Using extended Kalman filter for data assimilation and uncertainty quantification in shock-wave dynamics

Model assimilation of data strives to determine optimally the state of an evolving physical system from a limited number of observations. The present study represents the first attempt of applying the extended Kalman filter (EKF) method of data assimilation to shock-wave dynamics induced by a high-speed impact. EKF solves the full nonlinear state evolution and estimates its associated error-covariance matrix in time. The state variables obtained by the blending of past model evolution with currently available data, along with their associated minimized errors (or uncertainties), are then used as initial conditions for further prediction until the next time at which data becomes available. In this study, a one-dimensional (1-D) finite-difference code is used along with data measured from a 1-D flyer plate experiment. The results demonstrate that the EKF assimilation of a limited amount of pressure data, measured at the middle of the target plate alone, helps track the evolution of all the state variables with reduced errors