Sequential parameter estimation for stochastic systems

The quality of the prediction of the dynamical system evolutionis determined by the accuracy to which initial conditions andforcing are known. Availability of future observations permitsreducing the effects of errors in assessment the external modelparameters by means of a filtering algorithm. However, traditionalfiltering schemes do not take into account uncertainties in specifyingthe internal model parameters and thus cannot reduce their contributionto the forecast errors. An extension of the Sequential ImportanceResampling filter (SIR) is proposed to this aim. The filter is verifiedagainst the Ensemble Kalman filer (EnKF) in application to the stochasticLorenz system. It is shown that the SIR is capable to estimatethe system parameters and to predicts the evolution of the system witha remarkably better accuracy than the EnKF. This highlights a severedrawback of any Kalman filtering scheme: due to utilizing only first twostatistical moments in the analysis step it is unable to deal withprobability density functions badly approximated by the normaldistribution.