Zebo Zhou

Fast Complementary Filter for Attitude Estimation Using Low-Cost MARG Sensors

This paper proposes a novel quaternion-based attitude estimator with magnetic, angular rate, and gravity (MARG) sensor arrays. A new structure of a fixed-gain complementary filter is designed fusing related sensors. To avoid using iterative algorithms, the accelerometer-based attitude determination is transformed into a linear system. Stable solution to this system is obtained via control theory. With only one matrix multiplication, the solution can be computed. Using the increment of the solution, we design a complementary filter that fuses gyroscope and accelerometer together. The proposed filter is fast, since it is free of iteration. We name the proposed filter the fast complementary filter (FCF). To decrease significant effects of unknown magnetic distortion imposing on the magnetometer, a stepwise filtering architecture is designed. The magnetic output is fused with the estimated gravity from gyroscope and accelerometer using a second complementary filter when there is no significant magnetic distortion. Several experiments are carried out on real hardware to show the performance and some comparisons. Results show that the proposed FCF can reach the accuracy of Kalman filter. It successfully finds a balance between estimation accuracy and time consumption. Compared with iterative methods, the proposed FCF has much less convergence speed. Besides, it is shown that the magnetic distortion would not affect the estimated Euler angles.

Fast Linear Quaternion Attitude Estimator Using Vector Observations

As a key problem for multisensor attitude determination, Wahba’s problem has been studied for almost 50 years. Different from existing methods, this paper presents a novel linear approach to solve this problem. We name the proposed method the fast linear attitude estimator (FLAE) because it is faster than known representative algorithms. The original Wahba’s problem is extracted to several 1-D equations based on quaternions. They are then investigated with pseudoinverse matrices establishing a linear solution to

Optimal, Recursive and Sub-Optimal Linear Solutions to Attitude Determination from Vector Observations for GNSS/Accelerometer/Magnetometer Orientation Measurement

n

Analytic accelerometer–magnetometer attitude determination without reference information

-D equations, which are equivalent to the conventional Wahba’s problem. To obtain the attitude quaternion in a robust manner, an eigenvalue-based solution is proposed. Symbolic solutions to the corresponding characteristic polynomial are derived, showing higher computation speed. Simulations are designed and conducted using test cases evaluated by several classical methods, e.g., Shuster’s quaternion estimator, Markley’s singular value decomposition method, Mortari’s second estimator of the optimal quaternion, and some recent representative methods, e.g., Yang’s analytical method and Riemannian manifold method. The results show that FLAE generates attitude estimates as accurate as that of several existing methods, but consumes much less computation time (about 50% of the known fastest algorithm). Also, to verify the feasibility in embedded application, an experiment on the accelerometer–magnetometer combination is carried out where the algorithms are compared via C++ programming language. An extreme case is finally studied, revealing a minor improvement that adds robustness to FLAE, inspired by Cheng et al.Note to Practitioners—Attitude determination using vector observations can be applied in many areas. The most frequently involved are the accelerometer–magnetometer combination and star tracker array. Based on the proposed efficient fast linear attitude estimator algorithm, the time consumption of the sensor fusion can be significantly reduced, saving the execution time for fault detection, fail safe, and so on.

Critical issues on Kalman filter with colored and correlated system noises

The integration of the Accelerometer and Magnetometer (AM) provides continuous, stable and accurate attitude information for land-vehicle navigation without magnetic distortion and external acceleration. However, magnetic disturbance and linear acceleration strongly degrade the overall system performance. As an important complement, the Global Navigation Satellite System (GNSS) produces the heading estimates, thus it can potentially benefit the AM system. Such a GNSS/AM system for attitude estimation is mathematically converted to a multi-observation vector pairs matching problem in this paper. The optimal and sub-optimal attitude determination and their time-varying recursive variants are all comprehensively investigated and discussed. The developed methods are named as the Optimal Linear Estimator of Quaternion (OLEQ), Suboptimal-OLEQ (SOLEQ) and Recursive-OLEQ (ROLEQ) for different application scenarios. The theory is established based on our previous contributions, and the multi-vector matrix multiplications are decomposed with the eigenvalue factorization. Some analytical results are proven and given, which provides the reader with a brand new viewpoint of the attitude determination and its evolution. With the derivations of the two-vector case, the n-vector case is then naturally formed. Simulations are carried out showing the advantages of the accuracy, robustness and time consumption of the proposed OLEQs, compared with representative methods. The algorithms are then implemented using the C++ programming language on the designed hardware with a GNSS module, three-axis accelerometer and three-axis magnetometer, giving an effective validation of them in real-world applications. The designed schemes have proven their fast speed and good accuracy in these verification scenarios.

Fast Symbolic 3D Registration Solution.

Attitude determination using the accelerometer–magnetometer combination is basically an applied mathematical problem. Commonly, such attitude determination tasks should be accomplished with reference information of sensors, e.g. the magnetometer’s reference vector, from calibration processes. However, this piece of important information cannot be accurately acquired or would differ with the change of body’s position. In this paper, to solve such problem, the conventional accelerometer–magnetometer combination fusion equations are transformed into a brand new set of equations, which are free of reference information. Quaternion solutions to the novel equations are obtained via analytic computation techniques. According to the unique design, the proposed attitude estimator owns very fast computation speed compared with representative methods including iterative ones and algebraic ones. Experiments and simulations are carried out to give demonstrations and comparisons, which verify the correctness and effectiveness of the proposed method. The results also show that using the proposed quaternion solution, fusion with gyroscope can be more efficiently obtained.