MARG Sensors Research Articles

Attitude estimation for an all-rotating monocopter through attitude decomposition and MARG Sensor fusion

A monocopter is a biology-inspired aircraft based on samara. Due to the constant high spin during flight, attitude estimation is highly challenging. The difficulty of attitude estimation is extracting the effective gravity acceleration information from the large centripetal acceleration interference. Based on the characteristics of monocopters, our study proposes a method to accomplish monocopter attitude estimation through onboard sensor fusion. Our method decomposes the body attitude angles into two-disc attitude angles and three relative attitude angles. Through five steps (a priori body attitude estimation, relative attitude calculation, gravity acceleration information extraction, body attitude estimation through data fusion, and disc attitude estimation), a low-cost attitude determination method relying only on magnetic, angular rate, and gravity sensors is achieved. Finally, the performance of our proposed attitude estimation method is demonstrated through tests on a rotational platform and three degrees of freedom virtual flight testing of a monocopter. The test results show that the attitude estimation method has high precision and the ability for practical applications.

Augmentation for unmanned aerial vehicle position estimation using MARG and optical flow sensors

The optical flow sensor can detect the movement of the unmanned aerial vehicle (UAV) on the ground; thus, it is widely used for UAV flight control. The commonly used pinhole model of optical flow sensor describes the optical flow measurement in linear and angular velocities. It is not suitable in the case of discrete-time processing. A novel measurement model for the optical flow sensor is proposed, which directly gives the relationship between the optical flow and the UAV’s translational/angular motions in each sampling period. A data fusion scheme based on cubature transform is also presented, which can augment UAV’s position estimation using optical flow data. The proposed method is proven to be effective through flight tests on UAVs.

Upper limb orientation assessment as an articulated body chain.

Upper limb orientation estimation based on Magnetic, Angular Rate, and Gravity sensors considering multiple body segments is presented in this work. The proposal allowed assessing the activity of two or more body segments individually and jointly, regardless of their spatial relationship. A custom-made system was developed incorporating a complementary filter and a proportional-integral control for data sensor merging and, noise and instrumentation error reduction. Two controlled tests were carried out to assess the performance of the system. The former evaluated the response of the method in motionless conditions, while the latter assessed the feasibility to follow trajectories in 3D space. Ten volunteers were recruited to evaluate the system performance in three semi-controlled and daily life task tests. The system was evaluated using the common parameters in motion tracking methods and relied on a digital motion processor. The system's outcome presented a root mean square error in the range of 2.65°-3.98° for the semi-controlled tests and 0.48°-1.389° for the daily life task test. The system tests analysis proved that the proposal permitted obtaining the articulated body chain information of multiple segments when three or more MARG sensors are used.

Discrete-time complementary filter for attitude estimation based on MARG sensor

The MARG sensor, which stands for the combination of a magnetometer, an accelerometer, and a gyroscope, is widely used for 3D attitude measurement. Among the mainstream solutions for MARG-based attitude estimation, the complementary filter (CF) is normally regarded as a simplified alternative to the Kalman filter (KF), mainly because CF can reduce the amount of calculations. A dual-vector discrete-time CF (DV-DTCF) and its tuning methods are introduced in this paper. Different from the quaternion-based attitude estimation algorithms, DV-DTCF has a linear measurement model, since it utilizes the gravity and geomagnetic vectors as its state variables instead of quaternions. This feature of DV-DTCF can avoid linearization error or the use of nonlinear algorithms, and can also greatly reduce its computational complexity. More interestingly, it is analytically revealed, and experimentally proven, that the proposed DV-DTCF is fully equivalent to a fixed-gain KF. This fascinating fact leads straightforwardly to the tuning methods of DV-DTCF via the corresponding fixed-gain KF and Riccati equation. These tuning methods of DV-DTCF are based on the statistic characteristics of MARG sensor noise, and that makes them solid and feasible. According to experimental results, DV-DTCF can achieve the same accuracy as that of commonly-used KF algorithms in MARG-based attitude estimation, but with much lower time consumption. Hence, the proposed DV-DTCF is especially suitable for applications that have strict limitations on computational costs.

