Smartphone-based positioning, heralded for its widespread accessibility, encounters challenges due to its reliance on Global Navigation Satellite Systems (GNSS) in unfavorable conditions such as urban canyons, tunnels, and indoor areas. Even in clear-sky conditions, signal distortions, interruptions, and the limitations of cost-effective smartphone GNSS prompt researchers to explore alternative positioning methods. This has led to the adoption of sensor fusion techniques, often integrating the Inertial Measurement Unit (IMU) for its complementary features with GNSS. In pedestrian localization, the fusion of Pedestrian Dead Reckoning (PDR) and GNSS, traditionally employing the Kalman Filter (KF) as the main fusion algorithm, has been a standard practice. The emerging Factor Graph Optimization (FGO) algorithm has recently gained attention for its better accuracy for INS-GNSS fusion architectures, especially under GNSS outliers. However, the FGO implementation for PDR-GNSS fusion architecture has been less investigated and little is known about its performance under different PDR outliers. Due to the different gait dynamics of humans and transient variations in the way the smartphone is carried, the PDR system can generate Short and High Errors (SHE) or Continuous and Low Errors (CLE). We analyze the improvement of FGO over KF in mitigating these PDR errors in the PDR-GNSS fusion architectures for smartphone-based positioning. Since FGO is a smoothing technique and KF is a filtering method, for a fairer comparison we also implemented a smoothed KF (SKF) using the Rauch-Tung-Striebel Smoother (RTSS) technique. Our investigation, involving ten individuals with diverse heights, genders, and gait patterns in walking and running motions, underscores FGO’s superior performance in the presence of PDR errors and across various pedestrian and motion scenarios, achieving a stable 25% improvement for the mean position error and 30% for the median position error in comparison to KF and 24% mean improvement and 32% median improvement in comparison to SKF. Furthermore, the convergence time for FGO after the SHE PDR errors is comparably shorter than SKF and KF.

The availability of raw Global Navigation Satellites System (GNSS) measurements in Android smartphones fosters advancements in high-precision positioning for mass-market devices. However, challenges like inconsistent pseudo-range and carrier phase observations, limited dual-frequency data integrity, and unidentified hardware biases on the receiver side prevent the ambiguity resolution of smartphone GNSS. Consequently, relying solely on GNSS for high-precision positioning may result in frequent cycle slips in complex conditions such as deep urban canyons, underpasses, forests, and indoor areas due to non-line-of-sight (NLOS) and multipath conditions. Inertial/GNSS fusion is the traditional common solution to tackle these challenges because of their complementary capabilities. For pedestrians and smartphones with low-cost inertial sensors, the usual architecture is Pedestrian Dead Reckoning (PDR)+ GNSS. In addition to this, different GNSS processing techniques like Precise Point Positioning (PPP) and Real-Time Kinematic (RTK) have also been integrated with INS. However, integration with PDR has been limited and only with Kalman Filter (KF) and its variants being the main fusion techniques. Recently, Factor Graph Optimization (FGO) has started to be used as a fusion technique due to its superior accuracy. To the best of our knowledge, on the one hand, no work has tested the fusion of GNSS Post-Processed Kinematics (PPK) and PDR on smartphones. And, on the other hand, the works that have evaluated the fusion of GNSS and PDR employing FGO have always performed it using the GNSS Single-Point Positioning (SPP) technique. Therefore, this work aims to combine the use of the GNSS PPK technique and the FGO fusion technique to evaluate the improvement in accuracy that can be obtained on a smartphone compared with the usual GNSS SPP and KF fusion strategies. We improved the Google Pixel 4 smartphone GNSS using Post-Processed Kinematics (PPK) with the open-source RTKLIB 2.4.3 software, then fused it with PDR via KF and FGO for comparison in offline mode. Our findings indicate that FGO-based PDR+GNSS–PPK improves accuracy by 22.5% compared with FGO-based PDR+GNSS–SPP, which shows smartphones obtain high-precision positioning with the implementation of GNSS–PPK via FGO.

Smartphone-based pedestrian navigation has become increasingly popular due to the widespread availability of low-cost Android devices. However, these smartphones often suffer from low positional accuracy caused by inexpensive GNSS antennas and receivers. To address these limitations, fusion mechanisms are employed, with Factor Graph Optimization (FGO) emerging as a prominent method in navigation solutions, particularly for INS+GNSS integration. While FGO has also gained popularity in Simultaneous Localization and Mapping (SLAM) applications, its reliance on batch data processing, referred to as Batch Factor Graph Optimization (BFGO) and which is used as the baseline for this study, results in significant computational overhead, making it impractical for real-time or resource-constrained scenarios. To address these challenges, two windowing-based FGO approaches are proposed: the Naive Windowing FGO (NW-FGO) and the Marginalized Windowing FGO (MW-FGO). By incorporating marginalization, MWFGO retains critical information while reducing computational costs. Both methods are evaluated under two error conditions GNSS multipath and PDR errors to assess their impact on positional accuracy and efficiency. Our findings reveal that optimal window sizes, such as 50s for GNSS errors and 30s for PDR errors, achieve accuracy comparable to BFGO while significantly reducing computational time from 2500 seconds to 38 seconds with MWFGO. Furthermore, MWFGO outperforms NW-FGO, improving mean positional accuracy by 2.18% across varying window sizes, underscoring the effectiveness of marginalization. This study demonstrates the feasibility of windowing-based FGO, particularly MWFGO, in balancing computational efficiency and accuracy. By optimizing window sizes and leveraging marginalization, we provide a robust alternative to FGO, making real-time pedestrian navigation viable in resource-constrained environments.

The performance of smartphone-based pedestrian positioning strongly depends on the GNSS signal quality, the motion dynamics that influence PDR accuracy, and the way both sources of information are fused. While recent studies have shown the benefits of Factor Graph Optimization (FGO) for Pedestrian Dead Reckoning (PDR) Global Navigation Satellite Systems (GNSS) fusion, the interaction between human motion, PDR errors, and FGO window configuration has not been systematically examined. This work investigates how walking dynamics affect the optimal configuration of sliding-window FGO, and to what extent FGO mitigates motion-dependent PDR errors compared with the Kalman Filter (KF). Using data collected from ten pedestrians performing four motion types (slow walking, normal walking, jogging, and running), we analyze: (1) the relationship between walking speed and the FGO window size required to achieve stable positioning accuracy, and (2) the ability of FGO to suppress PDR outliers arising from motion irregularities across different users. The results show that a window size of around 10 poses offers the best overall balance between accuracy and computational load, providing substantial improvement over SWFGO with a 1-pose window and approaching the accuracy of batch FGO at a fraction of its cost. Increasing the window further to 30 poses yields only marginal accuracy gains while increasing computation, and this trend is consistent across all motion types. Additionally, FGO and SWFGO reduce PDR-induced outliers more effectively than KF across all users and motions, demonstrating improved robustness under gait variability and transient disturbances.