Assessment of Smartphone GNSS Measurements in Tightly Coupled Visual Inertial Navigation

Abstract

Precise, seamless, and high-rate navigation remains a major challenge, particularly when relying on low-cost sensors. With the decreasing cost of cameras, Inertial Measurement Units (IMUs), and Global Navigation Satellite System (GNSS) receivers, tightly coupled fusion frameworks, such as GVINS, have gained considerable attention. GVINS is an optimization-based factor-graph framework that integrates visual and inertial measurements with single-frequency GNSS-code pseudorange observations to provide robust and drift-free navigation. This study aimed to evaluate the potential of applying GVINS to low-cost, low-power, and single-frequency GNSS receivers, particularly those embedded in smartphones, by integrating 1 Hz GNSS measurements collected in three challenging urban scenarios into the GVINS framework to produce seamless 10 Hz positioning estimates. The experiments were conducted using an Xsens MTi-1 IMU and global-shutter (GS) cameras, as well as a Samsung A51 smartphone and a u-blox ZED-F9P GNSS receiver. GVINS was modified to process 1 Hz GNSS measurements. Differential corrections from a nearby GNSS reference station were also incorporated to assess their impact on optimization-based filters, such as GVINS. The performance of GVINS and Differential GVINS (D-GVINS) solutions using smartphone measurements was compared against standard point positioning (SPP) and differential GPS (DGPS) results obtained from the same smartphone GNSS receiver, as well as the GVINS solution derived from u-blox ZED-F9P measurements sampled at 1 Hz. Experimental results show that GVINS effectively operates with smartphone GNSS measurements, reducing 3D RMS errors by 80.4%, 64.9%, and 83.8% for the sports field, campus-walking, and campus-driving datasets, respectively, when differential corrections are applied relative to the SPP solution. These results highlight the potential of smartphone GNSS receivers within the GVINS framework: Even though they observe fewer constellations, lower signal quality, and a lower number of satellites, they can still achieve a performance comparable to that of a relatively higher-end dual-frequency GNSS receiver, the u-blox ZED-F9P. Further studies will focus on adapting the GVINS algorithm to run directly on smartphones to utilize all the available measurements, including the camera, IMU, barometer, magnetometer, and additional ranging sensors.

1. Introduction

Robust, high-rate, and precise navigation is a fundamental requirement for emerging technologies, particularly in robotics, mobile-augmented reality (MAR), and urban on-device navigation [1,2]. While achieving drift-free global positioning is essential for these applications, the widespread adoption of such technology is strictly governed by Size, Weight, Power, and Cost (SWaP-C) constraints [3,4]. Over the past several decades, significant computational advancements have allowed for the integration of spatially aware sensors into real-time frameworks, fusing cognitive sensors with conventional navigation aids [5]. However, real-world applications rely heavily on Global Navigation Satellite Systems (GNSSs). While GNSSs provide essential absolute positioning, their signals are notoriously unreliable in “urban canyons” and narrow pedestrian paths, where the Line of Sight (LOS) is frequently blocked or degraded [6]. These types of issues are more visible in the context of mass-marketed mobile devices, like smartphones. Unlike survey-grade receivers or complex Real-Time Kinematic (RTK) systems—which offer sub-meter accuracy but suffer from high communication burdens and slow convergence times [7,8]—smartphone GNSS receivers are designed primarily for cost efficiency. They typically utilize single-frequency, multi-constellation chipsets that rely on low-quality antennae highly susceptible to multipath interference [9,10]. Furthermore, strict power-saving constraints often force these chipsets into duty-cycling operations, frequently corrupting continuity in carrier-phase measurements and resulting in positioning errors of tens of meters [11]. Even in recent state-of-the-art studies that exploit partial wide-lane ambiguity resolution on specific smartphones, several-decimeter-level horizontal accuracy is achieved [12]. Google has recently introduced the Smartphone Decimeter Challenge to encourage advancements in high-accuracy positioning using only smartphone sensors [13]. The 2024 winner of the competition [14], demonstrated state-of-the-art GNSS/INS fusion using optimized timestamp alignment and adaptive measurement weighting. Even under these favorable conditions, the achieved public and private scores show sub-meter but not decimeter-level accuracy. In one study [15], the authors reported achieving approximately sub-meter accuracy by fusing smartphone GNSS and IMU measurements within an RTK framework (which requires a smartphone to provide carrier-phase observations). They also showed that their RTK-only smartphone positioning remained at the level of several meters, highlighting the significant benefit provided by the fused GNSS-INS approach. These results highlight that contemporary smartphone hardware, which provides code-pseudoranges at a single frequency, typically remains limited to performance on the order of meters in realistic environments without sophisticated fusion algorithms.

The fusion of different sensors available in smartphones (e.g., IMUs, magnetometers, and cameras) may compensate for the weaknesses of GNSSs through their complementary characteristics. Inertial Measurement Units (IMUs) are commonly used to provide seamless positioning in GNSS-challenged environments. However, IMUs suffer from drift due to systematic and stochastic errors stemming from their intrinsic design and environmental conditions, which introduce an additional burden to the error budget [16]. On the other hand, inertial information can also be derived by tracking visual landmarks across successive image frames. While monocular-camera-based methods require external scale information, stereo variants can resolve the depth estimation problem [17]. Consequently, the fusion of visual and inertial sensors handles the depth estimation problem in monocular cameras, as well as the rapid drift of MEMS IMUs [18] in vision-friendly environments. The fusion may be achieved by jointly optimizing the camera reprojection errors and the IMU preintegration residuals within a sliding-window nonlinear-optimization framework [19,20]. However, feature detection and tracking quality can be significantly degraded by a wide range of real-world factors, including motion blur, defocus, low texture, and challenging illumination, such as low light or overexposure. Additional degradation can arise from rolling-shutter distortions, focus instabilities, as well as scene dynamics, such as specular reflections, moving objects, or adverse weather conditions (e.g., fog, rain, or dust). These factors collectively reduce the number of reliable visual features and weaken the visual constraints used in the fusion process [18].

Consequently, the Visual–Inertial (VI) combination enables an effective navigation system in indoor areas, where rich textures and adequate lighting are available. Nevertheless, large-scale and global position determination requires a connection between local and global frames. This connection is provided by the three translation parameters of the local frame relative to the global frame, as well as the orientation. Therefore, combining GNSS with VI sensors can both recover translation parameters between these frames and reduce accumulated errors in VI, enabling long-term use [21]. On the other hand, the computational cost grows with the increasing number of tracked features, the size of the optimization window, the density of keyframes, the frequency of marginalization, and the dimensionality of the states and factors involved, requiring careful management to sustain real-time performance [22].

