Tracking points within noisy images

The paper derives an optimal fixed interval smoother for the linear time invariant output estimation problem. The smoother employs forward and adjoint Kalman predictors. The suboptimal time-varying case is discussed which includes the use of forward and adjoint extended Kalman predictors within a nonlinear smoother. The efficacy of the smoother to tracking points within sequences of noisy images is investigated. The results of a simulation study are presented in which it is demonstrated that a Kalman filter can outperform a so-called matched filter, and a fixed interval smoother can provide a further performance improvement when the images are sufficiently noisy.