Quaternion-based Extended Kalman Filter Research Articles

Improved Attitude and Heading Accuracy with Double Quaternion Parameters Estimation and Magnetic Disturbance Rejection.

The use of unmanned aerial vehicle (UAV) applications has grown rapidly over the past decade with the introduction of low-cost microelectromechanical system (MEMS)-based sensors that measure angular velocity, gravity, and magnetic field, which are important for an object orientation determination. However, the use of low-cost sensors has also been limited because their readings are easily distorted by unwanted internal and/or external noise signals such as environmental magnetic disturbance, which lead to errors in attitude and heading estimation results. In an extended Kalman filter (EKF) process, this study proposes a method for mitigating the effect of magnetic disturbance on attitude determination by using a double quaternion parameters for representation of orientation states, which decouples the magnetometer from attitude computation. Additionally, an online measurement error covariance matrix tuning system was implemented to reject the impact of magnetic disturbance on the heading estimation. Simulation and experimental tests were conducted to verify the performance of the proposed methods in resolving the magnetic noise effect on attitude and heading. The results showed that the proposed method performed better than complimentary, gradient descent, and single quaternion-based EKF.

Lightweight Extended Kalman Filter for MARG Sensors Attitude Estimation

Low-power consumption of orientation estimation using low-cost inertial sensors are crucial for all the applications which are resource constrained critically. This paper presents a novel Lightweight quaternion-based Extended Kalman Filter (LEKF) for orientation estimation for magnetic, angular rate and gravity (MARG) sensors. In this filter, with employing the quaternion kinematic equation as the process model, we derived a simplified measurement model to create the lightweight system model for Kalman filtering, where the measurement model works efficiently, and the involved computation of measurement model is reduced. It’s later proved that the proposed filter saves time consumption. Further, observations of the accelerometer and the magnetometer are dealt with the proposed nonlinear measurement model, the good performance should be guaranteed in theory. For the experiments, a commercial sensor for data collection, and an optical system to provide reference measurements of orientation, namely Vicon, are utilized to investigate the performance of the proposed filter. Evaluation for different application scenarios are considered, which primarily includes human motion capture and the drone application. Results indicate that the proposed filter performs well for both applications, and is proved to have a good anti-vibration ability. What’s more, the comparison experiment shows that the proposed filter provides good performance, as same as the basic UKF, but it consumes the least computing time among the compared methods.

Invariant Extended Kalman Filtering for Underwater Navigation

Recent advances in the utilization of Lie Groups for robotic localization have led to dramatic increases in the accuracy of estimation and uncertainty characterization. One of the novel methods, the Invariant Extended Kalman Filter (InEKF) extends the Extended Kalman Filter (EKF) by leveraging the fact that some error dynamics defined on matrix Lie Groups satisfy a log-linear differential equation. Utilization of these observations result in linearization with minimal approximation error, no dependence on current state estimates, and excellent convergence and accuracy properties. In this letter we show that the primary sensors used for underwater localization, inertial measurement units (IMUs) and doppler velocity logs (DVLs) meet the requirements of the InEKF. Furthermore, we show that singleton measurements, such as depth, can also be used in the InEKF update with minor modifications, thus expanding the set of measurements usable in an InEKF. We compare convergence, accuracy and timing results of the InEKF to a quaternion-based EKF using a Monte Carlo simulation and show notable improvements in long-term localization and much faster convergence with negligible difference in computation time.

An Embedded Quaternion-Based Extended Kalman Filter Pose Estimation for Six Degrees of Freedom Systems

This paper proposes a formulation of quaternion-based Extended Kalman Filter pose estimation for six degrees of freedom systems embedded in an FPGA with commercial processors. Our approach uses the fusion of a camera and an inertial measurement unit to estimate simultaneously the position and the orientation of the system of interest. In addition, a Stewart platform is used to validate and evaluate the estimated pose. Although this work considers the use of common low-cost sensors and the use of markers with simple geometry, the results show excellent performance of the developed filter, being able to estimate the pose and orientation with an error below 8.14 mm and 0.63o, respectively. Furthermore, the effectiveness of the approach has also been evaluated, showing that the filter is able to converge quickly when the markers are retrieved after a loss of camera data for a short period of time.

