Communications in Information and Systems

Volume 5 (2005)

Number 2

Two-stage Kalman filtering via structured square-root

Pages: 143 – 168



Stoyan Kanev (Delft Center for Systems and Control, Delft, The Netherlands)

Michel Verhaegen (Delft Center for Systems and Control, Delft, The Netherlands)


This paper considers the problem of estimating an unknown input (bias) by means of the augmented-state Kalman (AKF) filter. To reduce the computational complexity of the AKF, recently developed an optimal two-stage Kalman filter (TS-AKF) that separates the bias estimation from the state estimation, and shows that his new two-stage estimator is equivalent to the standard AKF, but requires less computations per iteration. This paper focuses on the derivation of the optimal two-stage estimator for the square-root covariance implementation of the Kalman filter (TS-SRCKF), which is known to be numerically more robust than the standard covariance implementation. The new TS-SRCKF also estimates the state and the bias separately while at the same time it remains equivalent to the standard augmented-state SRCKF. It is experimentally shown in the paper that the new TS-SRCKF may require less flops per iteration for some problems than the Hsieh’s TS-AKF. Furthermore a second, even faster (single-stage) algorithm has been derived in the paper by exploiting the structure of the least-squares problem and the square-root covariance formulation of the AKF. The computational complexities of the two proposed methods have been analyzed and compared the those of other existing implementations of the AKF.


two-stage augmented Kalman filter, square-root covariance implementation

Published 1 January 2005