GVINS [23] introduces a GNSS Visual–Inertial Navigation System that tightly fuses monocular camera images, inertial measurements of a MEMS IMU, and single-frequency raw measurements of a low-cost GNSS receiver in a sliding-window factor-graph optimization framework. The VI side of GVINS is based on the SLAM framework, VINS-mono [20]. GVINS uses the Lucas–Kanade method [24] to track a group of sparse-feature points [25] extracted from distortion-corrected [26] images as visual measurements. An improvement to GVINS, namely, P³-VINS [27], extends GVINS by incorporating the Ionosphere-Free (IF) combination of GNSS-carrier-phase measurements to operate the GNSS Precise-Point-Positioning (PPP) technique. Carrier-phase measurements are prone to cycle slips due to signal loss or low Signal-to-Noise Ratios (SNRs). P³-VINS introduces a novel factor, called the phase-ambiguity factor, to mitigate the cycle slip problem. This factor uses dual-frequency Melbourne–Wübbena and Geometry-Free combinations to handle cycle slips in the optimization process [28]. It incorporates the difference between the ambiguities of dual-frequency carrier-phase observations as a residual in the optimization problem. While this approach offers significant benefits by utilizing carrier-phase data, the ambiguities are handled as a float solution, which limits their actual contribution compared to that of an integer-ambiguity resolution. The most recent attempt to increase the accuracy of GVINS is the DGVINS method, which uses GNSS double-difference measurements [29]. This approach employs two dual-frequency GNSS receivers. Whereas one of the receivers is stationary at an accurately known position, the mobile receiver is bundled with GVINS sensors. Double differences cancel out satellites’ and receivers’ clock errors. Remaining errors are highly correlated with the distance between mobile and reference GNSS receivers. Thus, DGVINS works well within a few kilometers from the reference station by eliminating ionosphere- and troposphere-dependent effects. This method performs single-epoch integer-ambiguity resolution of the wide-lane combination without using cycle slip detection.

Although GVINS may provide a framework for tightly coupled GNSS VI fusion, it was originally built for a u-blox ZED-F9P receiver, which may be considered as a higher-grade receiver with a dedicated antenna compared to that of a smartphone. It relies on a 10 Hz measurement rate for code pseudoranges, which are also not available in mass-marketed smartphones. The success of GVINS on-device smartphone applications mainly depends on the smartphone GNSS accuracy. Recent studies have highlighted the limitations of smartphone GNSS measurements under several conditions. A deep investigation of pseudorange residuals and the Carrier-to-Noise density ratio (C/No) was conducted in [30] for assessing smartphones’ GNSS receiver quality and revealing their potential. In [31], Nexus 9 tablet measurements in both kinematic and static modes were used for evaluating the smoothing filter performance, and improved results were obtained through an enhanced Hatch filter solution. In [32], smartphone GNSS range errors in realistic environments were numerically evaluated using a geodetic receiver as a reference, and the effects of signal blockage, multipath, device placement, and constellation differences on the distribution and behavior of pseudorange biases were analyzed. GNSS observations generated via the Android API and common logging applications were examined in [33], where biases and inconsistencies degrading the positioning performance were identified, and the newly developed CSV2RINEX tool was shown to produce higher-quality observations with improved positioning accuracy. More reliable stochastic models for smartphone GNSS observations from two Samsung S20 devices were developed in [34], and significant positioning improvements were demonstrated by incorporating the derived variances. In [35], inequality constraints, such as heading, vertical velocity, and inter-device distance, were introduced, leading to notable enhancements in GNSS-only smartphone positioning. In [36], the performances of DGNSS, SPP, PPK, and PPP were compared across several smartphones. In [15], tightly coupled GNSS/INS integration was performed with multiple smartphones, and sub-meter positioning accuracy was achieved utilizing RTK measurements with carrier-phase data. Furthermore, in [37], a smartphone was employed as a GVINS sensor, and accuracy improvements of up to 70% relative to that of SPP were achieved.

In this study, a custom-hardware-supported experimental setup was developed to evaluate the GVINS performance with smartphone GNSS measurements. The developed hardware and software platform can collect measurements, which can be directly input into the original GVINS as well as replace high-rate GNSS measurements from u-blox ZED-F9P, with 1 Hz raw GNSS measurements collected from a Samsung A51 rigidly bound to the same data collection platform. Using this custom-developed hardware and software platform, three different real-world scenario datasets were collected, with varying difficulties in GNSS satellite visibility, from open-sky to dense urban-like environments, representing typical conditions faced in both pedestrian and vehicular navigation. In addition, differential corrections from the nearby IGS reference station (ANK2) were applied to evaluate their impacts on both DGPS and Differential-GVINS (DGVINS) performances. We performed a systematic evaluation across three datasets representing different environmental conditions, allowing us to assess smartphone GNSS behavior in diverse visibility and multipath scenarios. A custom Android-ROS interface that streams raw smartphone GNSS measurements into the GVINS pipeline was developed, which also provides a foundation for future efforts toward running GVINS directly on Android devices. For all the datasets, smartphone measurements are compared against a u-blox ZED-F9P receiver and the impacts of simple code-based differential corrections on both standalone GNSS solutions (SPP and DGPS) and on tightly coupled fusion methods (GVINS and DGVINS) are investigated. The GVINS was also updated to handle 1 Hz GNSS data. Furthermore, this study provides a practical and comprehensive assessment of how low-cost smartphone GNSS can be leveraged within an optimization-based navigation framework and outlines a pathway toward future smartphone–native GNSS-VIO integration.

The structure of the paper is organized as follows: Section 2 provides an overview of the GVINS framework and highlights the key methodologies employed in this study. Section 3 presents the experimental setup used for data collection, while Section 4 introduces the datasets. Section 5 describes the evaluation methods. Section 6 discusses the results and provides an in-depth analysis. Finally, Section 7 concludes the paper, summarizing the findings and suggesting directions for future research.

2. Methodology

This section provides a brief introduction to frame transformations, state definitions, and factor-graph representation. The definitions corresponding to the reference frames are provided in

Table 1. Frame definitions used in GVINS.

Frame Definition	Symbol	Frame Definition	Symbol
Earth-centered Earth-fixed (ECEF)	${(·)}^e$	Earth-centered inertial	${(·)}^E$
Local world frame	${(·)}^w$	Camera frame	${(·)}^c$
IMU frame or Body frame	${(·)}^i$ or ${(·)}^b$	East–north–up (ENU) frame	${(·)}^n$

. Relevant contributions to the GNSS factor are also outlined, while details of other factors can be found in a GVINS paper [23]. An overview of the proposed methodology is provided in Figure 1. The components highlighted in red in the flowchart indicate the additional modules incorporated into the original GVINS architecture as a part of our proposed extensions. The optional part enables the feeding of the differential corrections into GVINS.