다중 IMU 센서와 연합형 필터 융합 기반의 GPS-free 위치 추정

Localization techniques based on the integration of MEMSs(Micro Electro Mechanical Systems) and GPS(Global Positioning System) have been widely used in various fields, including aerospace, biomedical, automotive, and robotics, among others. However, it is well known that GPS signals are weakened or blocked in tunnels, urban canyons, or indoor environments. A solution is to use multiple IMU(Inertial Measurement Unit) sensors. In this paper, we present a federated fusion algorithm for GPS-free localization using multiple MEMS IMUs. The federated filter uses a master fusion algorithm to combine the outputs of independent sensors so that the current position can be estimated. The proposed structure exploits a quaternion-based extended Kalman filter and a linear Kalman filter for attitude estimations and velocity estimations, respectively. The effectiveness of the proposed algorithm was demonstrated with MATLAB simulation.

Contact-aided invariant extended Kalman filtering for robot state estimation

Legged robots require knowledge of pose and velocity in order to maintain stability and execute walking paths. Current solutions either rely on vision data, which is susceptible to environmental and lighting conditions, or fusion of kinematic and contact data with measurements from an inertial measurement unit (IMU). In this work, we develop a contact-aided invariant extended Kalman filter (InEKF) using the theory of Lie groups and invariant observer design. This filter combines contact-inertial dynamics with forward kinematic corrections to estimate pose and velocity along with all current contact points. We show that the error dynamics follows a log-linear autonomous differential equation with several important consequences: (a) the observable state variables can be rendered convergent with a domain of attraction that is independent of the system’s trajectory; (b) unlike the standard EKF, neither the linearized error dynamics nor the linearized observation model depend on the current state estimate, which (c) leads to improved convergence properties and (d) a local observability matrix that is consistent with the underlying nonlinear system. Furthermore, we demonstrate how to include IMU biases, add/remove contacts, and formulate both world-centric and robo-centric versions. We compare the convergence of the proposed InEKF with the commonly used quaternion-based extended Kalman filter (EKF) through both simulations and experiments on a Cassie-series bipedal robot. Filter accuracy is analyzed using motion capture, while a LiDAR mapping experiment provides a practical use case. Overall, the developed contact-aided InEKF provides better performance in comparison with the quaternion-based EKF as a result of exploiting symmetries present in system.

A Novel Design Framework for Tightly Coupled IMU/GNSS Sensor Fusion Using Inverse-Kinematics, Symbolic Engines, and Genetic Algorithms

Tightly-coupled (TC) fusion of Inertial Measurement Units (IMUs) with Global Navigation Satellite Systems (GNSSs) is a common technique that provides high-rate positioning even under GNSS interruptions. In order to provide accurate positioning, errors of IMU and GNSS must be modelled and estimated by filtering techniques such as Extended Kalman Filter (EKF). Due to nonlinearity and stochastic characteristics of IMU and GNSS system and measurement models, robust filter design has been a challenge. Conventional design techniques use mission-specific fixed models and trial-and-error noise parameter tuning to design IMU/GNSS filters. These conventional techniques are inflexible and do not always lead to accurate designs as there are no ways to verify the filter ability to estimate sensors errors accurately. To address this challenge, this paper presents a flexible design framework and a systematic procedure for TC IMU/GNSS fusion. The framework utilizes symbolic engines to represent and linearize system and measurement models. Symbolic engines are flexible in new models and fusion algorithms development. In order to evaluate the estimation of sensors errors, an Inverse-Kinematics module is developed to generate error-free sensors measurements which can be contaminated by known errors. The filter parameters are tuned using Genetic Algorithms and the performance is evaluated based on the accuracy of estimating all states including the added known errors. The framework has been used to develop a quaternion-based EKF design and verified on real raw IMU/GNSS data. The results showed that the developed framework greatly reduces efforts to design robust and accurate fusion systems for TC IMU/GNSS integration.

Measurement System for Attitude of Anterior Pelvic Plane and Implantation of Prothesis in THR Surgery

