In this tutorial, a new class of attitude estimation solutions is presented to determine the orientation of a robotic platform resorting only to a set of triaxial gyroscopes and an additional measurement of a constant inertial vector. This approach poses a significant advantage in terms of setup design and reduced mission costs since only one inertial measurement is required, in contrast with existing solutions that require at least two of these. Pertinent examples of viable applications include navigation of submarines or large ships, assisting autonomous robots in precise maneuvers, inertial platform stabilization, etc. The novelty of the solutions proposed herein exploit the well-known inertial information about the Earth's angular velocity by using high-grade gyroscopes that are sensitive to the planet's spin. Experimental results are presented to demonstrate the good performance achieved by the algorithms.