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This article presents a new immersion and invariance (I&I) observer for inertial microelectromechanical systems (MEMS) sensors-based, low-cost attitude-heading reference systems (AHRSs). Using the I&I methodology, the observer design problem is formulated as finding a dynamics system, called the observer, and a differentiable manifold in the extended state space of the Euler angles-observer dynamics. The manifold is required to be practically stable with respect to the system trajectories. By imposing this requirement, an observer is derived to robustly estimate the Euler angles. To show the efficacy of the I&I observer and to compare its performance with the extended Kalman filter, rigorous simulations are performed using the raw data of a set of urban vehicular AHRS tests. [ABSTRACT FROM AUTHOR]