A Numerical Feed-Forward Scheme for the Augmented Kalman Filter

In this paper we present a numerical feed-forward strategy for the Augmented Kalman Filter and show its application to a diffusion-dominated inverse problem: heat source reconstruction from boundary measurements. The method is applicable in general to forcing term estimation in lumped and distributed parameters models and gives a significant contribution where, in industry and science, probing signals are used through a diffusive material-body to estimate its localized internal properties in a non-destructive test, like in ultrasound or thermographic inspection.