⚡ electrical engineering

Foot Clearance Estimation Under Varying Gait Speeds: Comparative Analysis of Real-Time and Time-Normalized Approaches Using Inertial Measurement Units

This study demonstrates that a machine learning framework using foot-mounted inertial sensors can accurately estimate continuous foot clearance trajectories across varying walking speeds, with performance influenced by walking speed, temporal representation, and sensor feature selection.

Original authors: Mostafa Haj Lotfalian, Peyman Aghaie Ataabadi, Javad Sarvestan

Published 2026-07-06

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Mostafa Haj Lotfalian, Peyman Aghaie Ataabadi, Javad Sarvestan

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are walking through a crowded room. To avoid tripping over a rug or bumping into a chair, your brain subconsciously calculates exactly how high to lift your foot. This "safety gap" between your shoe and the floor is called foot clearance. If this gap is too small or wobbly, you might trip.

For years, scientists have been able to measure this gap perfectly, but only inside a fancy laboratory using expensive cameras that track tiny reflective dots on your feet. The problem? You can't wear a room full of cameras to the grocery store or while jogging in the park.

This study asks a simple question: Can we use a small, cheap sensor strapped to your foot (like a smartwatch for your shoe) to guess your foot clearance just as well as those big cameras?

Here is the breakdown of their experiment and what they found, explained simply.

The Experiment: The "Three-Speed" Test

The researchers gathered 68 healthy young people and strapped two small sensors (called IMUs) to their feet. These sensors act like a tiny pilot, feeling every shake, spin, and tilt of the foot.

To see if the sensors were accurate, they compared the sensor data against the "gold standard" (the big camera system). They had the participants walk on a treadmill at three different paces:

Slow: A leisurely stroll.
Preferred: Their natural, comfortable speed.
Fast: A brisk, hurried walk.

The Two Big Questions

The researchers didn't just want to know if the sensors worked; they wanted to know how to process the data to get the best results. They tested two main variables:

1. The "Time Travel" vs. "Real-Time" Approach

Time-Normalized (The "Recipe" Approach): Imagine you have a 10-minute song and a 20-minute song. To compare them, you stretch or squash them both to be exactly 1 minute long. This is what the researchers did with the walking data. They forced every step to look like the same percentage of a cycle, regardless of how fast the person was walking. This is common in science but throws away the actual timing.
Real-Time (The "Live Stream" Approach): This keeps the data exactly as it happened. If you walked fast, the step was short and quick. If you walked slow, the step was long and drawn out. The computer had to learn the pattern without squashing the time.

2. The "Full Toolkit" vs. "The Essentials"

Full Feature Set: The sensors have three tools: an accelerometer (feels speed), a gyroscope (feels rotation), and a magnetometer (feels Earth's magnetic field, like a compass). They used all three.
Reduced Feature Set: They turned off the "compass" (magnetometer). Why? Because compasses can get confused by metal lockers or electronics in the real world. They wanted to see if the other two tools were enough.

The Results: What Worked Best?

The researchers used a smart computer program (Machine Learning) to learn the connection between the sensor shakes and the actual foot height. Here is what they discovered:

The Sensors Worked Great: The computer's guesses were very close to the camera's measurements. It was like having a student who got an "A" on the test, matching the teacher's answer key about 75% to 85% of the time.
The "Compass" Helped, But Wasn't Essential: Using the full toolkit (including the magnetometer) gave slightly better results, especially in the lab. However, the "Essentials only" (accelerometer + gyroscope) still worked very well. This is good news because it means you don't need a perfect magnetic environment to get good data.
Speed Matters, But the Model Coped: Walking faster changed the data, but the model was smart enough to handle slow, normal, and fast walking without breaking.
Time vs. Real-Time: Surprisingly, the "Real-Time" approach (keeping the natural speed) worked just as well as the "Time-Normalized" approach (squashing the time). This is a big deal because "Real-Time" is exactly what you need for a wearable device that gives you feedback while you are walking, rather than after you've finished.

The Bottom Line

The study concludes that you can strap a small sensor to your foot and use a computer program to accurately track how high your foot lifts while walking, even if you change speeds.

For the Lab: If you have a controlled environment, using all the sensor data (including the compass) gives the absolute best precision.
For the Real World: If you want to build a device for everyday use (like a shoe insert or a clip-on gadget), you can skip the compass and use the "Real-Time" data. It's simpler, more robust against magnetic interference, and just accurate enough to be useful.

In short, the researchers proved that we don't need a room full of cameras to know if you are about to trip. A small sensor on your foot, paired with a smart algorithm, can tell us the same story, whether you are strolling or sprinting.

