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

Weighted Information Filtering, Smoothing, and Out-of-Sequence Measurement Processing