With the average age of population increasing in the world, the number of total hip replacement (THR) surgeries increases year by year. However, the failure rate of THR surgeries is up to 10% following primary surgery and 28% after revision arthroplasty, which has direct correlation to the implantation angles between prosthesis and pelvis. To improve the implanting accuracy of the prosthesis, we propose a measurement system and estimation algorithms. The system includes three parts: an initial attitude measurement instrument, which is used to determine the initial attitude of the anterior pelvic plane (APP), a real-time attitude measurement instrument, which aims to acquire the real-time attitude of the APP, and an acetabular cup angle measurement instrument, which obtains the relative angles between prosthesis and pelvis. Each of them is based on inertial measurement unit (IMU) and magnetometer. A quaternion-based extended Kalman filter is adopted to fuse the data from IMU and magnetometer to estimate the orientation, and the algorithm calculating the attitude of pelvis and relative angles between pelvis and prosthesis is designed in this paper. The reliability of this system, from the measurement point of view, has been verified by experiments. The experimental results show that the root-mean-square errors of APP attitude and acetabular cup implanting orientation are less than 1.6° and 3° with standard uncertainty of less than 0.22° and 0.17°, respectively. The accuracy of our system meets the requirement of the THR surgeries.

A Wearable Inertial Pedestrian Navigation System With Quaternion-Based Extended Kalman Filter for Pedestrian Localization

This paper presents a wearable inertial pedestrian navigation system and its associated pedestrian trajectory reconstruction algorithm for reconstructing pedestrian walking trajectories in indoor and outdoor environments. The proposed wearable inertial pedestrian navigation system is constructed by integrating a triaxial accelerometer, a triaxial gyroscope, a triaxial magnetometer, a microcontroller, and a Bluetooth wireless transmission module. Users wear the system on foot while walking in indoor and outdoor environments at normal speed without any external positioning techniques. During walking movement, the measured inertial signals generated from walking movements are transmitted to a computer via the wireless module. Based on the foot-mounted inertial pedestrian navigation system, a pedestrian trajectory reconstruction algorithm composed of the procedures of inertial signal acquisition, signal preprocessing, trajectory reconstruction, and trajectory height estimation has been developed to reconstruct floor walking and stair climbing trajectories. In order to minimize the cumulative error of the inertial signals, we have utilized a sensor fusion technique based on a double-stage quaternion-based extended Kalman filter to fuse acceleration, angular velocity, and magnetic signals. Experimental results have successfully validated the effectiveness of the proposed wearable inertial pedestrian navigation system and its associated pedestrian trajectory reconstruction algorithm.

Attitude measure system based on extended Kalman filter for multi-rotors

Attitude measure is the basis of multi-rotors flight control. An attitude measure system was constructed based on MEMS gyroscope, accelerometer and magnetometer to realize three-axis attitude measure of multi-rotors. The system included STM32F103 as controller, integrated accelerometer and gyroscope MPU6050, magnetometer HMC5883 as measure sensors. A sensor fusion quaternion-based extended Kalman filter compliant with this system was proposed. The attitude quaternion and the gyroscope bias were introduced as state vector, the acceleration and the magnetic measured by accelerometer and magnetometer were introduced as observation vector. Extended Kalman filter combined the nice performance of gyroscope in dynamic with accelerometer and magnetometer in static. The optimized covariance value combination can improve the accuracy of attitude estimation and had excellent tracking performance in dynamic. The measure system based on extended Kalman filter was testified and analyzed by static and dynamic tests. Experiment results illustrated that the system can obtain the information of each sensor. The attitude measure system based on extended Kalman filter realized precision attitude measure for multi-rotors in dynamic circumstances. It may lay foundation for UAV remote control.

Advanced information processing of MEMS motion sensors for gesture interaction

Abstract. Sensor-based gesture interaction technology has been widely adopted in consumer electronics. Nevertheless, bias, drift, and noise existing in sensor signals are difficult to eliminate, and accurate movement trajectory information is still needed to achieve flexible interaction application. This paper presents micro-electro-mechanical system (MEMS) motion sensor information processing algorithms designed on a gesture interaction system which integrates multiple low-cost MEMS motion sensors with ZigBee wireless technology to support embodied communication while acting together with machines. Sensor signal processing systems mainly solve noise removal, signal smoothing, gravity influence separation, coordinate system conversion, and position information retrieval. The attitude information which is an important movement parameter and required by position estimation is calculated with a quaternion-based extended Kalman filter (EKF). The effectiveness of the movement information retrieval of this gesture interface is verified by experiments and test analysis, both in static and moving cases. In the end, related applications of the described sensor information processing are discussed.

