Motion & Gesture Analysis from a Magnetic and Inertial Measurement Unit

This work details the processing chain that transforms biased data from a low-cost Magnetic and Inertial Measurement Unit (magnetometer, accelerometer, gyroscope) into real-time motion estimation, and how that data can be used for full gesture analysis.

Calibrating the sensors is a prerequisite for accurate orientation and displacement estimation, which we developed as our own sensor-fusion algorithm. This general-purpose motion-tracking system was then applied specifically to golf, for swing detection and gesture analysis, to extract meaningful data for players.

Keywords: MEMS, MIMU, sensor calibration, sensor fusion, dead reckoning, data analysis.

Acceleration at rest is expected to read 1g (gravity) along the vertical axis. Rotating the accelerometer to test every axis (X, Y, Z) reveals up to 5% error versus that ideal — corrected through calibration. After a few iterations of the algorithm, error drops under 1%; in real time, this takes under 10 seconds.

Good gyroscope calibration is essential to properly estimate device rotation. Raw data from low-cost IMUs is typically noisy and biased, which makes orientation estimation unreliable without correction.

In this test, starting from a known initial state, we rotate the device through several known intermediate states. Before calibration, integrating angular velocity does not yield a realistic rotation. After calibration, the same integration produces a far more accurate estimate of orientation.

Comparing raw and calibrated data shows fast convergence in real-time processing — under 200ms on a Cortex-M4 processor.

Real-time magnetometer calibration: raw data traces a tilted, shifted ellipsoid, detectable while the device is in motion. Once the model is correctly fit, calibration parameters update and subsequent points map onto a sphere. Magnetic disturbances are still detected and handled appropriately downstream in the sensor-fusion stage.

This model provides a strong reference for accurate magnetic measurement. Every magnetic disturbance (e.g. a magnet near the board) is detected and discarded (shown in red). Embedded and processed in real time, the model converges in under 30 seconds.

Features of the calibration algorithm:

• Removes hard-iron effects
• Removes soft-iron effects
• Removes most ambient noise
• Detects and discards point magnetic disturbances

Fusing the three sensors (accelerometer, gyroscope, magnetometer) is the basis for a reliable, real-time estimate of device orientation. Each sensor has its own strengths and weaknesses, and together they compensate for one another:

• Accelerometer: gives the direction of the gravity vector, but only when motion is low.
• Gyroscope: estimates rotation angle over a short period, but bias accumulates rapidly.
• Magnetometer: provides a reliable Earth-frame reference, but is sensitive to magnetic disturbance and doesn't always support a high update rate.