Fast and robust localization of surgical array using Kalman filter.

Intraoperative tracking of surgical instruments is an inevitable task of computer-assisted surgery. An optical tracking system often fails to precisely reconstruct the dynamic location and pose of a surgical tool due to the acquisition noise and measurement variance. Embedding a Kalman filter (KF) or any of its extensions such as extended and unscented Kalman filters (EKF and UKF) with the optical tracker resolves this issue by reducing the estimation variance and regularizing the temporal behavior. However, the current KF implementations are computationally burdensome and hence takes long execution time which hinders real-time surgical tracking. This paper introduces a fast and computationally efficient implementation of linear KF to improve the measurement accuracy of an optical tracking system with high temporal resolution. Instead of the surgical tool as a whole, our KF framework tracks each individual fiducial mounted on it using a Newtonian model. In addition to simulated dataset, we validate our technique against real data obtained from a high frame-rate commercial optical tracking system. We also perform experiments wherein a diffusive material (such as a drop of blood) blocks one of the fiducials and show that KF can substantially reduce the tracking error. The proposed KF framework substantially stabilizes the tracking behavior in all of our experiments and reduces the mean-squared error (MSE) by a factor of 26.84, from the order of $$10^{-1}$$ to $$10^{-2}$$  mm $$^{2}$$ . In addition, it exhibits a similar performance to UKF, but with a much smaller computational complexity.