Neural-Adaptive Stochastic Attitude Filter on SO(3)

This letter proposes a novel stochastic nonlinear neural-adaptive-based filter on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$SO(3)$ </tex-math></inline-formula> for the attitude estimation problem. The proposed filter produces good results given measurements extracted from low-cost sensing units (e.g., IMU or MARG sensor modules). The filter is guaranteed to be almost semi-globally uniformly ultimately bounded in the mean square. In addition to Lie Group formulation, quaternion representation of the proposed filter is provided. The effectiveness of the proposed neural-adaptive filter is tested and evaluated in its discrete form under the conditions of large initialization error and high measurement uncertainties.

Complementary Filter for Attitude Estimation Based on MARG and Optical Flow Sensors

The combination of tri-axial magnetometer, accelerometer, and gyroscope has been widely used for three-dimensional attitude measurement, and this combination is also called MARG sensor. However, the measurement of accelerometer contains both the gravitational and motional acceleration, and only the former is useful for attitude estimation. As a result, MARG-based attitude estimation is easily disturbed by motion acceleration. In this paper, we introduce a complementary filter that estimates gravity and geomagnetic vectors in parallel, and utilize an optical flow sensor to detect and compensate motion acceleration. Experiment results show that the proposed algorithm has better performance than the existing ones when experiencing linear acceleration.

Three-dimensional attitude determination using vector observations and optical flow sensors

Flight control of unmanned aerial vehicle relies on three-dimensional attitude determination, and the most commonly used solution is based on the combination of magnetometer, accelerometer, and gyroscope, namely the MARG sensor. Optical flow sensor is also widely applied on UAV to detect the motion of UAV relative to the ground. In this paper, we proposed a novel method that using multiple optical flow sensors to measure angular velocity. This method utilizes a linear model to resolve both linear and angular motion from the measurements of multiple optical flow sensors. In the case of in situ rotations, experiment results prove that the proposed method can effectively estimate the angular velocity, and it can be used to augment MARG-based attitude determination.

Human-interactive Mapping Method for Indoor Magnetic Based on Low-cost MARG Sensors

Indoor magnetic map (IMM) based on magnetic field fluctuations can be used in map assisted indoor positioning and navigation, etc. However, many IMM mapping solutions are time-consuming, labor-intensive, and high-cost, which limit the development and application of IMM. To solve the issues of accuracy, efficiency, and cost of IMM mapping collaboratively, we absorbed the idea of simultaneous localization and mapping (SLAM) method, and proposed a human-interactive mapping method of IMM based on the low-cost magnetometer, accelerometer, and rate gyro, i.e., MARG sensors. First, we defined IMM as the structured data set with a series of position stamps and magnetic field fluctuations. Then, we proposed the concept of general sensory calibration source (GSCS) and related metrics for human-interactive activities which provide virtual information to eliminate the time-accumulated error of position stamps and assist in obtaining stable magnetic field fluctuations. Finally, we conduct a series of experiments to verify the performance of the proposed method. The test results show that the proposed method can not only meet the requirements of mapping accuracy but also significantly improve mapping efficiency and reduce mapping cost, which is superior to other state-of-the-art algorithms. Specifically, the significant results are as follows: the mapping accuracy is about 0.31 m, and the mapping efficiency is 1800 m$^2$ per hour, and the cost of the main module of IMM mapping does not exceed U.S. $10.

Fast and Robust Position and Attitude Estimation Method Based on MARG Sensors

With the development of Internet of Things (IoT), people’s demand for location-based services is increasingly urgent. Based on magnetometer, accelerometer, and rate gyro, i.e., MARG sensors, the position and attitude estimation methods such as complementary filter (CF), Kalman filter (KF), and their various modifications have been the research hot spot. However, the CF-based methods are empirical and lack robustness; the KF-based methods are memory-free observers, whose solution may diverge when the filter lacks uniform observability. In this article, a virtual-measurement-combined extended KF (VMC-EKF) method is proposed by fusing the carrier’s motion state with EKF method. Similar to the graph optimization, the proposed method can measure the key information in VMC phase, and thus remove the requirement of uniform observability. The number of virtual measurements can be estimated based on carrier’s motion state and its gradient, which determines the number of iterations of the prediction phase and the correction phase. In order to verify the performance of the proposed method, a series of numerical simulation experiments, turntable experiments, and foot-mounted experiments are carried out. The corresponding testing platform is set up based on MPU9250, which is a typical and low-cost motion tracking integrated circuit (IC) of MARG sensors. The raw data of MARG sensors can communicate with the host computer via wired or wireless communication, and then be imported into MATLAB for processing and analysis by the compared methods. The test results show that the proposed method can achieve fast convergence of attitude estimation and avoid the divergence of position estimation compared with the state-of-the-art methods.

