Hassen Fourati

Complementary Observer for Body Segments Motion Capturing by Inertial and Magnetic Sensors

This paper presents a viable quaternion-based complementary observer (CO) that is designed for rigid body attitude estimation. We claim that this approach is an alternative one to overcome the limitations of the extended Kalman filter. The CO processes data from a small inertial/magnetic sensor module containing triaxial angular rate sensors, accelerometers, and magnetometers, without resorting to GPS data. The proposed algorithm incorporates a motion kinematic model and adopts a two-layer filter architecture. In the latter, the Levenberg Marquardt algorithm preprocesses acceleration and local magnetic field measurements, to produce what will be called the systems output. The systems output together with the angular rate measurements will become measurement signals for the CO. In this way, the overall CO design is greatly simplified. The efficiency of the CO is experimentally investigated through an industrial robot and a commercial IMU during human segment motion exercises. These results are promising for human motion applications, in particular future ambulatory monitoring.

A Nonlinear Filtering Approach for the Attitude and Dynamic Body Acceleration Estimation Based on Inertial and Magnetic Sensors: Bio-Logging Application

This paper addresses the problem of rigid body orientation and Dynamic Body Acceleration (DBA) estimation. This work is applied in bio-logging, an interdisciplinary research area at the intersection of animal behavior and bioengineering. The proposed approach combines a quaternion-based nonlinear filter with the Levenberg Marquardt Algorithm (LMA). The algorithm has a complementary structure design that exploits measurements from a three-axis accelerometer, a three-axis magnetometer, and a three-axis gyroscope. Attitude information is necessary to calculate the animals DBA in order to evaluate its energy expenditure. Some numerical simulations illustrate the nonlinear filter performance. Some quantitative assessments prove this efficiency such as the time constant of the filter ( ) and the rms magnitude of the quaternion error ( ). Moreover, the effectiveness of the algorithm is experimentally demonstrated. In the experiments a domestic animal is equipped with an Inertial Measurement Unit (MTi-G), which provides a truth attitude for comparison with the complementary nonlinear filter. The rms difference between the filter and MTi-G outputs in the free movement experiments is within 0.392 rms on roll, 0.577 rms on pitch, and 2.521 rms on yaw.

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

A comparative analysis of attitude estimation for pedestrian navigation with smartphones

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A quaternion-based Complementary Sliding Mode Observer for attitude estimation: Application in free-ranging animal motions

-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.

A complementary observer-based approach for the estimation of motion in rigid bodies using inertial and magnetic sensors

We investigate the precision of attitude estimation solutions in the context of Pedestrian Dead-Reckoning (PDR) with commodity smartphones and inertial/magnetic sensors. We propose a concise comparison and analysis of a number of attitude filtering methods in this setting. We conduct an experimental study with a precise ground truth obtained with a motion capture system. We precisely quantify the error in attitude estimation obtained with each filter which combines a 3-axis accelerometer, a 3-axis magnetometer and a 3-axis gyroscope measurements. We discuss the obtained results and analyse advantages and limitations of current technology for further PDR research.

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

This paper proposes a sensing method using a module of GAM sensors (3-axis Gyroscope, 3-axis Accelerometer, 3-axis Magnetometer) for more accurate measurement of the marine animals posture. The application in mind is that of Bio-logging. A quaternion-based algorithm is developed through the complementary filtering theory in order to combine all information sources and to obtain an accurate estimation of the attitude. By considering the rigid body kinematic model, a Complementary Sliding Mode Observer (CSMO) is proposed, taking advantages from strapdown inertial measurements and vector observations. The proposed algorithm is based on the multiplicative quaternion correction technique. The performance of the CSMO is shown with a set of preliminary experiments on domestic animals through sensor measurements provided by an Inertial Measurement Unit.

Attitude Estimation for Indoor Navigation and Augmented Reality with Smartphones

This paper addresses the problem of rigid body orientation tracking. A complementary nonlinear observer is proposed for attitude estimation using inertial/magnetic sensors. The approach developed here is applied in Bio-logging, an interdisciplinary research area at the intersection of animal behavior and bioengineering. We propose a state estimation algorithm that combines three complementary data obtained from a 3-axis accelerometer, a 3-axis magnetometer and a 3-axis gyroscope in order to provide the best attitude. The proposed algorithm is based on a nonlinear observer coupled with an Iterated Least Squares Algorithm (ISLA). The evaluation of the state estimator by simulation is followed by some experiments illustrating the efficiency of the proposed approach.

On attitude estimation with smartphones

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.

Travel time forecasting from clustered time series via optimal fusion strategy

Abstract We investigate the precision of attitude estimation algorithms in the particular context of pedestrian navigation with commodity smartphones and their inertial/magnetic sensors. We report on an extensive comparison and experimental analysis of existing algorithms. We focus on typical motions of smartphones when carried by pedestrians. We use a precise ground truth obtained from a motion capture system. We test state-of-the-art and built-in attitude estimation techniques with several smartphones, in the presence of magnetic perturbations typically found in buildings. We discuss the obtained results, analyze advantages and limits of current technologies for attitude estimation in this context. Furthermore, we propose a new technique for limiting the impact of magnetic perturbations with any attitude estimation algorithm used in this context. We show how our technique compares and improves over previous works. A particular attention was paid to the study of attitude estimation in the context of augmented reality motions when using smartphones.