2.1. State Definitions

The system states to be optimized in the factor graph, $\mathbf{\chi }$, are described as follows:

$$\mathbf{\chi }=[{\mathit{x}}_0,{\mathit{x}}_1,\dots ,{\mathit{x}}_n,{\rho }_0,{\rho }_1,\dots ,{\rho }_m,\psi ],$$

(1)

where $\rho$ is the inverse depth for each of the m visual features. The yaw angle between the ENU frame and the local world frame is also defined with $\psi$. The rest of the states are further defined with ${\mathit{x}}_{\mathit{k}}$ as follows for window size n:

$${\mathit{x}}_k=[{\mathit{p}}_{b_k}^w,{\mathit{v}}_{b_k}^w,{\mathit{q}}_{b_k}^w,{\mathit{b}}_a,{\mathit{b}}_{\omega },\delta \mathit{t},\dot{\delta t}],$$

(2)

where

• ${\mathit{p}}_{b_k}^w$, ${\mathit{v}}_{b_k}^w$, and ${\mathit{q}}_{b_k}^w$ are the position, velocity, and attitude of the body in the world frame;
• ${\mathit{b}}_a$ and ${\mathit{b}}_{\omega }$ refer to the accelerometer and gyroscope biases;
• $\delta \mathit{t}$ and $\dot{\delta t}$ define the clock biases and the drift. Even though the clock biases for each of the constellations are optimized separately, their drifts are assumed to be same. Therefore, the clock biases for the GPS (G), GLONASS (R), Galileo (E), and BeiDou (C) with respect to their system times are given as

  $$\delta \mathit{t}=[\delta t_G,\delta t_R,\delta t_E,\delta t_C].$$

  (3)

2.2. Factor-Graph Optimization

Inertial measurements, GNSS observations, and features extracted from forward-looking camera images are fed into the optimization framework following careful pre-elimination. These measurements are assumed to be uncorrelated and modeled with zero-mean Gaussian noise. The Factor-Graph Optimization (FGO) framework is derived from the Maximum A Posteriori (MAP) estimation problem [38]. The MAP estimator identifies the optimal states by maximizing the posterior probability given all the available measurements. This problem is then reformulated as the minimization of residuals from various factors and prior information as follows:

$$\begin{array}{cc}\hfill {\mathbf{\chi }}^{*}& =arg{\displaystyle \underset{\mathbf{\chi }}{max}}p(\mathbf{\chi }\mid \mathit{z})\hfill \\ \hfill & =arg{\displaystyle \underset{\mathbf{\chi }}{max}}p\left(\mathbf{\chi }\right)p(\mathit{z}\mid \mathbf{\chi })\hfill \\ \hfill & =arg{\displaystyle \underset{\mathbf{\chi }}{max}}p\left(\mathbf{\chi }\right){\displaystyle \prod _{i=1}^n}p({\mathit{z}}_i\mid \mathbf{\chi })\hfill \\ \hfill & =arg{\displaystyle \underset{\mathbf{\chi }}{min}}\left\{\left|\right|{\mathit{r}}_p-{\mathit{H}}_p{\mathbf{\chi }\left|\right|}^2+{\displaystyle \sum _{i=1}^n}\left|\right|\mathit{r}({\mathit{z}}_i,\mathbf{\chi }){\left|\right|}_{{\mathit{P}}_i}^2\right\},\hfill \end{array}$$

(4)

where $\mathit{z}$ encapsulates n independent sensor measurements, $\left|\right|{\mathit{r}}_p-{\mathit{H}}_p\mathbf{\chi }{\left|\right|}^2$ refers to the prior information of the system states, $\mathit{r}({\mathit{z}}_i,\mathbf{\chi })|$ denotes the residuals of factors, and ${\left|\right|.\left|\right|}_P$ represents the Mahalanobis distance. Factor-graph representation uses the decomposition of the MAP problem to the minimization of distinct factors. IMU, visual, and GNSS factors have been described in detail in [23]. Figure 2 represents the factor-graph formulation used in our system, where the system states are indicated by large colored nodes and the measurement factors by small black nodes. The factor types include inertial factors (i), visual factors (f), GNSS factors (g), and clock factors (c), while a prior factor (p) is attached to the first pose to define the local world frame. The inverse depths of the visual features, the yaw angle, and the states to be optimized are denoted by ${\rho }_i$, $\psi$, and $x_i$, respectively. Because smartphone GNSS measurements are available only at 1 Hz, the corresponding pseudorange/Doppler factors are added sparsely, only at epochs where a valid GNSS observation exists, whereas intermediate states are constrained solely by Visual–Inertial factors.

2.3. GNSS Factors

GNSS is the common name for different satellite-based positioning systems orbiting Earth, particularly known as GPS, GLONASS, Galileo, and BeiDou. The measurement principle of GNSS arises from the determination of the Time of Flight (ToF) of the signal emitted from the satellite antenna to the receiver antenna. Each of the satellites basically transmits modulated signals carrying ranging code and navigation messages. Current constellations feature various ranging code types, each tailored for specific purposes, employing diverse modulation schemes and different carrier signals across the range of GNSS frequencies. The time difference between the received ranging code and its receiver replica is multiplied by the speed of light, which gives a measurement called the code pseudorange. Tracking the carrier phase of the received signal provides the phase difference of the incoming carrier wave and the receiver replica. Only the fractional part of this phase difference is precisely known, but the integer representing the number of cycles is ambiguous. These observations also deviate from the geometric range due to the propagation medium (i.e., the troposphere and ionosphere) and hardware-induced biases. Moreover, the received signal can be degraded by low elevation angles and surrounding objects, resulting in noisy measurements and multipath effects. As a result, GNSS observation equations can be written as follows [39]:

$$P_r^s=\left|\right|{\mathit{p}}_s^E-{\mathit{p}}_r^E\left|\right|+c·(\delta t_r-\Delta t^s)+T_r^s+I_r^s+b_r-b^s+m_r^s+{ϵ}_p,$$

(5)

where $P_r^s$ denotes the code pseudorange measured from receiver r to satellite s. The geometric range (${\rho }_r^s$) represents the true distance between the satellite position (${\mathit{p}}_s^E$) and the receiver position (${\mathit{p}}_r^E$), expressed in the Earth-centered Inertial (ECI) frame. The terms $c\Delta t^s$ and $c\delta t_r$ correspond to the satellite and receiver clock errors, respectively, scaled by the speed of light, c. The atmospheric delay consists of two components: (1) the ionospheric delay ($I_r^s$), which depends on the total electron content along the signal path and causes a frequency-dependent excess range in the code measurements, and (2) the tropospheric delay ($T_r^s$), introduced by the neutral atmosphere and primarily influenced by temperature, pressure, and humidity. The term $m_r^s$ denotes multipath errors caused by reflected signals reaching the receiver’s antenna, which can introduce several meters of bias, especially in smartphone GNSS measurements. The hardware biases of the receiver and satellite, $b_r$ and $b^s$, represent constant or slowly varying delays introduced by their analog front-end electronics. Finally, ${ϵ}_p$ captures measurement noise and other unmodeled effects, including residual modeling errors not accounted for in the above terms.

The open-source library UMA-ROS [40] has been extended to publish raw GNSS measurements from smartphones in the same format required by GVINS. The measurements are collected following the formulation [41]:

$$\begin{array}{c}\hfill P_r^s=c·t_r^s=c·(\mathit{TimeNanos}-\mathit{ReceivedSvTimeNanos}\\ \hfill -(\mathit{fullBiasNanos}+\mathit{BiasNanos}))·{10}^{-9},\end{array}$$

(6)

where TimeNanos is the time according to GNSS receiver’s internal hardware clock in nanoseconds, and fullBiasNanos denotes the difference between the time according to the hardware clock inside the GPS receiver and the true GPS time since 6 January 1980, in nanoseconds. BiasNanos denotes the sub-nanosecond bias. On the satellite side, ReceivedSvTimeNanos corresponds to the transmission time of the GPS signal in the GPS time system. Therefore, $t_r^s$ denotes the pseudorange in nanoseconds.

