  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 with the
optical tracker resolves this issue by reducing the estimation variance and
regularizing the temporal behavior. However, the current rigid-body 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. The proposed KF framework
substantially stabilizes the tracking behavior in all of our experiments and
reduces the mean-squared error (MSE) from the order of $10^{-2}$ $mm^{2}$ to
$10^{-4}$ $mm^{2}$.
