Alternative equations for combining the results of Kalman filters
New equations are provided to combine the results of the Kalman filter applied in the usual way and the Kalman filter applied in the reverse direction in time. The new equations require fewer matrix inversions and are applicable under very mild conditions on the state space representation of the time series model. These equations form the basis of computationally efficient methods for investigating the possibility of anomalies such as outliers in a time series.
state space representation time series reverse kalman filter