Due to the common constraint, where mobile phone GNSS receivers typically offer a data collection frequency limited to 1 Hz, the GVINS algorithm required modification. While the original GVINS implementation typically rejects low-frequency GNSS data, this modified version was specifically adapted to accept and integrate the 1 Hz GNSS data stream. This adaptation ensures the algorithm’s applicability when utilizing the constrained data rates of mobile platforms. In addition, GVINS requires measurement variances to properly weight residuals. There are several ways to determine these variances. Following the approach proposed by [42], the standard deviation of an observation can be expressed as a function of C/No as follows:

$${\sigma }_C^2=C^2·{10}^{-{\displaystyle \frac{(C/No-40)}{20}}},$$

(7)

where C is a constant related to the observation noise scaling. In this study, we used $C^2=0.3$ for the variance computation. Alternatively, the ReceivedSvTimeUncertaintyNanos parameter could be employed to generate observation-specific variances, although it may not accurately represent the actual measurement uncertainty at the receiver.

GVINS also processes the Doppler measurements from the GNSS receiver. The GVINS framework [23] provides the foundation for incorporating this factor. In this study, the Doppler values and their uncertainties were obtained from the PseudorangeRateMetersPerSecond and PseudorangeRateUncertaintyMetersPerSecond fields of the android.location API, respectively. Doppler measurements were then converted to frequency units (Hz) by dividing by $-\lambda$, where $\lambda$ denotes the corresponding wavelength of the GNSS signal.

2.4. DGNSS Factors

In this study, a variant of the Differential GNSS (DGNSS) method is implemented. The proposed approach applies pseudorange-based corrections using measurements from a nearby reference station. The reference station is assumed to have precisely determined coordinates. Subsequently, the pseudorange observations can be expressed as follows [39]:

$$\begin{array}{cc}\hfill P_{base}^s& =\left|\right|{\mathit{p}}_s^E-{\mathit{p}}_{base}^E\left|\right|+\delta {\rho }_{orb}^S+c·(\delta t_{base}-\Delta t^s)-\delta t^S\hfill \\ & +T_{base}^s+I_{base}^s+b_{base}-b^s+m_{base}^s+{ϵ}_p,\hfill \end{array}$$

(8)

where subscript base represents the reference station. In addition, $\delta {\rho }_{orb}^S$ and $\delta t^S$ represent differences between the precise orbit and clock from broadcast values, respectively. Then, the differential corrections were obtained as:

$$\begin{array}{cc}\hfill D{C}_r^s& =P_{base}^s-\left|\right|{\mathit{p}}_s^E-{\mathit{p}}_{base}^E\left|\right|+c·\Delta t^s\hfill \\ \hfill & =\delta {\rho }_{orb}^S+c·\delta t_{base}-c·\delta t^S+T_{base}^s+I_{base}^s+b_{base}-b^s+m_{base}^s+{ϵ}_p,\hfill \end{array}$$

(9)

where, $D{C}_r^s$ is represents the differential correction, including orbital errors, tropospheric and ionospheric delays, and other satellite-specific errors. Since the base and rover receivers are located in proximity, satellite-specific (orbit, clock, etc.) and atmospheric errors can be considered in the common mode and, therefore, largely eliminated from the observations. The correction term also accounts for reference-receiver-specific biases; however, these are assumed to be absorbed into the estimation of the rover receiver’s clock bias. Therefore, for DGNSS calculations, corrections are subtracted from the rover’s pseudorange measurements as follows:

$$P_{rover}^s-D{C}_r^s=\left|\right|{\mathit{p}}_s^E-{\mathit{p}}_{rover}^E\left|\right|+c·(\delta t_{rover}-\delta t_{base}-\Delta t^s)+b_{rover}+m_{rover}^s+{ϵ}_p.$$

(10)

3. Experimental Setup

A custom hardware platform was developed for multi-sensor data collection. The processing unit consists of a Raspberry Pi 5 board equipped with 8 GB of RAM and an external 512 GB M.2 NVMe SSD. Two forward-looking global-shutter cameras featuring the Sony IMX296LQR-C image sensor were mounted to capture visual data (20–30 Hz). Inertial measurements were acquired from an Xsens MTi-1 IMU (at 100 Hz). Raw GNSS measurements from a Samsung A51 smartphone were logged at 1 Hz, while additional GNSS observations were collected from a u-blox ZED-F9P receiver operating at 10 Hz and connected to a dual-frequency (L1 + L2) u-blox antenna. An overview of our custom data collection platform is shown in Figure 3. The Xsens MTi-1 IMU (Xsens Technologies B.V., Enschede, The Netherlands), the u-blox receiver (u-blox AG, Thalwil, Switzerland), the Raspberry Pi 5 board (Raspberry Pi Ltd., Cambridge, United Kingdom), and the required power supplies are housed inside the enclosure shown in the figure.

The Samsung A51 integrates a built-in, single-frequency GNSS receiver that supports GPS, GLONASS, BeiDou, and Galileo; however, the exact GNSS RF front-end or chipset model used inside the Exynos 9611 platform is not publicly documented by its manufacturer [43]. During our experiments, Galileo signals were not observed when using Google’s open-source GnssLogger [44] application. This device, similar to most Android smartphones, provides raw GNSS measurements at a rate of 1 Hz. For smartphone GNSS data acquisition, the open-source Android ROS node UMA ROS [40] was modified to enable the collection of raw GNSS measurements. Additionally, ground-truth positions were recorded using the built-in GNSS-RTK engine of the u-blox ZED-F9P receiver by feeding RTCM correction streams from the Turkish Permanent CORS Network (TUSAGA–Active) to the receiver via the u-blox ROS driver and the RTKLIB [45] utility str2str.

The system time of the Raspberry Pi 5 computer was synchronized using a GPS time server by feeding a 1 PPS signal and NMEA messages from the u-blox ZED-F9P receiver to the Raspberry Pi IO ports. This ensures time consistency between the local sensors (camera and IMU) and the GNSS receiver. The datasets were recorded after time synchronization was completed. The sensor drivers were executed in separate docker containers since each driver required its own operating environment (ROS 1 or ROS 2) and software dependencies. Therefore, their runtime environments needed to be isolated from each other, which required the use of an additional node running the ROS bridge to enable communication between them.

Furthermore, the IMU intrinsic calibration was performed using six hours of static data with the Kalibr toolbox [46]. Based on an Allan variance analysis, the accelerometer and gyroscope noise densities were identified as ${\sigma }_a=8.0\times {10}^{-4}\mathrm{m}/{\mathrm{s}}^2/\sqrt{\mathrm{Hz}}$ and ${\sigma }_g=5.5\times {10}^{-5}\mathrm{rad}/\mathrm{s}/\sqrt{\mathrm{Hz}}$, with corresponding bias random-walk terms ${\sigma }_{ba}=2.4\times {10}^{-5}\mathrm{m}/{\mathrm{s}}^2/\sqrt{\mathrm{Hz}}$ and ${\sigma }_{bg}=5.4\times {10}^{-6}\mathrm{rad}/\mathrm{s}/\sqrt{\mathrm{Hz}}$, respectively. In addition, the cameras were manually focused using the adjustment screws prior to collecting calibration and experimental datasets, ensuring that the intrinsic calibration parameters remained stable throughout data processing and analysis. In addition, the IMU and cameras were rigidly attached to the device body to maintain stable relative poses throughout both extrinsic calibration and data collection. These calibrations were performed using AprilGrid targets with Kalibr [46].