3D motion tracking of the shoulder joint with respect to the thorax using MARG sensors and data fusion algorithm

A method for performing 3D motion tracking of the shoulder joint with respect to the thorax, using MARG sensors and a data fusion algorithm, is proposed. Two tests were done: (1) qualitative and quantitative analysis of the response of the sensors, static position and during motion, with and without the proposed data fusion algorithm; (2) motion tracking of the shoulder joint with the upper arm, the thorax, and the shoulder joint respect to the thorax. Qualitative analysis of experimental results showed that despite slight variations regarding the evaluated motion, these variations did not have repercussions on the estimated orientation. Quantitative analysis showed that the estimated orientation did not exhibit significant variations, in five minutes, such as drift errors (about 0.1° in static position and less than 1.8° during motion), variations due to noise or magnetic disturbances (RMSE less than 0.04° static position and less than 1° during motion); no singularity problems were reported.The main contributions of this research are a multisensor data fusion algorithm, which combines the complementary properties of gyroscopes, accelerometers, and magnetometers in order to estimate the 3D orientation of two body segments separately and with respect to another body segment considering the spatial relationship between them; and a method for performing 3D motion tracking of two body segments, based on the estimation of their orientation, including motion compensation. The proposed method is applicable to monitoring devices based on IMU/MARG sensors; the performance was evaluated using a customized motion analysis system.

Corrections to “Fast Complementary Filter for Attitude Estimation Using Low-Cost MARG Sensors”

In the reference by the authors [1] , the quaternion fusion from accelerometer and magnetometer measurements does not have proper mathematical form. The presented equation (43) in [1] , actually takes a unit quaternion for attitude representation with a direction vector n followed by a scalar s , which reads [2]

A new measurement for yaw estimation of land vehicles using MARG sensors

PurposeThe magnetometer measurement update plays a key role in correcting yaw estimation in fusion algorithms, and hence, the yaw estimation is vulnerable to magnetic disturbances. The purpose of this study is to improve the ability of the fusion algorithm to deal with magnetic disturbances.Design/methodology/approachIn this paper, an adaptive measurement equation based on vehicle status is derived, which can constrain the yaw estimation from drifting when vehicle is running straight. Using this new measurement, a Kalman filter-based fusion algorithm is constructed, and its performance is evaluated experimentally.FindingsThe experiments results demonstrate that the new measurement update works as an effective supplement to the magnetometer measurement update in the present of magnetic disturbances, and the proposed fusion algorithm has better yaw estimation accuracy than the conventional algorithm.Originality/valueThe paper proposes a new adaptive measurement equation for yaw estimation based on vehicle status. And, using this measurement, the fusion algorithm can not only reduce the weight of disturbed sensor measurement but also utilize the character of vehicle running to deal with magnetic disturbances. This strategy can also be used in other orientation estimation fields.

Attitude estimation using MARG sensors for unmanned aerial vehicles

Attitude estimation using MARG sensors for unmanned aerial vehicles

Heterogeneous data fusion for three-dimensional gait analysis using wearable MARG sensors

Heterogeneous data fusion for three-dimensional gait analysis using wearable MARG sensors

MSOE: Toward Abrupt Magnetic Change in MARG Orientation Using Multi-State Estimator With Smartphones

