Smartwatches must reliably estimate a user's movement direction during walking, running, and cycling, yet urban GNSS signal degradation and variable wrist orientations complicate existing methods. This paper presents a dualmode framework that adapts to the user's activity for robust movement direction tracking. In walking and running, Principal Component Analysis (PCA) isolates a relative inertial direction from periodic arm-swing accelerations, which is then fused with GNSS data via Covariance Intersection (CI) to maintain statistical consistency. During cycling, an Attitude and Heading Reference System (AHRS) yaw is calibrated by a yaw-to-direction ofset learned from GNSS bearing whenever signals are strong, allowing accurate direction estimates to persist through tunnels and underpasses when signals weaken. Field trials with a Samsung Galaxy Watch 5 in dense urban settings demonstrate that the proposed fusion consistently reduces direction errors compared to single-sensor baselines, automatically favoring GNSS on steady segments and leaning on the inertial estimate or ofset-corrected yaw when satellite coverage degrades.
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The challenge is even greater during cycling, because arm swings disappear, rendering PCA unusable, and the smartwatch’s yaw (from an Attitude and Heading Reference System, AHRS) is often misaligned with the bicycle’s true direction due to handlebar tilt or wrist posture. GNSS bearing can reveal the correct movement direction but only when signals are strong. Consequently, a hybrid solution must combine PCA-based inertial direction with GNSS direction for walking and running—without relying on feedback-based filters that can magnify errors—while also learning and applying a yaw-to-direction ofset whenever GNSS quality is high during cycling, then propagating that ofset through GNSS outages. This paper introduces a dual-mode framework that meets these requirements by employing Covariance
dense foliage.
Field trials in an urban apartment complex (walking/running) and on city bike lanes (cycling) with a Samsung Galaxy Watch 5 demonstrate that the proposed fusion consistently reduces root-mean-square error relative to single-sensor baselines. The framework proves resilient to multipath, brief GNSS outages, and changes in device orientation. The remainder of this paper first surveys related movementdirection estimation techniques, then details the proposed algorithm, including the CI formulation and the cycling ofset-learning strategy. A comprehensive experimental evaluation follows, after which limitations and future extensions are discussed.
Before the fusion strategy is introduced in Section 3, this section details how each sensor independently
estimates movement direction and the associated confidence (error covariance) under two exercise
scenarios—(i) walking or running and (ii) cycling. Throughout, movement direction (MD) denotes the
user’s horizontal direction in the navigation frame.
2.1. Inertial-sensor method
When a smartwatch is worn on the wrist, arm swings produce a highly periodic acceleration pattern.
Over a window of M steps, these samples form an ellipsoidal cloud whose long axis aligns with the true
MD. A PCA isolates that axis as follows:
(
) 1 with 1 ≥ 2 the largest eigenvalues of the sample covariance matrix. A sharply elongated distribution ( 1 ≫ 2) implies high confidence (small
); a more circular cloud indicates ambiguity [7].
During cycling, arm-swing excitation disappears, invalidating the PCA assumption. Instead, the smartwatch’s AHRS provides a yaw angle
, computed via a Kalman-filter–based quaternion fusion
of gyroscope, accelerometer, and, when available, magnetometer data. Because handlebar tilt or wrist
pronation can misalign yaw with the bicycle’s MD, Section 3 describes how a GNSS-derived ofset
compensates this bias. Wearable-based kinematic analysis has been studied in various contexts, further
underscoring the importance of correct orientation handling.
2.2. GNSS method
For GNSS-based movement-direction estimation, we run two independent Recursive-Least-Squares
(RLS)—one for the east axis and one for the north axis—to track velocity and position [8]. For each axis
∈ {, }
the 2-element state is xi(k) = [ , , , ] , and the RLS recursion is
(
After convergence the horizontal velocity vector v = [ , ] produces the heading ̂ = tan−1 ( ̂
)
̂
Its one-sigma uncertainty follows from first-order error propagation of the arctangent. Using the
receiver-reported horizontal position accuracy
axes), the result is
(assumed isotropic and uncorrelated between
2
= (
Android and most commercial GNSS receivers report bearing only above a minimum speed, a condition naturally satisfied during bicycling. When
outputs a bearing . This bearing directly serves as a GNSS MD estimate: ̂
= During temporary signal losses, no bearing is available; Section 3 explains how a previously learned yaw-to-bearing ofset maintains continuity.