A Linear Kalman Filter for MARG Orientation Estimation Using the Algebraic Quaternion Algorithm

Real-time orientation estimation using low-cost inertial sensors is essential for all the applications where size and power consumption are critical constraints. Such applications include robotics, human motion analysis, and mobile devices. This paper presents a linear Kalman filter for magnetic angular rate and gravity sensors that processes angular rate, acceleration, and magnetic field data to obtain an estimation of the orientation in quaternion representation. Acceleration and magnetic field observations are preprocessed through a novel external algorithm, which computes the quaternion orientation as the composition of two algebraic quaternions. The decoupled nature of the two quaternions makes the roll and pitch components of the orientation immune to magnetic disturbances. The external algorithm reduces the complexity of the filter, making the measurement equations linear. Real-time implementation and the test results of the Kalman filter are presented and compared against a typical quaternion-based extended Kalman filter and a constant gain filter based on the gradient-descent algorithm.

Pedestrian dead reckoning for MARG navigation using a smartphone

Abstract The demand for navigating pedestrian by using a hand-held mobile device increased remarkably over the past few years, especially in GPS-denied scenario. We propose a new pedestrian dead reckoning (PDR)-based navigation algorithm by using magnetic, angular rate, and gravity (MARG) sensors which are equipped in existing commercial smartphone. Our proposed navigation algorithm consists of step detection, stride length estimation, and heading estimation. To eliminate the gauge step errors of the random bouncing motions, we designed a reliable algorithm for step detection. We developed a BP neural network-based stride length estimation algorithm to apply to different users. In response to the challenge of magnetic disturbance, a quaternion-based extended Kalman filter (EKF) is introduced to determine the user's heading direction for each step. The performance of our proposed pedestrian navigation algorithm is verified by using a smartphone in providing accurate, reliable, and continuous location tracking services.

The Use of an Orientation Kalman Filter for the Static Postural Sway Analysis

The paper presents a quaternion-based extended Kalman filter for postural instability evaluation during stance. It uses low-cost MEMS inertial sensors attached on the lower back of the person at a known height in order to instrumenting the static balancing test. Generally, patients with Parkinson's disease or vestibular-loss are at greater risk for having this problem. The objective of this study was to assess the feasibility of using Kalman filter to characterize the postural steadiness. The Kalman filter is used here as a data fusion algorithm to estimate the orientation of the body based on acceleration and angular rate signals. In order to get the coordinate of the body's centre of mass (CoM), the height of the sensor is projected on the horizontal plane by using the estimated orientation. Many parameters such as the mean velocity of sway, lateral/anterior-posterior range and others are then obtained from the sway path, which help the clinicians to assess the postural instability. The method was tested on 9 healthy individuals (21-31 years). Three different test conditions, namely feet comfortable stance with eyes-open, feet together stance with closed eyes and one-leg stance with eyes-open were evaluated here. The proposed algorithm showed successful estimation of the time-domain parameter for the postural sway analysis.

Experiment of a Quaternion-Based Extended Kalman Filter with Noise Reduction Technique Using MEMS Sensors for Attitude State Estimation

Position and orientation acquirement is one hot topic in sensor data fusion research and application area. Micro-Electro-mechanical Systems (MEMS) sensor is a kind of low-cost and feasible tool that could measure some movement information, including acceleration and angular rate and so on, while burst noise and outlier signal influence the sensor data for accurate information acquirement and related application analysis. Some advanced digital signal processing techniques could realise the improvement of signal quality. The algorithm of median filter, combined with mean filter, was implemented to output better data for orientation estimation with fewer burst noise and outlier signals. Considering our designed and developed sensor system, including a tri-axis accelerometer, a dual-axis pitch and roll gyroscope and a yaw gyroscope used in this research, the construction of sensor model and a kind of quaternion-based extended Kalman filter (EKF) method and involved formulas for attitude state estimation are described in this paper. The experiment of this quaternion-based EKF with noise reduction processing was implemented using MEMS sensors. Regarding the EKF result of orientation estimation, this paper analyses the reason why the yaw drift generated. The EKF result of orientation estimation proves the feasibility of 2 degrees of freedom for attitude state estimation application.

