We recruited twenty-five recreational runners (15 male, 10 female) through local running clubs and social media advertisements. Participant characteristics are detailed in Table 1.

Inclusion criteria for participation were: (1) age between 18 and 45 years; (2) an average weekly running volume of at least 15 km over the past year; (3) the ability to run continuously at 12 km/h for at least 5 min; and (4) no history of cardiovascular or neurological diseases. Exclusion criteria included: (1) any lower-limb musculoskeletal injuries that affected running gait within the past 6 months; (2) current pain or undergoing rehabilitation for a running-related injury; or (3) any known balance disorders. All participants provided written informed consent prior to testing, as approved by the Institutional Review Board (IRB Protocol #2024-118).

We used the Xsens MVN Awinda inertial motion capture system (Xsens Technologies B.V., Netherlands) as the gold standard. This system comprises 17 wireless IMUs (MTw2) sampling at 100 Hz. Sensors were attached to the head, sternum, pelvis (L5/S1), and bilaterally on the upper arms, forearms, hands, thighs, shanks, and feet using manufacturer-recommended Velcro straps. The Xsens system, which uses proprietary sensor fusion algorithms to provide 3D full-body kinematics, has been widely validated for gait analysis (Poitras et al., 2019). All trials were conducted on a Woodway Pro (Woodway USA, Inc.) treadmill, which provided stable and controllable running speeds.

Participants attended a single 60-min laboratory session. The main protocol consisted of three 3-min running trials at fixed speeds of 8 km/h, 10 km/h, and 12 km/h, representing slow, medium, and tempo paces. A 2-min standing rest period was provided between trials. The order of speeds was randomized to mitigate fatigue effects. During all trials, data from all 17 IMUs were synchronously recorded by the Xsens MVN Analyze software.

The performance of the finalized models was evaluated on the unseen 5-subject test set using three standard regression metrics.

The Coefficient of Determination ( R 2 ), which measures the proportion of the variance in the target variable that is predictable from the input features:

In the above equations, y i is the actual value, y ^ i is the predicted value, y ¯ is the mean of the actual values, and n is the number of data points. Agreement was assessed using Bland-Altman plots.

As expected from the statistical analysis, running speed had a significant systematic effect on gait parameters. With increasing speed, GCT significantly decreased ( p < 0.001 ), Flight Time (FT) significantly increased ( p < 0.001 ), Cadence slightly increased ( p < 0.05 ), and VO significantly increased ( p < 0.001 ). This confirmed our protocol successfully elicited a range of gait patterns suitable for a robust regression task.

Before evaluating the sensor configurations, a comparative analysis was conducted to validate the choice of the Random Forest (RF) algorithm. On the full feature set, the RF model significantly outperformed a baseline Linear Regression model ( R 2 improvement of >0.15 for GCT), confirming the non-linear nature of gait dynamics. Furthermore, the RF model achieved predictive accuracy comparable to a Long Short-Term Memory (LSTM) deep neural network (Mean Absolute Error difference <1.5 ms), but with approximately 10% of the training time and significantly lower computational complexity.

The core findings for the sensor configurations using the optimized RF model are summarized in Table 3. The results confirm that the specific sensor subsets contain varying degrees of information sufficiency.

To assess the model’s robustness against running speed variations, we stratified the performance analysis by the three speed protocols (8, 10, and 12 km/h).

As detailed in Table 4, the model demonstrated high stability. While the prediction error (MAPE) for temporal parameters like Ground Contact Time marginally increased at the highest speed (12 km/h), this performance drop is attributed to the increased soft tissue artifacts and higher-magnitude impact transients typical of faster running speeds, which introduce non-linear noise into the accelerometer signal (e.g., sensor saturation or skin motion). Despite this, the coefficient of determination ( R 2 ) remained consistently above 0.90 across all conditions. This suggests that the selected feature set effectively captures the biomechanical variations associated with speed changes.

This quantitative performance is visualized in the scatter plots of predicted versus actual values for the test set (Figure 3). The models for VO (Figure 3A) and GCT (Figure 3B) from Config 1 (Lumbar-Only) showed data points tightly clustered around the line of identity ( y = x ), confirming their high accuracy. In contrast, the plot for SI from Config 1 (Figure 3C) revealed a scattered pattern with poor correlation. This was corrected in the plot for SI from Config 3 (Lumbar + Ankles) (Figure 3D), which once again showed a tight cluster around the identity line, visually confirming the necessity of the ankle sensors for symmetry assessment.