This section describes how the individual movement-direction (MD) estimates from Section 2—namely, PCA (inertial direction), AHRS (yaw), RLS (velocity-based direction), and direct GNSS Bearing—are integrated to produce a single, high-confidence direction in real time. Table
overview of how each sensor’s availability and accuracy change under walking/running versus cycling, illustrating that PCA is especially accurate for pedestrian motion and that AHRS plus an ofset correction is more suitable when riding a bike.
Because arm-swing is present only in walking/running, PCA becomes invalid during cycling, while GNSS Bearing typically yields high accuracy at bicycle speeds. Consequently, two distinct fusion strategies are employed to accommodate these sensor diferences. 3.1. Fusion for walking and running For walking/running, the two main contributors are PCA (inertial direction) and GNSS direction. The smartwatch’s AHRS yaw is typically less reliable in this context, because arm swing and wrist pronation frequently reorient the watch. We therefore fuse: 1̂ = ̂ , 1 = 2 , 2̂ = ̂ , 2 = 2
Although standard Kalman filtering requires known correlations, real-world conditions—especially in urban canyons—make such correlations uncertain. We adopt CI, which provides a statistically consistent way to fuse estimates without assuming specific correlation structures [ 9]. CI computes the fused variance and direction as:
−1 = 1−1 + (1 − ) 2−1, ̂ = ( 1−1 1̂ + (1 − ) 2−1 2̂)
∗ =
min | 1 + (1 − ) 2|
where the mixing parameter ∈ [0, 1] is chosen to minimize the fused covariance. In one dimension,
the determinant criterion reduces to
The mixing parameter automatically balances the contributions based on each sensor’s instantaneous
reliability. When GNSS provides stable direction estimates (high C/N0, straight paths), approaches
values that favor GNSS; when satellite signals degrade or multipath increases, shifts toward the PCA
estimate. This adaptive weighting occurs without requiring explicit correlation modeling, making
the fusion robust to model uncertainties that are particularly challenging to characterize in urban
environments. By design, CI never yields an over-optimistic variance estimate. During long, straight
segments, GNSS direction can provide a solid reference, while in the presence of turns or poor signals,
PCA takes precedence and stabilizes the result.
(
can be quite accurate if C/N0 is suficiently high. Our strategy is to learn an ofset between AHRS yaw and the GNSS bearing under reliable conditions, and then maintain that ofset during GNSS outages or degraded signals.
To estimate this ofset, we gather AHRS yaw values () and GNSS bearing () over n consecutive samples while the bicycle follows a roughly straight path. The time-averaged yaw and bearing are: yielding a yaw-to-direction ofset: ̄ ̄ () = 1 () = 1 −1 ∑ ̂
−1 ∑ =0 =0 ̂ = ̄ − ̄ ( − ) ( − ) which continues to give an accurate direction even if GNSS drops out temporarily (e.g., under bridges or in tunnels).
With CI fusion for pedestrians and ofset-compensated yaw for cyclists, this dual-mode framework provides a single, continuous MD estimate accompanied by a realistic covariance. It naturally exploits each sensor’s strengths: PCA excels at capturing slow or periodic motions on wrist, GNSS enriches direction on straight segments or higher speeds, and AHRS plus ofset keeps cyclists’ direction accurate through signal drops. Section 4 details the experimental design and evaluates the system’s performance across three distinct outdoor settings, highlighting the advantages of this hybrid approach over singlesensor baselines.
