Teaching Hidden Markov Models Through Multidimensional Trajectory Learning: A Hands-On MATLAB Journey

Abstract

Hidden Markov Models (HMMs) are a tool widely used in robotics, language processing, speech recognition and signal processing, yet their instruction in engineering courses remains challenging due to the gap between mathematical formalism and
realistic applications. Existing resources either rely on abstract derivations or black-box software libraries that obscure the modeling pipeline, leaving students without the conceptual tools to adapt HMMs to novel problems. This paper presents an publicly
available MATLAB LiveScript tutorial that guides students through the complete HMM pipeline for trajectory learning: from synthetic data generation and noise augmentation, through geometric simplification and symbolic encoding, to model training
and Viterbi-based reconstruction. Each stage exposes one conceptual layer transparently, producing an inspectable intermediate result. The design is grounded in established engineering education principles, including guided instruction, reduction of unnecessary cognitive load, and active learning through parameter exploration. The tutorial is publicly available and immediately deployable in undergraduate and graduate courses in artificial intelligence, robotics, and data processing.