Bias-correction of Kalman filter estimators associated to a linear state space model with estimated parameters

• The bias propagation of Kalman filter predictors is analyzed.
• Analytical expressions for the bias of the Kalman filter predictors are presented.
• Invariant state space models are analyzed having into account the KF steady state.
• A bias-correction procedure is proposed in order to reduce the KF predictors’ bias.
• The performance of the bias-correction procedure is illustrated in two data sets.

This paper aims to discuss some practical problems on linear state space models with estimated parameters. While the existing research focuses on the prediction mean square error of the Kalman filter estimators, this work presents some results on bias propagation into both one-step ahead and update estimators, namely, non recursive analytical expressions for them. In particular, it is discussed the impact of the bias in the invariant state space models. The theoretical results presented in this work provide an adaptive correction procedure based on any parameters estimation method (for instance, maximum likelihood or distribution-free estimators). This procedure is applied to two data set: in the calibration of radar precipitation estimates and in the global mean land–ocean temperature index modeling.