The data were collected using the described equipment on 31 August 2025 and 5 October 2025. These datasets were recorded as rosbag files via ROS noetic. Furthermore, RINEX observation files were also collected using the GnssLogger [44] application to enable an external check and to generate standalone SPP solutions independent of the ROS-based framework. In order to assess the performance under varying environmental conditions, camera, IMU, and GNSS measurements were gathered in diverse scenarios, including an open sports field, pedestrian walkways between campus buildings, and campus roads, using both walking and driving modes. During walking experiments, the Samsung A51 and the u-blox antennae were positioned within 10 cm, whereas in driving experiments, they were vertically separated by about 50 cm, which was later compensated.

4. Experimental Dataset

Three experimental scenarios were carefully designed to represent different levels of GNSS difficulty commonly encountered in real-world pedestrian and vehicular navigation.

Sports Field: This environment provides an open-sky condition with minimal multipath and strong satellite visibility. It serves as a baseline scenario to assess the best achievable performance of smartphone GNSS measurements when integrated into the GVINS framework.

Campus Walking: This scenario includes narrow pedestrian pathways surrounded by tall buildings and trees, creating an urban canyon-like environment with severe multipath, intermittent satellite blockage, and highly variable signal quality. It reflects typical challenges faced in smartphone-based pedestrian localization.

Campus Driving: The vehicular route covers a larger geographic area with varying building densities, partial obstructions, and transitions between open and moderately constrained environments. It is representative of navigation conditions encountered in urban and suburban driving applications.

In these three scenarios, the experimental setup captures a wide range of GNSS observability conditions, from ideal open-sky visibility to highly degraded urban environments, allowing a thorough evaluation of GVINS and DGVINS performances using smartphone GNSS measurements.

Figure 4 illustrates the ground-truth trajectory derived from the GNSS-RTK reference positions collected at the Hacettepe University Beytepe Campus. The purple dots in Figure 4 indicate the locations corresponding to the sample images shown in Figure 5. For differential corrections, ANK2 was selected as a base receiver. This reference station is located approximately 4.5 km away from Hacettepe University’s Beytepe Campus, where the dataset was collected. Prior to computing the corrections, the precise coordinates of the reference station were obtained from the CSRS-PPP online service [47], which provides a PPP solution based on precise ephemeris and satellite clock products. The resulting reference station coordinates have an accuracy of approximately 2–3 cm.

5. Evaluation Methods

This study aims to reveal the potential of smartphone GNSS receivers in visual–inertial navigation approaches and to evaluate the accuracy improvement achieved by incorporating differential corrections. Therefore, five distinct positioning modes are examined using the collected dataset.

Differential corrections were extracted using pyrtklib (v0.2.7) [48] software, a Python (v3.8.10) binding of RTKLIB [45], based on RINEX files with a 30 s data interval. During each 30 s period, orbital errors, as well as tropospheric and ionospheric delays, were assumed to remain constant. Consequently, corrections were estimated every 30 s. If a correction was unavailable for a given epoch, the corresponding satellite was excluded from the differential positioning computation.

• The first approach (M1-SPP), Standard Point Positioning (SPP), was implemented using pyrtklib [48], based on RINEX observation and navigation files. Broadcast ephemeris was used together with a 7° elevation cutoff, a 25 dB-Hz C/No mask, the Saastamoinen tropospheric model, and the Klobuchar ionospheric model with broadcast parameters. Only GPS satellites were utilized, as GPS-only processing provided the most stable and consistent positioning results in the SPP solutions. In addition, only satellites with available differential corrections are included in the SPP computation to clearly assess the impact of these corrections when compared with the M2-DGPS results.
• The second approach (M2-DGPS) employed Differential GNSS (DGNSS) corrections derived from the nearby reference station (ANK2). DGNSS solutions were computed using pyrtklib with both tropospheric and ionospheric models disabled and with the TGD parameter set at zero, differing from the SPP configuration since these effects are inherently compensated by differential corrections. In a manner similar to that of M1-SPP, only GPS satellites with available differential corrections were used.

The remaining analyses were conducted using the GVINS framework [23], which performs tight fusion of visual, inertial, and GNSS data collected from an Xsens MTi-1 IMU and global-shutter cameras, combined with GNSS measurements from either a Samsung A51 smartphone or a u-blox ZED-F9P. The elevation mask was set at 30°, and the C/No threshold was set at 25 dB-Hz for the M3, M4, and M5 modes.

• The third approach (M3-GVINS A51) corresponds to the GVINS solution utilizing Samsung A51 GNSS data sampled at 1 Hz. All the available GPS, GLONASS, and BeiDou satellites were used.
• The fourth approach (M4-DGVINS A51), the Differential GVINS (D-GVINS) solution, was obtained by applying differential corrections derived from the ANK2 reference station to the Samsung A51 GNSS observations. When applying differential corrections in GVINS, the tropospheric, ionospheric, and TGD corrections were assumed to be zero for both the anchor point computation and the pseudorange factor residual calculation. All the GPS, GLONASS, and BeiDou satellites with available differential corrections were used.
• The fifth approach (M5-GVINS u-blox) represents the GVINS processing of u-blox ZED-F9P measurements, which were downsampled to 1 Hz for consistency. All the available GPS, GLONASS, Galileo, and BeiDou satellites were used.

6. Results

This section presents the quantitative evaluation of the five methods using both smartphone-based and u-blox ZED-F9P GNSS measurements across the three experimental scenarios. Although the original GVINS framework [23] requires 10 Hz GNSS observations, it was modified in this work to accommodate 1 Hz smartphone GNSS measurements. Moreover, a ROS node running on the smartphone was implemented in Android to publish GNSS data. The differential GNSS approach was also evaluated both as a standalone GNSS-processing method and as a part of the GVINS factor-graph optimization framework. The following subsections present the results for each dataset, comparing all the processing modes and highlighting how environmental conditions, satellite visibility, and measurement quality affect the performance of the fused solutions.

Errors in the east, north, and up directions (${\epsilon }_e,{\epsilon }_n,{\epsilon }_u$) are calculated by converting the position output of the sensor fusion solution to the ENU frame, using the RTK solution as the origin at each measurement epoch. In a manner similar to that of GVINS [23], the solutions are evaluated separately for each ENU axis, as well as for horizontal (2D) and 3D errors, using metrics such as the Mean Absolute Error (MAE), Root-Mean-Square Error (RMSE), and standard deviation of RMSEs.

$$MAE={\displaystyle \frac{1}{m}}{\displaystyle \sum _{i=1}^m}\sqrt{{\left({\epsilon }^i\right)}^2},$$

(11)

$$RMSE=\sqrt{{\displaystyle \frac{1}{m}}{\displaystyle \sum _{i=1}^m}{\left({\epsilon }^i\right)}^2},$$

(12)

$$STD=\sqrt{{\displaystyle \frac{1}{m}}{\displaystyle \sum _{i=1}^m}{({\epsilon }^i-\widehat{\epsilon })}^2},$$

(13)

where $\widehat{\epsilon }$ is the mean value of the errors.