To understand how the models were making predictions, we analyzed the Gini importance rankings from the Random Forest algorithm. For the successful Lumbar-Only GCT model (Config 1), the most predictive features were dominated by metrics from the vertical (Z-axis) and anteroposterior (X-axis) accelerometers (Table 5; Figure 4). This finding is biomechanically sound, as these axes capture the primary signals related to ground impact and braking/propulsion forces. This increases confidence that the models are learning biomechanically relevant patterns rather than spurious correlations.

To move beyond correlation and assess true agreement, Bland-Altman plots were constructed for the predictions from the optimal configurations. As shown in Figure 5 for GCT predicted by Config 3 (Lumbar + Ankles), the mean difference (bias) was clinically negligible at − 0.8 ms , and the 95% limits of agreement were narrow ( − 11.2 ms , + 9.6 ms ). Crucially, the errors were randomly distributed around the mean, indicating no systematic or proportional bias across the range of GCT values. This confirms that the model is robust and accurate, not just for the group average, but for individual step measurements.

The central finding of this study is the remarkable efficacy of a single, lumbosacral-mounted IMU when combined with a machine learning model. Our results compellingly demonstrate that it is possible to accurately predict key running gait parameters without resorting to a complex “Christmas tree” sensor setup. The ability of the Lumbar-Only configuration to predict cadence, vertical oscillation, and ground contact time with R 2 values exceeding 0.95—and with low, non-systematic bias confirmed by Bland-Altman analysis—challenges the long-standing assumption that multi-sensor systems are essential for accurate gait analysis. This finding alone has significant implications for consumer-grade wearables, which could be algorithmically upgraded to provide insights previously reserved for laboratory-grade equipment.

However, our study also clearly defines the “blind spot” of this single-sensor approach: gait asymmetry. The model’s complete failure to predict the Gait Symmetry Index ( R 2 = 0.52 ) is logical and biomechanically grounded. The lumbosacral sensor, positioned near the Center of Mass (CoM), captures the integrated summation of forces from both limbs. This “smoothing effect” effectively filters out the distinct high-frequency impact transients of individual foot strikes required to calculate bilateral differences. A single central sensor cannot differentiate whether a specific vertical acceleration peak originated from the left or right leg, making it inherently incapable of detecting asymmetry without external context (Sadeghi et al., 2000). Advanced cross-validation studies confirm that while trunk-mounted sensors effectively capture center-of-mass energy, they often filter out the distal high-frequency transients essential for identifying subtle side-to-side biomechanical discrepancies (Caldas et al., 2017).

This is precisely why the Lumbar + Ankles configuration (Config 3) emerged as the “minimal-optimal” solution. By adding two ankle sensors—the most logical locations to capture discrete foot-ground contact events—this 3-sensor setup overcomes the single-sensor’s primary limitation. It successfully combines the global-parameter strength of the lumbar sensor with the temporal and asymmetry-detecting strengths of the ankle sensors, achieving high performance ( R 2 > 0.91 ) across all measured parameters.

The success of our models is rooted in a synergy between biomechanical principles and the pattern-recognition capabilities of machine learning. The lumbar sensor (Config 1) is effective because its position near the body’s center of mass (CoM) captures an integrated signal of whole-body motion. The dynamics of the CoM, particularly its vertical and anteroposterior acceleration (which our feature importance analysis confirmed as critical), are a direct reflection of the forces produced by and acting upon the lower limbs (Willy and Davis, 2011). The ML model effectively “decoded” this integrated signal to infer parameters like GCT and VO. The ankle sensors (Config 2) were superior for temporal metrics because their signals provide unambiguous, high-amplitude spikes and reversals corresponding to the discrete events of initial contact (IC) and toe-off (TO) (Aminian et al., 2002). Config 3’s success comes from fusing both data streams, allowing the model to see both the “whole” (CoM) and the “parts” (individual limbs).

This work extends the existing literature by providing a systematic, data-driven comparison of minimal sensor configurations. Unlike previous research that primarily utilized machine learning for activity classification (e.g., distinguishing walking from running), our study focuses on the precise regression of continuous biomechanical parameters.