The phone attitude angle has been used as an effective tool to many applications, which will be a tough problem when it suffers the change of external environment, such as the magnetic field abrupt variation. In this paper, we present a novel orientation estimation and calibration algorithm MSOE, a multiple states orientation estimation based on the smartphones inertial measurement units consisting of tri-axis accelerometer, gyroscope, and MARG sensors. MSOE is divided into two parts, MSOE calibration (MSOE-C) and MSOE remainder (MSOE-R). MSOE-C skillfully borrows the crowdsourcing data expressed in the form of variational quaternions measured by the phones in the same magnet field. As the non-uniform nature exists inevitably when the crowd-phones are far away from the determinand, the crowdsourcing data may be erroneous. MSOE-R provides us a reminder by warning the control center to prevent measuring by the magnetometer and mainly utilize the gyroscope for estimation during the period with unstable environment. MSOE also incorporates a compensation filter for the tri-axis sensors deviation, especially for the gyroscope drifting. Performance has been evaluated empirically in two different Android platforms with four types of phones based on the available measurement system. Performance is also benchmarked against some current estimation algorithms and MSOE provides two times improvement on the accuracy of attitude angle estimation.

An Accurate and Fault-Tolerant Target Positioning System for Buildings Using Laser Rangefinders and Low-Cost MEMS-Based MARG Sensors.

Target positioning systems based on MEMS gyros and laser rangefinders (LRs) have extensive prospects due to their advantages of low cost, small size and easy realization. The target positioning accuracy is mainly determined by the LR’s attitude derived by the gyros. However, the attitude error is large due to the inherent noises from isolated MEMS gyros. In this paper, both accelerometer/magnetometer and LR attitude aiding systems are introduced to aid MEMS gyros. A no-reset Federated Kalman Filter (FKF) is employed, which consists of two local Kalman Filters (KF) and a Master Filter (MF). The local KFs are designed by using the Direction Cosine Matrix (DCM)-based dynamic equations and the measurements from the two aiding systems. The KFs can estimate the attitude simultaneously to limit the attitude errors resulting from the gyros. Then, the MF fuses the redundant attitude estimates to yield globally optimal estimates. Simulation and experimental results demonstrate that the FKF-based system can improve the target positioning accuracy effectively and allow for good fault-tolerant capability.

Detecting Elementary Arm Movements by Tracking Upper Limb Joint Angles With MARG Sensors.

This paper reports an algorithm for the detection of three elementary upper limb movements, i.e., reach and retrieve, bend the arm at the elbow and rotation of the arm about the long axis. We employ two MARG sensors, attached at the elbow and wrist, from which the kinematic properties (joint angles, position) of the upper arm and forearm are calculated through data fusion using a quaternion-based gradient-descent method and a two-link model of the upper limb. By studying the kinematic patterns of the three movements on a small dataset, we derive discriminative features that are indicative of each movement; these are then used to formulate the proposed detection algorithm. Our novel approach of employing the joint angles and position to discriminate the three fundamental movements was evaluated in a series of experiments with 22 volunteers who participated in the study: 18 healthy subjects and four stroke survivors. In a controlled experiment, each volunteer was instructed to perform each movement a number of times. This was complimented by a seminaturalistic experiment where the volunteers performed the same movements as subtasks of an activity that emulated the preparation of a cup of tea. In the stroke survivors group, the overall detection accuracy for all three movements was 93.75% and 83.00%, for the controlled and seminaturalistic experiment, respectively. The performance was higher in the healthy group where 96.85% of the tasks in the controlled experiment and 89.69% in the seminaturalistic were detected correctly. Finally, the detection ratio remains close ( ±6%) to the average value, for different task durations further attesting to the algorithms robustness.

