This paper presents a general derivation of the discrete Kalman filter (DKF) in context of education, with the objective to integrate teaching and research by promoting control and signal processing as a field that embraces science, technology, engineering and mathematics (STEM). In more detail, this contribution showcases a possible lecture structure of the discrete Kalman filter together with an innovative laboratory experiment, suitable for an audience that does not require a strong mathematical background. The importance of finding appropriate didactic methods in the context of KF is due to the intrinsic difficulty which characterises this algorithm to be understood by the students. In general the Kalman filter is one of the most used algorithms in all fields of control systems, thanks to its effectiveness and efficiency. In this contribution the filter is used as a state observer to estimate the velocity of a stimulus-responsive polymerfibre actuator in the proposed laboratory experiment. Besides the theoretical aspects of the discrete Kalman filter algorithm, a step-by-step development for its implementation is presented. The proposed structure is general and can be used as a basic frame for research in the context of control and signal processing. In this sense, this contribution proposes a better understanding of the role of integrating teaching and research in education.