Our approach demonstrates distinct advantages over traditional threshold-based algorithms. Studies relying on simple peak-detection methods (e.g., González et al., 2010) often report increased error rates when foot-strike patterns shift (e.g., from rearfoot to forefoot) at higher speeds. In contrast, our ML-based fusion model dynamically adapts to speed-induced kinematic shifts, maintaining consistent accuracy across the tested range (8–12 km/h).

Furthermore, the proposed “minimal-optimal” 3-sensor configuration compares favorably against current commercial wearable solutions. While widely used consumer devices (e.g., Garmin Running Dynamics, Polar) typically report Ground Contact Time errors in the range of 5%–10% when compared to force plates (Wouda et al., 2018; Napier et al., 2015), our fusion model achieved a MAPE of <4%. This demonstrates that by strategically placing just two additional sensors on the ankles to complement the lumbar unit, we can bridge the gap between consumer-grade estimates and laboratory-grade precision.

Our methodological framework—using a full gold-standard system to programmatically create and test minimal subsets—is a key contribution that can be applied to optimize sensor arrays for any human movement, effectively quantifying the trade-off between hardware complexity and information gain.

The choice of Random Forest provides tangible benefits for embedded implementation. While deep learning techniques have demonstrated exceptional performance in complex biomedical tasks, such as the real-time reconstruction of focal temperature fields (Esteva et al., 2017) and automated cancer scoring from medical images (Litjens et al., 2017), they often demand significant computational resources. Unlike Deep Neural Networks (DNNs) or LSTMs, which require computationally expensive matrix multiplications and substantial RAM for activation maps, the RF inference process consists of a series of simple conditional checks (if-else statements). We estimate that the finalized “minimal-optimal” model (with reduced features) would require less than 200 KB of memory and could be executed in microseconds on standard low-power microcontrollers (e.g., ARM Cortex-M4). This low computational footprint allows for “on-sensor” processing, significantly extending battery life by reducing the need to transmit raw high-frequency data via Bluetooth.

Furthermore, the theoretical justification for choosing RF over recurrent architectures (like LSTMs) lies in our feature engineering strategy. While RF is not inherently a temporal model, the sliding-window approach combined with frequency-domain feature extraction (FFT) effectively “encodes” the temporal evolution of the gait cycle into the feature space. By explicitly providing the model with temporal proxies—such as spectral energy distribution and signal periodicity metrics—we compensate for the lack of internal memory states. This allows the RF model to capture the continuous dynamics of steady-state running with accuracy comparable to LSTMs ( R 2 > 0.98 ), but with significantly lower computational latency.

Despite the promising results, several limitations must be acknowledged. First, this study was conducted on a treadmill, which provides a homogenous, flat surface. We acknowledge that treadmill running lacks the surface variability and air resistance of overground running, and gait mechanics may differ slightly (Van Hooren et al., 2020).

Second, the validated speed range (8–12 km/h) represents steady-state endurance running. It is crucial to note that the proposed “minimal-optimal” configurations cannot be directly extrapolated to sprinting or high-intensity interval running (>15 km/h). In sprinting scenarios, gait mechanics undergo fundamental shifts—specifically, ground contact times shorten significantly (<150 ms) and vertical impact forces rise sharply—which may require distinct sensor fusion logic and higher sampling frequencies.

Third, regarding the hardware specifications, the IMUs were sampled at 100 Hz (10 ms temporal resolution). While theoretically limiting for capturing high-speed impacts, our regression-based approach achieved a Mean Absolute Error of <2 ms for temporal parameters. This sub-sample precision is achievable because the machine learning model learns from the overall morphological features of the signal wave (e.g., spectral energy, variance) rather than relying on simple, grid-bound peak detection methods. However, at the highest tested speed (12 km/h), we observed a marginal increase in error. This is likely attributable to Soft Tissue Artifacts (STA)—the secondary motion of the sensor relative to the bone caused by skin deformation during high-impact landing—rather than the temporal resolution itself. Future hardware implementations should prioritize more rigid mounting solutions to mitigate this mechanical noise.

However, this controlled environment was a necessary prerequisite to establish an “algorithmic ground truth” and validate the sensor fusion logic against the optical gold standard before introducing the environmental noise of outdoor scenarios. Future studies must validate these models in “in-the-wild” scenarios with variable terrain and slopes. Preliminary field studies suggest that terrain variability significantly increases the non-linear noise in IMU signals, necessitating more sophisticated sensor fusion architectures to maintain the R 2 levels observed in controlled laboratory settings (Norris et al., 2014).