Real-time Kalman filter applied to biomechanical data for state estimation and numerical differentiation

Area of Science:

• Biomechanics
• Signal Processing
• Control Systems

Background:

• Accurate estimation of displacement and velocity from noisy biomechanical data is crucial for human movement analysis.
• Standard Kalman filters can be sensitive to noise and modeling errors in real-time applications.

Purpose of the Study:

• To evaluate a modified two-state Kalman filter incorporating a numerical tachometer and median smoother for enhanced biomechanical data processing.
• To compare the performance of the modified filter against a standard Kalman filter in estimating displacement and velocity.

Main Methods:

• Implementation of a numerical tachometer integrating finite difference derivative estimates into the Kalman filter.
• Augmentation of the numerical tachometer with a median smoother to mitigate erroneous measurements before differentiation.
• Simulation environment used to test filter performance under typical human movement science sampling frequencies and noise levels.

Main Results:

• The modified Kalman filter demonstrated a 10% reduction in root mean square error for displacement and a 54% reduction for velocity.
• The enhanced filter showed reduced sensitivity to signal and noise modeling errors compared to the standard implementation.
• The median smoother improved robustness against additive white Gaussian noise and canceled isolated noise spikes.

Conclusions:

• The proposed numerical tachometer and median smoother modification significantly improves Kalman filter performance for biomechanical data.
• This enhanced filtering approach offers more accurate and robust real-time estimation of displacement and velocity in human movement studies.
• The method provides a valuable tool for researchers dealing with noisy sensor data in biomechanics.