Technical Summary: Foot Clearance Estimation Under Varying Gait Speeds

Problem Statement
Foot clearance, defined as the vertical trajectory of the foot during the swing phase, is a critical biomechanical marker for assessing trip risk and gait stability. While optical motion capture (MoCap) systems serve as the reference standard for measuring this variable, their high cost, laboratory-bound nature, and inability to support continuous monitoring or real-time biofeedback limit their utility in daily environments. Inertial Measurement Units (IMUs) offer a portable, low-cost alternative; however, estimating continuous foot-clearance trajectories from IMU signals remains technically challenging. Traditional signal-processing approaches relying on double integration and coordinate transformations are prone to error propagation, particularly when walking speeds vary, as speed changes alter swing duration, foot trajectory, and the temporal relationship between gait events and peak motion. Furthermore, a methodological gap exists regarding how gait time series should be represented for modeling: whether to use time-normalized data (common in biomechanics but which removes absolute temporal information) or real-time, non-normalized data (which preserves native structure but introduces variable-length sequences). Additionally, the impact of sensor-feature configurations, specifically the inclusion or exclusion of magnetometer data, on estimation accuracy across different speeds remains unclear.

Methodology
The study developed and evaluated a machine learning framework to estimate continuous foot-clearance trajectories using foot-mounted IMUs.

Participants: 68 healthy young adults (mean age 21.8 ± 3.6 years) walked on a treadmill at three speeds: slow (20% below preferred), preferred, and fast (20% above preferred).
Data Acquisition: Synchronized data were collected using an optoelectronic MoCap system (120 Hz, up-sampled to 250 Hz) as the ground truth and two foot-mounted IMUs (250 Hz). The IMUs provided tri-axial accelerometer, gyroscope, and magnetometer signals. Notably, the IMU data were preprocessed at the firmware level (calibration, bias compensation, orientation estimation via Madgwick algorithm) rather than being raw measurements.
Experimental Design: The study compared two temporal representations:
1. Time-Normalized (TN): Gait cycles were normalized to a fixed percentage (1300 points per participant).
2. Real-Time (RT): Raw data were extracted from the first heel strike to the end of the 13th cycle without normalization (variable length, ~2500–3500 points).
Feature Configurations: Two input sets were tested for the machine learning model:
1. Full Set: 18 features (all accelerometer, gyroscope, and magnetometer axes from both feet).
2. Reduced Set: 12 features (accelerometer and gyroscope only, excluding magnetometer data).
Modeling: A Bagged Tree Regression model was trained on 85% of the data (58 participants) and tested on 15% (10 participants). Hyperparameters were optimized via grid search with 5-fold cross-validation.
Analysis: Performance was assessed using Bland–Altman analysis, Root Mean Square Error (RMSE), Coefficient of Determination ( $R^2$ ), Intraclass Correlation Coefficient (ICC), and bias. A three-way repeated-measures ANOVA examined the effects of Speed, Temporal Representation, and Feature Set.

Key Results

Overall Performance: The model demonstrated strong agreement with the MoCap reference across all conditions. $R^2$ values ranged from approximately 0.75 to 0.83, and ICC values ranged from 0.75 to 0.88.
Feature Set Impact: The Full feature set (including magnetometer data) generally produced lower RMSE and higher reliability compared to the Reduced set. However, the Reduced set remained reliable, particularly under faster walking conditions.
Temporal Representation: Real-time and time-normalized approaches yielded broadly comparable performance. While statistical differences were found (RT showed slightly lower RMSE in some comparisons), neither approach was universally superior across all conditions.
Speed and Interactions: Walking speed significantly influenced estimation error. Crucially, significant interaction effects were observed between Speed, Temporal Representation, and Feature Set. This indicates that the impact of speed on error is not isolated but depends on the specific combination of temporal representation and sensor features used. For instance, under Real-Time conditions, differences between High and Low/Mid speeds were significant, whereas under Time-Normalized conditions, all pairwise speed comparisons were significant.

Significance and Claims
The paper claims to address a methodological gap in wearable gait analysis by clarifying how temporal representation and sensor-feature selection influence foot-clearance estimation under varying speeds.

Feasibility: The study supports the feasibility of using foot-mounted IMUs combined with machine learning to estimate continuous foot-clearance trajectories, not just discrete events like minimum toe clearance.
Methodological Guidance: The findings suggest that preserving native temporal information (Real-Time approach) is sufficient for accurate estimation and may be preferable for future online, wearable applications as it avoids the need for post-hoc gait-cycle normalization.
Practical Deployment: While the full feature set offers the best laboratory performance, the reduced magnetometer-free configuration is highlighted as a practical alternative for real-world deployment. This is because magnetometers are susceptible to magnetic disturbances in uncontrolled environments, whereas the reduced set (accelerometer/gyroscope only) remains reliable and simplifies implementation in embedded systems.
Robustness: The framework demonstrates robustness across slow, preferred, and fast walking speeds, though the authors note that the model's performance is condition-dependent rather than entirely speed-independent.

Limitations
The authors acknowledge that the study was conducted on healthy young adults in a controlled treadmill environment, limiting generalizability to older adults, clinical populations, overground walking, or uneven surfaces. Additionally, the reliance on preprocessed IMU data (firmware-level) rather than strictly raw signals means the findings apply to sensor-level measurements as provided by the manufacturer. Finally, the use of optical motion capture as a reference, while standard, is subject to its own limitations regarding marker placement and soft tissue artifacts.

The Experiment: The "Three-Speed" Test

The Two Big Questions

The Results: What Worked Best?

The Bottom Line

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