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This paper proposes a novel fast deterministic quaternion attitude determination method for accelerometer and magnetometer combination (AMC). After taking insight to the attitude determination theory, an important relationship between the sensor outputs and the magnetometer's reference vector is successfully derived. Based on the relationship, the optimal quaternion associated with the attitude of a certain object is easily calculated. The main breakthrough of this paper is that it significantly simplifies the determination of the magnetometer's reference vector which always needs systematic calibration or iterative estimation in existing methods. We name the proposed method the Fast Accelerometer-Magnetometer Fusion (FAMF). Our proposed method has the advantages of better computation accuracy and less time consumption. Several experiments are carried out to illustrate the attitude determination results. Besides, comparisons with existing representative methods are also presented in the experimental section of this paper, which verify the effectiveness of the proposed FAMF. Finally, we experimentally show that the FAMF's roll and pitch angles are immune to magnetic distortion, which ensures the robustness under complex environments for micro air vehicles (MAV). In diesem Beitrag wird eine neuartige, auf Quaternionen basierende Methode präsentiert, um die Orientierung einer Plattform im Raum aus Beschleunigungs- und Magnetfeldsensordaten (AMC) zu bestimmen. Nach einer Einführung in die Theorie der Lageschätzung wird eine wichtige Beziehung zwischen den Sensorausgangssignalen und dem Magnetometer-Referenzvektor abgeleitet. Darauf basierend wird die optimale Quaternion der Orientierung hergeleitet. Der Hauptaspekt dieses Betrags, die Entwicklung der Fast Accelerometer-Magnetometer Fusion (FAMF), besteht in der signifikanten Vereinfachung bei der Bestimmung des Magnetometer-Referenzvektors, welcher bei alternativen Schätzmethoden entweder iterativ bestimmt oder durch Ka

3-D registration has always been performed invoking singular value decomposition (SVD) or eigenvalue decomposition (EIG) in real engineering practices. However, these numerical algorithms suffer from uncertainty of convergence in many cases. A novel fast symbolic solution is proposed in this article by following our recent publication in this journal. The equivalence analysis shows that our previous solver can be converted to deal with the 3-D registration problem. Rather, the computation procedure is studied for further simplification of computing without complex-number support. Experimental results show that the proposed solver does not loose accuracy and robustness but improves the execution speed to a large extent by almost 50%-80%, on both a personal computer (PC) and an embedded processor. IEEE

In micro air vehicles (MAVs), a magnetometer is usually employed for heading estimation. However, in real flight campaigns the magnetometer can easily suffer interference from external magnetic disturbances. In this paper, a simple novel method is proposed to conduct real-time calibration of the magnetometer subject to external disturbances with the aid of gravity and global navigation satellite system measurements. First, two equalities are derived from the rigid-body rotation equations. Then, the closed-form solution to the pseudo magnetometer biases is derived according to these equalities. To enhance the robustness of the solver, an optimizer based on a gradient-descent algorithm is proposed. The bifurcation analysis and convexity proofs are given to show that the proposed optimization has a unique solution and no local optimum. The execution time analysis of the proposed method also indicates that it is a very fast algorithm. Finally, the calibration parameters are determined by algebraic equations formed by pseudo biases. The proposed method is attitude-free, simple and easy-to-implement. The experiments on a real-world fixed-wing MAV demonstrate that the method is effective.

In the past several years, there have been several representative attitude determination methods developed using derivative-based optimization algorithms. Optimization techniques e.g. gradient-descent algorithm (GDA), Gauss-Newton algorithm (GNA), Levenberg-Marquadt algorithm (LMA) suffer from local optimum in real engineering practices. A brief discussion on the convexity of this problem is presented recently [1] stating that the problem is neither convex nor concave. In this paper, we give analytic proofs on this problem. The results reveal that the target loss function is convex in the common practice of quaternion normalization, which leads to non-existence of local optimum. © 2019 IEEE.

Attitude estimation from vector observations is widely employed in aerospace applications for accurate integrated navigation using solutions to Wahba's problem. Wahba's solutions are practical but may corrupt facing critical cases in the presence of almost collinear reference vector measurements, which is inevitable in robotic applications with redundant sensor arrays or platforms with celestial vision sensors in similar directions. Different from existing algorithms, this study presents a novel sequential multiplicative quaternion attitude estimation method from various vector sensor outputs. The unique linear constitution of the algorithm leads to its specific name of Recursive Linear Quaternion Estimator (RLQE). The algorithm's architecture is designed to use each single pair of vector observation linearly so that the vector observations can be arbitrarily chosen and fused. The closed-form covariance of the RLQE is derived that builds up the existence of a highly reliable RLQE Kalman filter. Simulations and experiments are carried out to give the performances of the authors' algorithm and representative ones. Compared with other works, the proposed RLQE maintains good precision, better consistency and lower variance bounds. Moreover, the attitude estimation performance with critical cases is especially much better than conventional Wahba's solution on its continuity, accuracy and variance.