index by author

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Keywords

fused location provider (FLP), integer ambiguity resolution (IAR), multipath, real-time kinematic (RTK), smartphone positioning