Quaternion-based Kalman Filter Research Articles

IMU Auto-Calibration Based on Quaternion Kalman Filter to Identify Movements of Dairy Cows.

This work is focused on developing a self-calibration algorithm for an orientation estimation of cattle movements based on a quaternion Kalman filter. The accelerometer signals in the earth's frame provide more information to confirm that the cow is performing a jump to mount another cow. To obtain the measurements in the earth's frame, we propose a self-calibration method based on a strapdown inertial navigation system (SINS), which does not require intervention by the user once deployed in the field. The self-calibration algorithm uses a quaternion-based Kalman filter to predict the angular orientation with bias correction, and update it based on the measurements of accelerometers and magnetometers. The paper also depicts an alternate update to adjust the inclination using only the accelerometer measurements. We conducted experiments to compare the accuracy of the orientation estimation when the body moves similarly to cow mount movements. The comparison is between the proposed self-calibration algorithm with the IvenSense MPU9250 and Bosch BNO055 and the quaternion attitude estimation provided in the BNO055. The auto-calibrating algorithm presents a mean error of 0.149 rads with a mean consumption of 308.5 mW, and the Bosch algorithm shows an average error of 0.139 rads with a mean consumption of 307.5 mW. When we executed this algorithm in an MPU9250, the average error was 0.077 rads, and the mean consumption was 277.7 mW.

Low-Cost IMU Sensors for Satellite Maturity Improvement

The satellite technology proves its impact in the modern era with its wide benefits and applications. However, the cost of the development in this field presents gaps in many countries, almost the developed countries. Therefore, this paper provides a rich platform around low-cost sensors in order to improve maturity in space technology, mostly the system of attitude determination and control. The development of this knowledge turns out to be very interesting in order to achieve a space mission which leads to the progression of the spatial technology readiness level (TRL) defined by the international measurement scale which is able to estimate the technological maturity. Thus, the idea is carried out for the development of low-cost sensors’ system for attitude determination around an Arduino board. A sensor fusion method was applied on three types of sensors: accelerometer, magnetometer, and gyroscope in order to detect the reliable orientation. It is aimed to apply quaternion based Kalman filter on different platform than previous systems. It is succeeded therefore to improve measurement accuracy around low-cost sensor to achieve the main goal of this paper.

Wearable wireless low-cost electrogoniometer design with Kalman filter for joint range of motion measurement and 3D modeling of joint movements.

Joint movements are the key factor for the mobility of the people during daily activities. The evaluation of the joint movements is determined by the range of motion (ROM) parameters. The ROM might change due to age, gender, and some diseases. Therefore, it is essential to measure ROM accurately and compare it with the normal values of the healthy people. In this study, a low-cost, wireless, and wearable electrogoniometer was designed for highly precise and accurate measurements. The stability of the measurements is guaranteed with the quaternion based Kalman filter. The measurements of the developed system are compared with the traditional goniometer. The concordance correlation coefficient is calculated as a similarity metric, and the result is obtained as . In addition, a GUI was prepared to present 3D visualization of the movements in real-time with the ROM measurements and give visual feedback to the physiotherapists during physical examinations and to the patient during the home therapy sessions. The measurements also can be recorded using the GUI for retrospective analysis.

A New Quaternion-Based Kalman Filter for Human Body Motion Tracking Using the Second Estimator of the Optimal Quaternion Algorithm and the Joint Angle Constraint Method with Inertial and Magnetic Sensors.

Human body motion tracking is a key technique in robotics, virtual reality and other human–computer interaction fields. This paper proposes a novel simple-structure Kalman filter to improve the accuracy of human body motion tracking, named the Second EStimator of the Optimal Quaternion Kalman Filter (E2QKF). The new algorithm is the combination of the Second Estimator of the Optimal Quaternion (ESOQ-2) algorithm, the linear Kalman filter and the joint angle constraint method. In the proposed filter, the ESOQ-2 algorithm is used to produce an observation quaternion by preprocessing accelerometer and magnetometer measurements. The compensation for the accelerometer added in the ESOQ-2 algorithm is to eliminate the influence of human body motion acceleration included in the results. The state vector of the filter is the quaternion, which is calculated with gyroscope measurements, and the Kalman filter is to calculate the optimal quaternion by fusing the state quaternion and the observation quaternion. Therefore, the filter becomes a simple first-order linear system model, which avoids the linearization error of measurement equations and reduces the computational complexity. Furthermore, the joint angle constraint is considered in the proposed algorithm, which makes the results more accurate. To verify the accuracy of the proposed algorithm, inertial/magnetic sensors are used to perform the upper limb motion experiment, and the result of E2QKF (without joint angle constraint) is compared with an optical motion capture system and two traditional methods. Test results demonstrate the effectiveness of the proposed filter: the root mean square error (RMSE) of E2QKF is less than 2.0° and the maximum error is less than 4.6°. The result of E2QKF (with joint angle constraint) is compared with E2QKF (without joint angle constraint). Test results demonstrate the superiority of E2QKF (with joint angle constraint): the joint angle constraint method can further improve the accuracy of human body motion tracking.