6.1. Sports Field

For the sports field dataset, GNSS, IMU, and camera measurements were collected over multiple laps around the field, covering a total duration of 796 s on 5 October 2025. Figure 6 presents the sky-plots of the GPS, GLONASS, and BeiDou constellations observed using the Samsung A51, where the bold numbers indicate the satellite vehicle numbers. The C/No observations from the smartphone exhibit abrupt fluctuations, causing the corresponding colors of the C/No values to change rapidly in the figures. During data collection, eleven GPS, five GLONASS, and nine BeiDou satellites were visible to the Samsung A51.

The mean C/No values of the u-blox and Samsung A51 GNSS measurements are presented in Figure 7. The results indicate that the A51 exhibits an approximately 10 dB lower C/No compared to that of the u-blox receiver. Compared to smartphones, u-blox receivers include advanced algorithms and hardware features to mitigate multipath effects. Their high-precision module’s primary function is maximizing the position accuracy and signal quality. A smartphone’s chip, conversely, must prioritize low power consumption, small size, and integration with a complex system, often leading to worse signal quality. Furthermore, some satellites are not commonly observed using both receivers. Although the u-blox receiver was tracking 40 satellites, the Samsung A51 observed 25 satellites, 24 of which were common between the two receivers.

The number of satellites available for processing modes over time are shown in Figure 8. For the M1 and M2 processing modes, only GPS satellites with available differential corrections were selected. These satellites were then filtered with a C/No of greater than 25 dB-Hz and an elevation angle of above 7°. Thus, for M1 and M2 modes, the median value of the satellite number is seven. In contrast, the M3 and M4 modes included satellites from the GPS, GLONASS, and BeiDou constellations under the conditions of C/No >25 dB-Hz and elevation >30°. The median numbers of satellites for the M3 and M4 modes are eleven and nine, respectively. Lastly, the u-blox receiver observed the highest number of satellites (including Galileo satellites), with a median number of 21, in the same configuration as M3 and M4.

The results presented in

Table 2. Performance comparison of positioning methods (2D, up, and 3D errors) in the sports field dataset.

Method	2D Error (m)			Up Error (m)			3D Error (m)
	RMS	MAE	STD	RMS	MAE	STD	RMS	MAE	STD
M1-SPP A51	9.998	7.102	7.037	20.020	15.753	14.145	22.378	18.294	12.888
M2-DGPS A51	8.645	6.474	5.729	13.301	8.711	13.119	15.863	11.566	10.857
M3-GVINS A51	4.710	4.531	1.285	11.984	11.514	3.548	12.876	12.581	2.744
M4-DGVINS A51	1.667	1.368	0.953	4.050	3.718	2.414	4.380	4.116	1.497
M5-GVINS u-blox	1.576	1.543	0.320	8.753	8.716	0.805	8.894	8.857	0.811

summarize the horizontal (2D), vertical (Up), and three-dimensional (3D) positioning errors together with their standard deviations. First, applying differential corrections (M2-DGPS) improved the 3D positioning performance of the M1-SPP method by approximately 29.1%, 37.8%, and 15.8% in RMS, MAE, and STD metrics, respectively. It can be observed that the 3D standard deviation is approximately 11–13 m for the M1 (SPP) and M2 (DGPS) cases, indicating a relatively high dispersion in the positioning results. In contrast, the u-blox receiver achieves sub-meter precision, demonstrating superior measurement quality. Furthermore, the application of differential corrections (M4-DGVINS) significantly improves the performance of the Samsung A51, reducing the 3D RMSE, MAE, and STD from approximately 12.9 m, 12.6 m, and 2.74 m to 4.4 m, 4.1 m, and 1.5 m, corresponding to 66%, 67.3%, and 45.3% improvements, respectively.

Figure 9 shows the time series plot of each ENU axis. The results show the potential of the smartphone GNSS receivers in tightly coupled navigation systems. GVINS provides high-rate and seamless positioning, even with low-cost GNSS sensors.

The cumulative probability of position errors is presented in Figure 10. The results indicate that 95% of the horizontal errors are approximately below 3 m for the M4 case and below 6 m for the M3 case, demonstrating the benefit of applying differential corrections. The vertical error distribution may further highlight the significant improvement achieved through differential correction for both the M1-M2 and M3-M4 comparisons. Additionally, applying differential corrections in GVINS may reduce the 95% 3D position error from roughly 32 m to 6 m, corresponding to an approximate 80% improvement compared to the SPP-processing mode.

Figure 11 illustrates the horizontal scatter plots of the five positioning methods. The horizontal errors of the GVINS solutions (M3 and M5) without differential corrections exhibit noticeable biases with respect to the ground truth. In contrast, the standalone GNSS solutions (SPP and DGPS) show a much wider dispersion. The DGVINS (M4) method appears to be a promising candidate for improving positioning accuracy by reducing the bias around the mean values. The GVINS u-blox case, though slightly biased, provides the higher precision and consistency expected from a higher-grade GNSS receiver.

6.2. Campus Walking

The campus-walking dataset represents a more challenging scenario, collected during a 688 s walk within the university campus on 31 August 2025. The main difficulties arise from degraded GNSS signal conditions compared to those of the sports field dataset. The area is largely surrounded by buildings, trees, and other structures, which significantly obstruct satellite visibility and degrade signal quality. Figure 12 shows the sky-plot of the observed satellites, where most low-elevation satellites are blocked by environmental obstacles. Moreover, Figure 13 presents the mean C/No values, which are slightly lower than those in the sports field dataset. While the u-blox receiver observed 30 satellites, the Samsung A51 GNSS receiver tracked 21 of them. The Samsung A51 tracked nine GPS, six GLONASS, and six BeiDou satellites, but no Galileo signals were received.

Figure 14 illustrates the variation in the number of satellites available for processing over time. In the M1 and M2 modes, the Samsung A51 tracked a median of seven GPS satellites, with a C/No ratio of greater than 25 dB-Hz and an elevation angle of above 7°. For the M3 and M4 modes, the median number of satellites increased to 12 and 11, respectively, including observations from the GPS, GLONASS, and BeiDou constellations, under thresholds of a C/No ratio of >25 dB-Hz and an elevation of >30°. In the same configuration, the u-blox receiver (M5) achieved the highest satellite visibility, with a median of 20 satellites. Around TOW = 53,140–53,170, the trajectory passed through a deep canyon surrounded by buildings and trees, where the number of visible satellites decreased significantly.

M1 and M2 results rely entirely on noisy GNSS measurements, which are highly susceptible to multipath, especially in urban environments. On the other hand, the IMU and camera provide high-rate measurements of the device’s motion and environment. These continuous, locally accurate measurements effectively filter the GNSS noise, constraining the estimated position to be much better than those measured using SPP and DGPS. As summarized in

Table 3. Performance comparison of positioning methods (2D, up, and 3D errors) in campus-walking dataset.