Attitude Determination Using a MEMS-Based Flight Information Measurement Unit

Obtaining precise attitude information is essential for aircraft navigation and control. This paper presents the results of the attitude determination using an in-house designed low-cost MEMS-based flight information measurement unit. This study proposes a quaternion-based extended Kalman filter to integrate the traditional quaternion and gravitational force decomposition methods for attitude determination algorithm. The proposed extended Kalman filter utilizes the evolution of the four elements in the quaternion method for attitude determination as the dynamic model, with the four elements as the states of the filter. The attitude angles obtained from the gravity computations and from the electronic magnetic sensors are regarded as the measurement of the filter. The immeasurable gravity accelerations are deduced from the outputs of the three axes accelerometers, the relative accelerations, and the accelerations due to body rotation. The constraint of the four elements of the quaternion method is treated as a perfect measurement and is integrated into the filter computation. Approximations of the time-varying noise variances of the measured signals are discussed and presented with details through Taylor series expansions. The algorithm is intuitive, easy to implement, and reliable for long-term high dynamic maneuvers. Moreover, a set of flight test data is utilized to demonstrate the success and practicality of the proposed algorithm and the filter design.

Kalman-Filter-Based Orientation Determination Using Inertial/Magnetic Sensors: Observability Analysis and Performance Evaluation

In this paper we present a quaternion-based Extended Kalman Filter (EKF) for estimating the three-dimensional orientation of a rigid body. The EKF exploits the measurements from an Inertial Measurement Unit (IMU) that is integrated with a tri-axial magnetic sensor. Magnetic disturbances and gyro bias errors are modeled and compensated by including them in the filter state vector. We employ the observability rank criterion based on Lie derivatives to verify the conditions under which the nonlinear system that describes the process of motion tracking by the IMU is observable, namely it may provide sufficient information for performing the estimation task with bounded estimation errors. The observability conditions are that the magnetic field, perturbed by first-order Gauss-Markov magnetic variations, and the gravity vector are not collinear and that the IMU is subject to some angular motions. Computer simulations and experimental testing are presented to evaluate the algorithm performance, including when the observability conditions are critical.

Towards Miniaturization of a MEMS-Based Wearable Motion Capture System

This paper presents a modular architecture to develop a wearable system for real-time human motion capture. The system is based on a network of smart inertial measurement units (IMUs) distributed on the human body. Each of these modules is provided with a 32-bit RISC microcontroller (MCU) and miniaturized MEMS sensors: three-axis accelerometer, three-axis gyroscopes, and three-axis magnetometer. The MCU collects measurements from the sensors and implement the sensor fusion algorithm, a quaternion-based extended Kalman filter to estimate the attitude and the gyroscope biases. The design of the proposed IMU, in order to overcome the problems of the commercial solution, aims to improve performance and to reduce size and weight. In this way, it can be easily embedded in a tracksuit for total body motion reconstruction with considerable enhancement of the wearability and comfort. Furthermore, the main achievements will be presented with a performance comparison between the proposed IMU and some commercial platforms.

Attitude estimation based on fusion of gyroscopes and single antenna GPS for small UAVs under the influence of vibration

An attitude estimation method is presented for small unmanned aerial vehicles (UAVs) powered by a piston engine which is the major source of vibration. Vibration of the engine significantly degrades the accuracy of the inertial measurement unit, especially for low-cost sensors that are based on micro electro-mechanical system. Therefore, a vibration model for a small UAV is proposed in order to examine the influence of vibration on attitude estimation with different sensors. The model is derived based on spectrum analysis with short-time Fourier transform. The vibration is compared with the drift of the gyroscope in order to examine the impact on attitude estimation. An attitude estimation method that fuses the gyroscopes and single antenna global positioning system (GPS) is proposed to mitigate the influence of engine vibration and gyroscope drift. The quaternion-based extended Kalman filter is implemented to fuse the sensors. This filter fuses the angular rates measured by the gyroscopes and the pseudo-attitude derived from the GPS velocity to estimate the attitude of the UAV. Simulations and experiment results indicate that the proposed method performs well both in short-term and long-term accuracy even though the gyroscopes are affected by drift and vibration noise, while the pseudo-attitude contains severe noise.

Orientation Estimation for Sensor Motion Tracking Using Interacting Multiple Model Filter

In this letter, we present a real-time orientation estimation and motion tracking scheme using interacting multiple model (IMM) based Kalman filtering method. Two nonlinear filters, quaternion-based extended Kalman filter (QBEKF) and gyroscope-based extended Kalman filter (GBEKF) are utilized in the proposed IMM-based orientation estimator for sensor motion state estimation. In the QBEKF, measurements from gyroscope, accelerometer and magnetometer are processed; while in the GBEKF, sole measurements from gyroscope are processed. The interacting multiple model algorithm is used for fusing the estimated states via adaptive model weighting. Simulation results validate the proposed design concept, and the scheme is capable of reducing overall estimation errors in sensor motion tracking.