Attitude Determination Algorithm based on Relative Quaternion Geometry of Velocity Incremental Vectors for Cost Efficient AHRS Design

A novel attitude determination method is investigated that is computationally efficient and implementable in low cost sensor and embedded platform. Recent result on attitude reference system design is adapted to further develop a three-dimensional attitude determination algorithm through the relative velocity incremental measurements. For this, velocity incremental vectors, computed respectively from INS and GPS with different update rate, are compared to generate filter measurement for attitude estimation. In the quaternion-based Kalman filter configuration, an Euler-like attitude perturbation angle is uniquely introduced for reducing filter states and simplifying propagation processes. Furthermore, assuming a small angle approximation between attitude update periods, it is shown that the reduced order filter greatly simplifies the propagation processes. For performance verification, both simulation and experimental studies are completed. A low cost MEMS IMU and GPS receiver are employed for system integration, and comparison with the true trajectory or a high-grade navigation system demonstrates the performance of the proposed algorithm.

Didactic satellite based on Android platform for space operation demonstration and development

Space technology plays a pivotal role in society development. It offers new methods for telemetry, monitoring and control. However, this sector requires training, research and skills development but the lack of instruments, materials and budgets affects the ambiguity to understand satellite technology. The objective of this paper is to describe a demonstration prototype of a smart phone device for space operations study. Therefore, the first task was carried out to give a demonstration for spatial imagery and attitude determination missions through a wireless communication. The smart phone’s Bluetooth was used to achieve this goal inclusive of a new method to enable real time transmission. In addition, an algorithm around a quaternion based Kalman filter was included in order to detect the reliability of the prototype's orientation. The second task was carried out to provide a demonstration for the attitude control mission using the smart phone’s orientation sensor, including a new method for an autonomous guided mode. As a result, the acquisition platform showed real time measurement with good accuracy for orientation detection and image transmission. In addition, the prototype kept the balance during the demonstration based on the attitude control method.

Smartphone Orientation Estimation Algorithm Combining Kalman Filter With Gradient Descent.

Availability and all-in-one functionality of smartphones have become a multipurpose personal tool to improve our daily life. Recent advancements in hardware and accessibility of smartphones have spawn huge potential for assistive healthcare, in particular telerehabilitation. However, using smartphone sensors face certain challenges, in particular, accurate orientation estimation, which is usually less of a problem in specialized motion tracking sensor devices. Drift is one of the challenges. We first propose a simple feedback loop complementary filter (CFF) to reduce the error caused by the integration of the gyroscope's data in the orientation estimation. Next, we propose a new and better orientation estimation algorithm which combines quaternion-based kalman filter with corrector estimates using gradient descent (KFGD). We then evaluate CFF's and KFGD's performance on two early-stage rehabilitation exercises. The results show that CFF is capable of fast motion tracking and confirm that the feedback loop can correct the error caused by the integration of gyroscope data. The KFGD orientation estimation is comparable to XSENS Awinda and has shown itself to be stable than and outperforms CFF. KFGD also outperforms the prominent Madgwick algorithm using mobile data. Thus, KFGD is suitable for low-cost motion sensors or mobile inertial sensors, especially during early recovery stage of sport injuries and exercise for the elderly.

Compensation of Load Dynamics for Admittance Controlled Interactive Industrial Robots Using a Quaternion-Based Kalman Filter

The paper describes a control architecture for industrial robotic applications allowing human/robot interactions, using an admittance control scheme and direct sensing of the human inputs. The aim of the proposed scheme is to support the operator of an industrial robot, equipped with a force/torque (F/T) sensor on the end-effector, during human/robot collaboration tasks involving heavy payloads carried by the robot. In these practical applications, the dynamics of the load may significatively affect the measurements of the F/T sensor. Model-based compensation of such dynamic effects requires to compute linear acceleration and angular acceleration/velocity of the load, that in this paper are estimated by means of a quaternion-based Kalman filter and assuming that the only available measurements come from the forward kinematics of the robot. Experimental results demonstrate the feasibility of the approach and its industrial applicability.

