Advanced signal processing using automated uncertainty propagation—An educational approach

Abstract

Automated uncertainty propagation (AUP) is a powerful tool that enables a shift in focus from computation to the interpretation and analysis of the uncertainty. A teaching concept based on a software toolbox for automated uncertainty propagation has been previously developed. This work extends that concept towards the use of uncertainty in statistical signal processing, where two advanced techniques, Bayesian Estimation and Compressive Sensing are presented in the context of uncertainty propagation. The Bayesian Linear Minimum Mean Square Estimation (BLMMSE) is introduced with AUP. It is demonstrated that concepts like the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF) are easily implemented following the same approach as for the already introduced uncertainty quantification, since the toolbox supports linearization, Unscented Transform and Monte Carlo methods and the code for these variants is compact and equivalent. Additionally, the uncertainty analysis of signals and parameters reconstructed from compressed measurements can be easily assessed, as well as the impact of uncertainty in the expected performance of the recovery technique. This approach facilitates the integration of complex topics—such as late fusion, posterior state estimation or sparse recovery—into measurement science education. Its applicability is demonstrated through three examples, highlighting the benefits of the Unscented Transform method for AUP in sensor and data fusion.