  The augmented, iterated Kalman smoother is applied to system identification
for inverse problems in evolutionary differential equations. In the augmented
smoother, the unknown, time-dependent coefficients are included in the state
vector, and have a stochastic component. At each step in the iteration, the
estimate of the time evolution of the coefficients is linear. We update the
slowly varying mean temperature and conductivity by averaging the estimates of
the Kalman smoother. Applications include the estimation of anomalous diffusion
coefficients in turbulent fluids and the plasma rotation velocity in plasma
tomography.