Novel MARG-Sensor Orientation Estimation Algorithm Using Fast Kalman Filter

Orientation estimation from magnetic, angular rate, and gravity (MARG) sensor array is a key problem in mechatronic-related applications. This paper proposes a new method in which a quaternion-based Kalman filter scheme is designed. The quaternion kinematic equation is employed as the process model. With our previous contributions, we establish the measurement model of attitude quaternion from accelerometer and magnetometer, which is later proved to be the fastest (computationally) one among representative attitude determination algorithms of such sensor combination. Variance analysis is later given enabling the optimal updating of the proposed filter. The algorithm is implemented on real-world hardware where experiments are carried out to reveal the advantages of the proposed method with respect to conventional ones. The proposed approach is also validated on an unmanned aerial vehicle during a real flight. Results show that the proposed one is faster than any other Kalman-based ones and even faster than some complementary ones while the attitude estimation accuracy is maintained.

Attitude determination algorithm using state estimation including lever arms between center of gravity and IMU

In this paper, an enhanced attitude determination algorithm is proposed to decrease the estimation error by including an additive state variable for the lever arm. Attitude determination generally is carried out by measurements from an IMU (inertial measurement unit), which is typically located at the center of gravity of the vehicle. The IMU lever arm, which spans the distance between the IMU and the center of gravity, causes extra acceleration in the accelerometer and increases the error in attitude estimates. However, if the extra accelerations caused by the lever arm can be removed from the measurements of accelerometers, the increased attitude error caused by the IMU lever arm can be prevented. Because an IMU lever arm is fixed in a vehicle after installation, it can be considered as an additive element of the state vector in Kalman filter for attitude determination. The proposed algorithm is composed of a quaternion-based Kalman filter and includes an estimation of the IMU lever arm. In addition, in order to determine components of lever arm, the gross measure of modal observability is investigated for the system. An evaluation of the proposed algorithm is carried out by simulations with a noise model based on an actual IMU. Evaluations through simulations show that the proposed algorithm improves the performance with regard to errors.

An Efficient Attitude Reference System Design Using Velocity Differential Vectors under Weak Acceleration Dynamics

This paper proposes a new method achieving computationally efficient attitude reference system for low cost strapdown sensors and microprocessor platform. The main idea in this method is to define and compare velocity differential vectors, geometrically computed from INS and GPS data with different update rate, for generating attitude error measurements which is further used for filter construction. A quaternion based Kalman filter configuration is applied for the attitude estimation with the adapted measurement model of differential vector comparison. Linearized model for Extended Kalman Filter and low pass filtered characteristics of measurement greatly extend the affordability of the proposed algorithm to the field of simple low cost embedded systems. For performance verification, experiment are done employing a practical low cost MEMS IMU and GPS receiver specification. Performance comparison with a high grade navigation system demonstrated good estimation result.

Quaternion-based pseudo kalman filter for wearable inertial/magnetic sensor applications

This paper deals with orientation estimation using miniature inertial/magnetic sensor comprised of a tri-axial rate gyro, a tri-axial accelerometer, and a tri-axial magnetometer. Particularly, a novel quaternion-based pseudo Kalman filter (KF) is proposed by modifying an indirect KF, in order to maximize the computational efficiency and implementation simplicity. In the proposed pseudo KF, time-update process for prediction is based on the quaternion itself, while measurement-update process for correction is performed through the quaternion error. Experimental tests were conducted to verify performance of the proposed algorithm in various dynamic conditions. By designing the pseudo KF structure, matrix operations required in a typical KF are simplified. For instance, the proposed KF does not require the evaluation of the a priori and a posteriori error covariance matrices. Thus, the proposed algorithm achieves higher computational efficiency even than a typical indirect KF, without sacrificing estimation accuracy. Due to its high efficiency, the proposed algorithm can be suitable for battery-powered and low cost processor-based wearable inertial/magnetic sensor applications.

Convergence evaluation of quaternion-based attitude estimation using MEMS sensors

In this study, the extended Kalman filter was firstly explicated on the basis of quaternion. In order for the attitude estimation to be improved, multiplicative quaternion-based Kalman filter was presented. This filter helps to increase the convergence, and decrease sensitivity to the primitive conditions. In this research, inertia and reference sensors have been utilised for attitude estimation. Also, modelling and simulation of quaternion-based attitude estimation is initially performed and partially verified. Subsequently, an approximate statistical method was utilised to evaluate filter convergence. According to the simulation result, attitude and bias gyroscope fall in a safe region. Finally, a Mont Carlo simulation was also performed. The comparison and verification of statistical results indicated a small and acceptable deviation between the two approaches, thus, it can be concluded that the simpler approximate statistical approach is also valid for elevation filter convergence and can provide valuable knowledge needed in the filter design.

