Design of a Parallel Kalman Filter with Variable Forgetting Factors

One of the historical limitations to wide-spread use of discrete sequential estimation techniques has been an unavoidable trade-off between filter speed of response and filter accuracy. Filters which respond to process changes within a few iterations also demonstrate a high level of sensitivity to process noise and measurement noise. Conversely, accurate filters generally require a great deal of data before accuracy can be assured and these filters tend to be unacceptably slow to respond to true state and parameter changes. In this study, the areas where the existing methods exhibit poor performance were identified, and a modified approach to Kalman filtering was developed to overcome eath of these deficiencies. The result is the parallel Kalman filter, which uses two Kalman filters with the Ydstie variable forgetting factor specified with two different memory lengths. The parallel filter is dynamically modified so that under any set of process conditions, at least one filter is specified property. Based on real-time logic and a modified Hagglund fault detection method, the covariance from the short memory length component filter is substituted into the long memory length component filter when a validated fault is detected. The state or parameter estimates from the long memory length filter, subject to the influence of the short memory length filter, are the estimates provided by the parallel filter algorithm.