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Due to the need for accurate navigation in minimally invasive surgery, many methods have been introduced to the operating room for tracking the position and orientation of instruments. This paper considers the subproblem of using integrated inertial and magnetic sensing to track the attitude (orientation) of surgical instruments. In this scenario, it is usually assumed that the sensor is quasi-static and the surrounding magnetic field is steady. For practical hand-held surgical instruments, perturbations exist due to intended and unintended (e.g., tremor) motion and due to distortion of the surrounding magnetic field. We consider the problem of estimating the gravity and magnetic field in the inertial sensor frame with small perturbations. The dynamics of the gravity and magnetic field is studied under perturbations, their relationships to gyroscope measurements are analyzed, and Kalman filters (KFs) are formulated to reduce these perturbations. The estimated gravity and magnetic values (outputs of the KFs) are subsequently used in an extended KF for attitude estimation. In this filter, the prediction model is given by the system dynamics, formulated using quaternions, and the observation model is given by vector analysis of the estimated gravity and magnetic field. Experiments are performed to validate the algorithms under clinically realistic motions. The complete system demonstrates an improvement in the accuracy of the attitude estimate in the presence of small perturbations, and satisfies the specified accuracy requirement of 1°.
Date of Publication: April 2012