Quaternion-Based Kalman Filter for AHRS Using an Adaptive-Step Gradient Descent Algorithm

This paper presents a quaternion-based Kalman filter for real-time estimation of the orientation of a quadrotor. Quaternions are used to represent rotation relationship between navigation frame and body frame. Processing of a 3-axis accelerometer using Adaptive-Step Gradient Descent (ASGD) produces a computed quaternion input to the Kalman filter. The step-size in GD is set in direct proportion to the physical orientation rate. Kalman filter combines 3-axis gyroscope and computed quaternion to determine pitch and roll angles. This combination overcomes linearization error of the measurement equations and reduces the calculation cost. 3-axis magnetometer is separated from ASGD to independently calculate yaw angle for Attitude Heading Reference System (AHRS). This AHRS algorithm is able to remove the magnetic distortion impact. Experiments are carried out in the small-size flight controller and the real world flying test shows the proposed AHRS algorithm is adequate for the real-time estimation of the orientation of a quadrotor.

Quaternion-Based Kalman Filter With Vector Selection for Accurate Orientation Tracking

Human body orientation estimation from microinertial/magnetic sensor units is highly important for synthetic environments, robotics, and other human-computer interaction applications. In practice, the main challenge is how to deal with linear acceleration interference and magnetic disturbance which always cause significant attitude-estimation errors. In this paper, we present a novel quaternion-based Kalman filter with vector selection scheme for accurate human body orientation estimation using an inertial/magnetic sensor unit. In the proposed algorithm, the gyroscope measurement is used as an input to construct the linear process equation, and the accelerometer and magnetometer measurements are manipulated to establish the linear pseudomeasurement equation. A linear Kalman filter is then deployed to estimate the body orientation. In the Kalman filter framework, a vector selection scheme is designed to protect the algorithm against undesirable conditions such as temporary intensive movement and magnetic disturbance and enable it to acquire more accurate orientation estimation. The experimental results have shown that the proposed algorithm can provide accurate attitude estimations with regard to the ground truth.

Minimum-Order Kalman Filter With Vector Selector for Accurate Estimation of Human Body Orientation

This paper describes a new quaternion-based Kalman filter (KF) for estimating human body orientation using an inertial/magnetic sensor. The proposed algorithm is comprised of a quaternion measurement step and a KF step that are connected in feedback relationship. This allows the algorithm to have a minimum-order structure (i.e., fourth order) that is computationally very efficient. Furthermore, to offer more reliable information to the quaternion measurement step, a vector selector scheme is adopted, which effectively adds the gyro measurement to the so-called Wahba's problem that conventionally uses only the accelerometer and magnetometer measurements. This protects the algorithm against undesirable conditions such as fast movements and temporary magnetic disturbances, enabling it to compute an accurate orientation estimate. Due to the computational efficiency of the algorithm, it is suitable for real-time ambulatory human motion tracking applications that require multiple and untethered inertial/magnetic sensors with low-cost onboard processing.

Design, Implementation, and Experimental Results of a Quaternion-Based Kalman Filter for Human Body Motion Tracking

Real-time tracking of human body motion is an important technology in synthetic environments, robotics, and other human-computer interaction applications. This paper presents an extended Kalman filter designed for real-time estimation of the orientation of human limb segments. The filter processes data from small inertial/magnetic sensor modules containing triaxial angular rate sensors, accelerometers, and magnetometers. The filter represents rotation using quaternions rather than Euler angles or axis/angle pairs. Preprocessing of the acceleration and magnetometer measurements using the Quest algorithm produces a computed quaternion input for the filter. This preprocessing reduces the dimension of the state vector and makes the measurement equations linear. Real-time implementation and testing results of the quaternion-based Kalman filter are presented. Experimental results validate the filter design, and show the feasibility of using inertial/magnetic sensor modules for real-time human body motion tracking

Quaternion-Based Kalman Filter for Micro-machined Strapdown Attitude Heading Reference System

AbstractA Kalman filter used in strapdown AHRS (Attitude Heading Reference System) based on micro-machined inertial sensors is introduced. The composition and principle of the system are described. The attitude algorithm and error model of the system are derived based on the quaternion formulation. The real-time quaternion-based Kalman filter is designed. Simulation results show that accuracy of the system is better than 0.04 degree without disturbance of lateral acceleration and reduced to 0.44 degree with lateral acceleration of 0.1 g/1Hz. Primary tests show that the static accuracy of the system is + / − 0.2 degree for pitch and roll, and + / − 0.3 degree for azimuth.

A Least Squares Estimate of Satellite Attitude

A Least Squares Estimate of Satellite Attitude