| Abstract: | Kalman filter (KF) and its variants are widely used for real-time state updating and prediction in environmental science and engineering. Whereas in many applications the most important performance criterion may be the fraction of the times when the filter performs satisfactorily under different conditions, in many other applications estimation and prediction specifically of extremes, such as floods, droughts, algal blooms, etc., may be of primary importance. Because KF is essentially a least squares solution, it is subject to conditional biases (CB) which arise from the error-in-variable, or attenuation, effects when the model dynamics are highly uncertain, the observations have large errors and/or the system being modeled is not very predictable. In this work, we describe conditional bias-penalized KF, or CBPKF, based on CB-penalized linear estimation which minimizes a weighted sum of error variance and expectation of Type-II CB squared and comparatively evaluate with KF through a set of synthetic experiments for one-dimensional state estimation under the idealized conditions of normality and linearity. The results show that CBPKF reduces root mean square error (RMSE) over KF by 10–20% or more over the tails of the distribution of the true state. In the unconditional sense CBPKF performs comparably to KF for nonstationary cases in that CBPKF increases RMSE over all ranges of the true state only up to 3%. With the ability to reduce CB explicitly, CBPKF provides a significant new addition to the existing suite of filtering techniques for improved analysis and prediction of extreme states of uncertain environmental systems. |