Method	2D Error (m)			Up Error (m)			3D Error (m)
	RMS	MAE	STD	RMS	MAE	STD	RMS	MAE	STD
M1-SPP A51	11.082	9.056	6.388	21.339	16.777	19.013	24.045	20.268	12.937
M2-DGPS A51	10.912	8.891	6.325	17.801	13.410	17.768	20.879	17.366	11.591
M3-GVINS A51	5.202	4.428	2.729	3.678	2.489	2.993	6.370	5.593	3.050
M4-DGVINS A51	4.351	3.745	2.214	7.224	6.502	7.047	8.432	7.948	2.818
M5-GVINS u-blox	1.166	1.020	0.566	2.449	2.098	1.264	2.713	2.458	1.147
(*) M3-GVINS A51	6.670	6.021	2.870	3.890	1.844	3.851	7.722	6.544	4.099
(*) M4-DGVINS A51	3.835	3.494	1.581	4.967	3.368	4.712	6.275	5.253	3.433

(*) Results correspond to the time interval TOW = 52,950–53,120.

, the GVINS solution based on smartphone GNSS measurements (M3-GVINS) markedly outperforms the conventional SPP (M1) and DGPS (M2) approaches, yielding significant reductions in RMS, MAE, and STD metrics. These improvements correspond to reductions of 73.5%, 72.4%, and 76.4% when comparing M3-GVINS with M1-SPP. Furthermore, the application of differential corrections in the M2-DGPS solution helped to reduce RMSE, MAE, and STD by 13.2%, 14.3%, and 10.4%, respectively, compared to those of the M1-SPP case. Therefore, these results may indicate the benefits of applying differential corrections.

However, due to the urban-canyon-like environment around TOW = 53, 140–53, 170, differential corrections may have been insufficient to mitigate error sources, resulting in a sudden jump in the up component. In the M1-SPP and M2-DGPS cases, the effects of such jumps do not persist long, as the solutions are computed on an epoch-by-epoch basis without memory. In contrast, for GVINS-based solutions, once the global position drifts significantly, removing its effect from a memory-based filter—such as the factor-graph optimization window—is not an instantaneous process. Additional results presented in Table 3, corresponding to the time interval TOW = 52,950–53,120, just before entering the urban canyon, further demonstrate the benefits of applying differential corrections in GVINS. According to this subset of the results, the 3D RMSE, MAE, and STD are reduced from 7.7 m, 6.5 m, and 4.1 m to 6.3 m, 5.3 m, and 3.4 m, representing improvements of 18.7%, 19.7%, and 16.2%, respectively.

Considering the 2D position, the M4 configuration is roughly 16% better than solutions without differential corrections.

As expected, the u-blox GVINS (M5) yielded the most precise results, with 3D RMS errors of around 2.7 m, attributed to its advanced algorithms, higher signal quality, and dedicated antenna. Overall, these findings demonstrate that tightly coupled GNSS–Visual–Inertial integration and differential corrections can substantially enhance the performances of low-cost, single-frequency smartphone receivers. However, the measurements from such devices remain highly susceptible to environmental conditions, which may hinder their ability to approach the accuracy of high-grade GNSS sensors.

Figure 15 illustrates the time series obtained from this dataset. All the GVINS-based positioning modes produce seamless trajectories compared to those produced by the SPP and DGPS cases. By fusing visual and inertial measurements, the GVINS framework is capable of producing 10 Hz position estimates from 1 Hz GNSS observations, effectively bridging temporal gaps and maintaining solution continuity during GNSS signal degradation. As a result, the GVINS solutions demonstrate significantly higher temporal consistency and robustness than conventional GNSS-only methods.

Figure 16 shows the cumulative distribution of the positioning errors. The CDF plots illustrate the overall performances of the five different methods. By applying differential corrections to the SPP case, the 3D 95% position error was moderately reduced from around 44 m to approximately 41 m. With the integration of visual–inertial sensors, the error further decreased to about 10 m.

The scatter plots in Figure 17 illustrate the spatial distribution of position errors for each method. In the smartphone-based SPP (M1) and DGPS (M2) solutions, the error points are widely dispersed, indicating unstable positioning performance and significant horizontal deviation. In contrast, the GVINS (M3) and DGVINS (M4) results exhibit a much denser cluster of points around the origin, demonstrating improved precision and consistency. The u-blox GVINS (M5) shows the tightest concentration of errors, confirming its superior accuracy due to higher-quality GNSS observations. Overall, the scatter plots clearly visualize the progressive improvement in positioning stability and error reduction achieved through visual–inertial integration.

6.3. Campus Driving

The campus-driving dataset corresponds to 779 s of data collected by car on university campus roads on 5 October 2025. Visual features were mainly derived from static structures, such as road markings and buildings, with only a limited number of dynamic objects (e.g., vehicles and pedestrians) present at the scenes. Figure 18 and Figure 19 present the sky-plots and mean C/No values. The sky-plot indicates that the sky is mostly unobstructed down to low elevation angles, and the mean C/No values are comparable to those of the sports field dataset. The u-blox receiver tracked 33 satellites, 25 of which were commonly observed using the Samsung A51. Satellites tracked using the Samsung A51 included ten GPS, six GLONASS, and nine BeiDou satellites, while Galileo signals were not acquired.

Figure 20 presents the temporal evolution of the number of satellites used in positioning. For the M1 and M2 configurations, the Samsung A51 maintained visibility to a median number of six GPS satellites satisfying C/No >25 dB-Hz and elevation >7°. In comparison, the M3 and M4 configurations benefited from multi-constellation tracking, providing a median of 10 satellites from GPS, GLONASS, and BeiDou, with C/No >25 dB-Hz and elevation >30°. The u-blox receiver exhibited the highest satellite availability, maintaining a median of 20 visible satellites throughout the session.

Based on the results presented in

Table 4. Performance comparison of positioning methods (2D, up, and 3D errors) in the campus-driving dataset.

Method	2D Error (m)			Up Error (m)			3D Error (m)
	RMS	MAE	STD	RMS	MAE	STD	RMS	MAE	STD
M1-SPP A51	15.995	10.638	11.945	27.038	21.813	19.905	31.415	25.844	17.861
M2-DGPS A51	13.752	9.798	9.649	18.289	13.205	18.204	22.882	17.785	14.397
M3-GVINS A51	6.573	3.393	5.629	10.735	10.178	3.892	12.588	11.188	5.768
M4-DGVINS A51	3.747	3.181	1.980	3.423	2.944	2.232	5.075	4.596	2.152
M5-GVINS u-blox	1.464	1.410	0.396	5.423	5.394	0.568	5.618	5.592	0.533

, the 3D RMSE, MAE, and STD improved by 27.2%, 31.3%, and 19.4%, respectively, when differential corrections were applied to the M1-SPP case. These errors were further reduced through visual–inertial navigation, as seen in the M3-GVINS configuration, reaching 12.6 m, 11.2 m, and 5.8 m, which correspond to improvements of 59.9%, 56.7%, and 67.7% compared to those of the M1-SPP case. The integration of GNSS with visual–inertial measurements helps to mitigate the high noise level inherent in GNSS measurements, resulting in smoother and more consistent positioning solutions.

In addition, the differential GVINS (M4-DGVINS) approach achieved the highest positioning accuracy among all the configurations in 3D RMSE and MAE. The RMSE, MAE, and STD values for the A51 DGVINS solution were significantly lower than those for the M3-GVINS, indicating the effective mitigation of common-mode errors through differential corrections. While the u-blox GVINS (M5) provided the most precise overall solution due to its receiver quality, the smartphone-based DGVINS achieved approximately 5 m accuracy, demonstrating the feasibility of enhancing low-cost smartphone GNSS data with differential corrections and tightly coupled visual–inertial integration.

