Exact Kalman Filtering of Respiratory Motion

In this paper we propose a novel Exact Kalman Filter for state estimation of quasi-periodic signals such as respiratory motion. Nonlinear functions of interest are approximations as truncated Fourier series. Instead of relying on approximations provided by Extended Kalman Filter or Unscented Kalman Filter, our filter performs exact calculation of the mean and covariances of interest. We then compare, through simulations, the performance of our filter to the two. Our results show that the theoretically derived mean and covariance calculations result in either comparable or better estimation performance depending on the circumstances.