In this paper, we propose a novel method for pedestrian dead reckoning (PDR) using microelectromechanical system magnetic, angular rate, and gravity sensors, which includes a double-step unscented Kalman filter (DUKF) and hidden Markov model (HMM)-based zero-velocity-update (ZVU) algorithm. The DUKF divides the measurement updates of the gravity vector and the magnetic field vector into two steps in order to avoid the unwanted correction for the Euler angle error. The HMM-based ZVU algorithm is developed to recognize the ZVU efficiently. Thus, the proposed PDR method can reduce the position drift caused by the heading error and fault zero-velocity measurement. Experimental results demonstrate that the proposed method achieves better yaw estimate, as well as zero-velocity measurement, and obtains more accurate dead-reckoning position than other methods in the literature.

This paper addresses the intractable problem of attaining precise attitude estimation efficiently using MEMS MARG (magnetic, angular rate, and gravity) sensors for 3-D motion tracking, which is called attitude and heading reference system (AHRS). The performance of AHRS is adversely affected by sensor noise and measurement disturbances. To overcome this problem, we propose a novel adaptive extended Kalman filter (AEKF) in this paper, including a multiplicative extended Kalman filter (MEKF) and a hidden Markov Model (HMM) recognizer. MEKF is built on sensor noise model. An HMM recognizer is developed to identify the measurement disturbance caused by motion or environmental interference and then to adjust the noise covariance of MEKF adaptively. The proposed AEKF was assessed with a high-precision test platform by using a high-caliber commercial AHRS. Experimental results indicate that the proposed method achieves a higher level of stability and accuracy in comparison to other attitude estimators, especially in dynamic tests, which demonstrates the availability of 3-D motion tracking.

This article approaches the problem of attitude estimation using biased gyro and body-referenced measurements of inertial vectors. First, a new observer for attitude estimation is proposed through introducing a family of synergistic potential functions with explicit expression of synergistic gap. Furthermore, it is convenient to adjust the design by adding additional state-dependent gains without adapting the switching rules. The proposed observer exhibits faster convergence for large attitude estimation errors than similar work in literature. Second, to achieve better steady-state performance, we unite this global observer with a traditional local observer, i.e., multiplicative extended Kalman filter (MEKF). The new uniting observer inherits the desired transient and steady-state performance from the two sub-observers, respectively. The performance of the proposed methods has been evaluated via simulation and experiments.

Existing research has reported that the topological obstructions pose inherent difficulty to attitude estimation. This article copes with the problem of obtaining a good estimation of attitude and gyro-bias using inertial measurements. First, we propose a quaternion-based scheme for the design and stability analysis of nonlinear attitude observers. Under the scheme, we expose the potential pitfalls of traditional observers: almost global asymptotic stability (GAS) and slow convergence for a continuous state-feedback observer, nonrobustness to arbitrary small measurement noises for a discontinuous state-feedback observer. Second, to address these limitations, we develop a generic quaternion-based hybrid scheme with guaranteed GAS and robustness to measurement noises, in the sense that knowledge of a specific potential function suffices to design an attitude and gyro-bias observer with desired properties. Furthermore, we give a new observer within the scheme. Simulation and experimental results demonstrate the fast convergence and robustness of the proposed observer.

This article addresses the problem of estimating the attitude and gyro bias using biased gyro and inertial vector measurements. Two nonlinear observers are presented. One of the two is the passive observer evolving on the semisphere of quaternion, which decouples the gyro measurements from the reconstructed attitude. The other is the explicit observer evolving on the $SO(3)$ , which uses directly body-frame measurements of known inertial vectors. The proposed observers achieve faster convergence for large attitude estimation errors than similar observers in literature, guarantee asymptotical stability for almost arbitrary initial conditions, achieve similar steady-state performance with lower computational cost than multiplicative extended Kalman filter, which is the workhorse of attitude estimation, and are suitable for implementation using a low-cost inertial measurement unit. Simulation and experimental results prove the fast convergence and steady-state performance of the proposed observers.

This paper investigates the problem of global coordinated stabilization for a multi-agent system, which consists of a general class of mechanical systems that evolve on compact connected Lie groups. First, a distributed synergistic hybrid controller is synthesized by leveraging a coadjoint incidence matrix to assign to neighboring agents a hybrid feedback that is based on their relative position. It leads to robust and global asymptotic stability in tree networks. Second, the existence of synergistic potential functions (SPFs)—the key ingredient for deriving the hybrid feedback—is established on compact Lie groups. Moreover, a direct extension shows that there exists an SPF on the non-compact special Euclidean group $\rm{SE}(n)$ . In contrast with some existing results, the proposed controller removes the invariance condition on the hybrid feedback, and the existence of the SPF ensures that our controller is applicable to many Lie groups of practical interests. Finally, a worked example of multiple planar rigid-body systems on $\rm{SE} (2)$ is used to illustrate our approach.