This paper 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 (EKF), rigorous simulations are performed using the raw data of a set of urban vehicular AHRS tests.

SUMMARY: This paper reports an extended state observer (ESO)-based robust dynamic surface control (DSC) method for triaxial MEMS gyroscope applications. An ESO with non-linear gain function is designed to estimate both velocity and disturbance vectors of the gyroscope dynamics via measured position signals. Using the sector-bounded property of the non-linear gain function, the design of an $\mathcal{L}_2$ -robust ESO is phrased as a convex optimization problem in terms of linear matrix inequalities (LMIs). Next, by using the estimated velocity and disturbance, a certainty equivalence tracking controller is designed based on DSC. To achieve an improved robustness and to remove static steady-state tracking errors, new non-linear integral error surfaces are incorporated into the DSC. Based on the energy-to-peak ( $\mathcal{L}_2$ - $\mathcal{L}_\infty$ ) performance criterion, a finite number of LMIs are derived to obtain the DSC gains. In order to prevent amplification of the measurement noise in the DSC error dynamics, a multi-objective convex optimization problem, which guarantees a prescribed $\mathcal{L}_2$ - $\mathcal{L}_\infty$ performance bound, is considered. Finally, the efficacy of the proposed control method is illustrated by detailed software simulations.