4.1. Setup Experiments were carried out with a Samsung Galaxy Watch 5 worn on the participant’s left wrist. For ground truth, an Xsens MTi-680G inertial/GNSS unit was rigidly co-mounted on an acrylic plate above the watch so that both instruments experienced identical attitude changes (see figure 1 for equipment). The MTi-680G ran in RTK mode, and its velocity vector was numerically diferentiated to yield the reference MD. Table 2 lists the three outdoor venues, chosen to represent distinct satellite environments and motion dynamics. All experiments were conducted in outdoor environments to evaluate the proposed GNSS-inertial fusion under realistic satellite signal conditions, which represents the primary contribution of this work. For indoor scenarios where GNSS signals are unavailable, the framework automatically operates using only the PCA-based inertial direction estimation (Section 2.1), which remains efective regardless of satellite availability due to its reliance on consistent arm-swing patterns. The outdoor experimental design ensures comprehensive evaluation of the dual-sensor fusion capability while the PCA component alone provides robust indoor direction estimation as demonstrated in our previous work [7]. 4.2. Results Throughout each trial, the fusion algorithm produced an MD estimate at the smartwatch’s sampling rate. The instantaneous direction error (algorithm minus reference, unwrapped) was logged, and its root-mean-square error (RMSE) computed for each method. Table 3 provides a summary of the resulting direction RMSE for the inertial sensor only, GNSS only, and the proposed fusion approach.
1) Park (walking): With average HDOP < 3.9 and C/N0>28 [dB-Hz], the user’s path included several sharp turns (figures 2, 3). These turns degraded the GNSS-only direction, causing momentary spikes in error. The inertial PCA, however, remained stable and accurately tracked the overall direction. By blending GNSS and PCA, CI lowered error by 9 [deg] compared with GNSS alone and incurred only a small penalty relative to the inertial baseline. This demonstrates how CI adaptively trusts GNSS on straights but relies more on PCA during turns.
2) Track (running): In an open-sky stadium track (figures 4, 5), HDOP was below 3.8, and C/N0 often exceeded 28.5 [dB-Hz]. Despite the relatively ideal conditions, GNSS position jitter introduced noticeable direction noise on the long straights. CI again outperformed GNSS-only and stayed within 0.6 deg of the PCA estimate. As before, this result shows how CI automatically down-weights GNSS data when it becomes noisy or inconsistent, preventing large fusion errors.
3) Riverside (cycling): In the 3 km cycling route (figures 6, 7), the participant passed under multiple bridges, causing intermittent satellite outages. Whenever C/N0 was healthy, the algorithm updated the yaw-to-bearing ofset; during outages, it relied on ofset-compensated yaw. This significantly reduced direction error relative to uncompensated yaw and prevented large spikes when GNSS data were lost. The fusion method remained within 7 [deg] RMSE even through complete signal gaps, whereas yaw alone could drift by over 10 [deg]. Overall, this highlights the importance of periodic ofset calibration in cycling contexts.
Across all exercises, the proposed fusion consistently delivered the lowest RMSE (see Table 3). CI leverages GNSS information when it is reliable (long straights, high C/N0) yet defaults to PCA when satellites falter or the path turns sharply. During cycling, ofset calibration was crucial for mitigating yaw drift and maintaining robust direction estimates. These findings validate the dual-mode framework of Sections 2 and 3, demonstrating robust smartwatch-based MD estimation under diverse urban conditions.
This paper presented a dual-mode framework for reliable smartwatch-based movement-direction tracking under walking, running, and cycling. For pedestrian motion, a PCA-based inertial direction and a GNSS-based direction are combined via Covariance Intersection to yield a statistically consistent estimate. For cycling, the framework periodically learns a yaw-to-bearing ofset under favorable GNSS conditions, then applies the ofset during GNSS outages.
Outdoor experiments revealed that this fusion consistently lowered RMSE compared to single-sensor baselines across three distinct scenarios, achieving average improvements of 47.9 % (walking), 28.2 % (running), and 34.8 % (cycling) relative to GNSS-only approaches. The proposed method maintained sub-12 [deg] RMSE across all test conditions while operating within a 1 [ms] computational budget per sample.
Future work will automate mode switching, address magnetometer bias for indoor usage, and examine long-term drift across multiple users and devices. By reducing direction errors under varied conditions, this approach promises more reliable navigation, coaching, and safety applications on everyday smartwatch platforms.
This research was supported by the National Research Foundation of Korea funded by the Ministry of
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