Simultaneous estimation of time-varying temperature field and boundary heat flux in participating medium by the improved Kalman filter algorithm

By using future measured signals, the improved Kalman filter (IKF) algorithm is proposed to retrieve time -varying internal temperature field (Tfield(t)) and boundary heat flux (q(t)) of 1D participating medium in near real time. The unknown heat flux irradiates the left boundary of the medium. In order to realize non-intrusive measurement, only the temperature on the right boundary of the medium is served as measurement informa-tion. A residual method is used to estimate the optimal number of future time steps without knowing the exact boundary heat flux. When the thermophysical parameters of medium are uniform, the estimated results of IKF are more accurate and the IKF uses less future temperature information, compared to those of the Kalman smoothing (KS) algorithm. Compared with the unscented Kalman smoothing (UKS) in solving the strong nonlinear inverse problem with temperature-dependent thermophysical parameters, the IKF uses less future temperature information and the estimated results by IKF are more accurate. The IKF is also employed to solve the strong nonlinear inverse problem in participating medium with graded refractive index. All the recon-struction results indicate that the IKF algorithm is suitable and accurate for the near on-line prediction of the Tfield(t) and q(t) in strong nonlinear systems.