A new approach of the Kalman filter using future temperature measurements for nonlinear inverse heat conduction problems

An extended version of a smoothing technique applied to the Kalman filter estimates is developed in order to solve a nonlinear one-dimensional inverse heat conduction problem. This new algorithm introduces the use of future time measurements and so provides a best estimation of the surface conditions, involving heat flux density and temperature, in which time lag and sensitivity to measurement errors are reduced. An optimal number of future temperature measurements leads to a symmetrical response of the Kalman filter compared with the exact solutions. The effect of the number of future time data is also analyzed with respect to the modeling error, the location of the interior measurement needed for the inversion, and the inverse time step.