Figure 21 illustrates the north, east, and up positioning errors obtained in all the tested modes. Among these, the M5-GVINS solution achieved the highest precision and stability, exhibiting minimal temporal fluctuations compared to the other methods. The M4-DGVINS configuration provided the most accurate vertical estimates in terms of the RMSE, while the larger standard deviation indicates less consistency and a higher noise level in the up component. When compared to the M1 and M2 modes, all the GVINS-based approaches (M3, M4, and M5) produced smoother and more reliable trajectories, confirming the advantages of tightly coupled visual–inertial–GNSS integration in improving precision.

Figure 22 presents the cumulative distribution functions (CDFs) of the 2D, vertical, and 3D positioning errors in all the modes. The 95th percentile of the 3D positioning error exceeds 40 m for the M1 and M2 cases, indicating relatively lower standalone and differential GPS performances. When GVINS is employed, the 3D error is significantly reduced to approximately 15 m, demonstrating the benefit of integrating visual–inertial information with GNSS. Furthermore, the application of differential corrections further enhances the accuracy, achieving a performance level comparable to that of the M5 u-blox receiver case.

Figure 23 illustrates the spatial distributions of the positioning errors in all the tested modes. Among them, the M5-GVINS solution exhibits the most compact scatter, indicating the highest positioning precision. However, a small bias is observed toward the negative north direction, suggesting the presence of a systematic offset. Overall, when comparing GVINS-based approaches (M3-M5) with non-GVINS modes (M1-M2), significant improvements in precision and consistency are achieved, highlighting the effectiveness of the tightly coupled visual–inertial–GNSS integration.

7. Conclusions

This study aimed to evaluate the potential of low-cost, low-power, noisy, single-frequency GNSS receivers available in mass-marketed smartphones, within the tightly coupled visual–inertial navigation framework of GVINS. A custom hardware and software platform was developed to support dataset collection and evaluation using a Raspberry Pi 5 computer, integrating two global-shutter cameras and an Xsens MTi-1 IMU, with all the components operating under different ROS distributions that were interconnected via a ROS bridge. GNSS measurements were recorded using a u-blox ZED-F9P receiver with a dedicated antenna and a Samsung A51 smartphone rigidly attached together, enabling a direct performance comparison between the results of GVINS using measurements from the two devices. Android raw GNSS measurements were collected using a custom Android application. Ground-truth positions were obtained using a GNSS Network RTK provided by the Turkish Permanent CORS Network, TUSAGA–Active, and a u-blox receiver–antenna pair. The Raspberry Pi system time was synchronized with a GPS time server to ensure that the timestamps of the local sensors (camera and IMU) were aligned with GPS time (GPST). Three different datasets were collected to represent diverse real-world scenarios, including an open-sky sports field, an urban area surrounded by buildings, and a driving experiment within a campus environment. Differential corrections were obtained from the nearby IGS station (ANK2) using a code-pseudorange-based method in order to evaluate the DGVINS method. Five distinct evaluation schemes were used: SPP, DGPS, GVINS, and DGVINS with Samsung A51 measurements and GVINS with u-blox measurements. This study also evaluated the performance of the u-blox ZED-F9P receiver within the GVINS framework using 1 Hz measurements, whereas the original work [23] reported results based on 10 Hz data.

The u-blox ZED-F9P GNSS receiver provided the most reliable and precise results due to its advanced algorithms, higher signal quality, and dedicated antenna. The smartphone-based solution still achieved reasonably accurate positioning despite the inherent hardware limitations when integrated into the GVINS framework. Our results show that the improvements achieved by M4-DGVINS compared to M1-SPP are 80.4%, 64.9%, and 83.8% for the sports field, campus-walking, and campus-driving datasets, respectively, in terms of 3D RMS errors. Although these percentages are broadly consistent across the scenarios, the campus-walking dataset exhibits noticeably lower improvement. This may be primarily due to the urban canyon conditions observed along parts of the walking trajectory, where the number of visible satellites drops sharply. In these segments, the GVINS solution may experience a GNSS-induced position deviation caused by degraded satellite geometry, and applying differential corrections during these periods may also be insufficient to mitigate these errors. When such degraded GNSS factors enter the factor-graph optimization window, their influence cannot be removed immediately; even after satellite visibility improves, the optimizer requires time to dilute the effect of these erroneous constraints. Consequently, the residual global bias persists over a portion of the trajectory, reducing the net improvement achieved by DGVINS in this scenario. In contrast, the open-sky sports field provides uninterrupted satellite visibility and pseudorange measurements obtained under higher C/No conditions, while the campus-driving dataset benefits from longer segments with less severe satellite blockage compared with those in the campus-walking scenario. These conditions may allow differential corrections to be utilized effectively, resulting in larger relative improvements with DGVINS. Beyond these environment-specific effects, the remaining differences among the scenarios can be explained by the general error sources present in smartphone GNSS data, including measurement noise, multipath, atmospheric delay variations, and residual satellite orbit and clock errors. Even under these limitations, the results highlight the potential of smartphone GNSS receivers within the GVINS framework. Although they receive signals from fewer constellations, with lower signal quality and a lower number of satellites, they can still achieve performances comparable to that of a relatively higher-end dual-frequency GNSS receiver, the u-blox ZED-F9P. In addition to these findings, the relative performance of M4-DGVINS with respect to M3-GVINS varied significantly across the test scenarios. Improvements of 66.0% and 59.7% were obtained in the sports field and campus-driving datasets for 3D RMSE, whereas a 32.4% degradation occurred in the campus-walking dataset collected under more challenging conditions. A similar dataset-dependent trend was also observed in the standalone GNSS results: DGPS improved the 3D RMSE compared to that of SPP by 29.1% and 27.2% in the sports field and campus-driving datasets but only by 13.2% in the campus-walking dataset. These results may indicate that the effectiveness of differential corrections is condition dependent.

Smartphones are also equipped with various sensors beyond the IMU, camera, and GNSS. Once reasonable performance is achieved using the rolling-shutter cameras and low-cost IMUs that may be affected under dynamic conditions, additional sensors, such as barometers, magnetometers, and ranging sensors based on UWB, LiDAR, Wi-Fi, 5G, or Bluetooth, can also be incorporated to further enhance the performance. Deploying GVINS directly on Android devices would allow real-time operation under the restricted processing power and energy budget of smartphones, motivating the development of lightweight feature extraction and tracking modules and the exploration of shorter optimization windows that can still deliver comparable performances. The findings of this study demonstrate that developing Android-based GVINS software holds strong potential for both indoor and outdoor augmented reality applications. In addition, higher-end smartphones containing dual-frequency GNSS receivers may be evaluated, as their improved chipsets, enhanced antennae, and better signal-processing capabilities have the potential to provide significantly higher-quality measurements and reduce many of the limitations observed in current devices. Modern smartwatches are increasingly equipped with GNSS receivers, while emerging wearable devices, such as smart glasses, integrate cameras and IMUs. The combination of these complementary sensing modalities across multiple wearable platforms presents a promising opportunity for future on-device, tightly fused navigation, enabling more robust and continuous positioning, even in challenging environments.