Tracking the motion of hidden segments using kinematic constraints and Kalman filtering.

This research paper discusses the application of kinematic constraints and an extended Kalman filter to accurately estimate the movement of hidden or connected skeletal segments. This method is particularly useful for the study of biomechanics, such as the movement of small segments in the human ankle complex or horse phalanges, that are generally obscured by joint capsules and ligaments.

Understanding Biomechanical Applications

In the field of biomechanics, researchers often use sensors or markers attached to the skin to study body movements. However, this doesn’t always yield accurate results due to the movement of skin and muscles relative to the underlying segment. This research aims to enhance the accuracy of these estimates by introducing kinematic constraints and a modified Kalman filter:

• Kinematic constraints limit the degrees of freedom between two articulating segments, reducing the estimation error due to movements of the skin and muscles relative to the skeletal segment.
• The Kalman filter is a mathematical algorithm that uses a series of measurements observed over time and produces estimates that are more precise than those based on a single measurement alone.

The Extended Kalman Filter

The paper further discusses how an extended Kalman filter can be used to track a system of connected segments. The system investigated in this research comprises of rigid segments connected by simplified joint models. They define the position and orientation of the mechanism with a set of generalized coordinates that represent the mechanism’s movements:

• The generalized coordinates and their first time derivatives (rates of change) can be used to create a state space model. This model governs the kinematics, or the motion, of the mechanism.
• Data is collected from the trajectories of skin-mounted markers. The state vector, which contains the generalized coordinates and their rates of change, is linked to the positions of these markers through a nonlinear function.
• The Jacobian, the matrix of derivatives of the function, is then determined and used in the Kalman filter.

Practical Applications and Conclusions

The proposed method was practically tested on a model of the horse’s distal limb. Monte Carlo simulations, a statistical method, were used to generate marker data:

• The study found that the proposed method significantly improved results compared to methods that do not use joint constraints.
• However, it’s crucial that the model used is a good approximation of the true mechanism.
• Applying the method to actual movement data from a horse’s limb showed consistency between trials and minor differences between measured and predicted marker positions, confirming the effectiveness of the method.