  We consider the problem of state estimation in dynamical systems and propose
a different mechanism for handling unmodeled system uncertainties. Instead of
injecting random process noise, we assign different weights to measurements so
that more recent measurements are assigned more weight. A specific choice of
exponentially decaying weight function results in an algorithm with essentially
the same recursive structure as the Kalman filter. It differs, however, in the
manner in which old and new data are combined. While in the classical KF, the
uncertainty associated with the previous estimate is inflated by adding the
process noise covariance, in the present case, the uncertainty inflation is
done by multiplying the previous covariance matrix by an exponential factor.
This difference allows us to solve a larger variety of problems using
essentially the same algorithm. We thus propose a unified and optimal, in the
least-squares sense, method for filtering, prediction, smoothing and general
out-of-sequence updates. All of these tasks require different Kalman-like
algorithms when addressed in the classical manner.