Study and development of a low cost “OptInertial” 3D scanner

• Design and development of a flexible 3D scanner, completely disjoined by trackers and markers. • 3D acquisition by the use of optical technologies together with an inertial MARG sensors. • The device measurement accuracy and flexibility guarantee the possibility of its usage for reverse engineering applications. The 3D scanner domain normally relies on the presence of many tools and technologies. They are mainly divided between contact and non-contact ones, but at present a new trend is coming up, starting from the articulated arms family, where the traditional mechanical joints, allowing flexible measures on complex objects, have been replaced by handy scanner with laser trackers, or with markers. These new systems have the advantage to get the entire object shape without changing the object position itself, but moving the scanning device without the involvement of long software alignments and post treatment operations. Anyway, the use of laser trackers obliges the operator to maintain the scanner head always visible, while the marker usage is quite critical because the measure precision depends strongly on the marker position. Starting from these considerations, the research project presented in this paper has been focused on the design and development of a flexible 3D scanner, without trackers and markers, that merge low-cost optical technologies together with low-cost inertial sensors. Thanks to this synergy, the developed 3D scanner is able to measure the three-dimensional shape of the object recording its movement and transferring it to a control unit for obtaining a point cloud. The paper presents the main concepts of the 3D scanner design and is concluded by an experimental phase made with the use of a benchmark.

Attitude and heading reference system with acceleration compensation

PurposeThe purpose of this paper is to employ an extended Kalman filter for implementing an AHRS (attitude and heading reference system) with acceleration compensation, thereby improving the reliability of such systems, since this removes the usual restrictive assumption that the vehicle is undergoing a non‐accelerated maneuver.Design/methodology/approachMARG (magnetic, acceleration and rate gyros) sensors constitute the basic hardware, which are integrated by the Kalman filter. The error dynamics for attitude and gyro biases is obtained in the navigation frame, providing a much simpler approach than usually taken in the literature, since it relies on direct quaternion differentiation. The state vector associated to the error dynamics possesses six components: three are associated to the quaternion error and three concern gyro bias estimates.FindingsThe AHRS is implemented in an ARM (Advanced RISC Machine) processor and tested with experimental data. The accelerated case is treated by two complementary approaches: by changing the noise variance in the Kalman filter, and by obtaining an acceleration information from GPS (global positioning system) velocity measurements. Experimental results are presented and the performance is compared with commercial ARHS systems.Practical implicationsThe proposed AHRS can be implemented with low cost MARG sensors, and GPS aiding, with use for instance in UAV (unmanned aerial vehicle) and small aircrafts' attitude estimation, for navigation and control applications.Originality/valueUsually the AHRS designs employ as states total gyro bias and Euler angles, or quaternion, and do not consider the accelerated case. Here the state is comprised by gyro bias and quaternion error variables, which attenuates the effect of nonlinearities, and two complementary procedures tackle the accelerated case: acceleration correction by using a GPS derived acceleration signal and change in the output noise covariance used by the Kalman filter.

Attitude estimation by divided difference filter in quaternion space

This article considers the application of Divided Difference Filter (DDF) to the orientation estimation, based on a quaternion-error continuous-discrete time model. DDF is a nonlinear estimator that in contrast to Taylor's expansion of extended Kalman Filter (EKF), exploit the polynomial approximations as a multivariable extension of Stirling's interpolation formula and require no derivatives. The DDF can be based on 1st and 2nd order Stirling's interpolation, which is named the divided difference filter-1st order (DDF1) and the divided difference filter-2nd order (DDF2). The orientation kinematics is defined in a quaternion vector space that unlike the Euler angle representation does not have any singularity problem. The presented nonlinear orientation model is an exact error model and is independent of the rigid body dynamics. The nonlinear process model includes six error-states in which only non-scalar elements of quaternion error vector are included in the error-state equations. The fourth element of quaternion error vector, which obeys unit norm constraint, is removed from system states to alleviate the estimated error covariance matrix divergence. The measurement system is a MARG sensor, which consists of a tri-axial rate gyro, a tri-axial accelerometer and a tri-axial magnetometer. The nonlinear measurement model is obtained based on the principals of magnetometer and accelerometer and the properties of the quaternion vector space. For the presented nonlinear orientation model, the performance of three filters namely DDF, EKF and Unscented Kalman Filter (UKF) is compared for different sampling frequencies in terms of the rms error, the captured area under the error norm curve, the estimated state variance and the computational cost. It is shown that under the same initial angle-error conditions, DDFs and UKF are more robust than EKF. The DDFs perform better than unscented Kalman filter (UKF) although the computational load for UKF is less. Among DDF1 and DDF2, DDF2's performance is slightly better but with more computation load. In the case of no initial angle-error conditions, the performance of the four filters is the same especially when the low noise level condition is considered.