Eric R. Bachmann

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

An extended Kalman filter for quaternion-based orientation estimation using MARG sensors

Presents an extended Kalman filter for real-time estimation of rigid body orientation using the newly developed MARG (magnetic, angular rate, and gravity) sensors. Each MARG sensor contains a three-axis magnetometer, a three-axis angular rate sensor, and a three-axis accelerometer. The filter represents rotations using quaternions rather than Euler angles, which eliminates the long-standing problem of singularities associated with attitude estimation. A process model for rigid body angular motions and angular rate measurements is defined. The process model converts angular rates into quaternion rates, which are integrated to obtain quaternions. The Gauss-Newton iteration algorithm is utilized to find the best quaternion that relates the measured accelerations and earth magnetic field in the body coordinate frame to calculated values in the earth coordinate frame. The best quaternion is used as part of the measurements for the Kalman filter. As a result of this approach, the measurement equations of the Kalman filter become linear, and the computational requirements are significantly reduced, making it possible to estimate orientation in real time. Extensive testing of the filter with synthetic data and actual sensor data proved it to be satisfactory. Test cases included the presence of large initial errors as well as high noise levels. In all cases the filter was able to converge and accurately track rotational motions.

A Simplified Quaternion-Based Algorithm for Orientation Estimation From Earth Gravity and Magnetic Field Measurements

Orientation of a static or slow-moving rigid body can be determined from the measured gravity and local magnetic field vectors. Some formulation of the QUaternion ESTimator (QUEST) algorithm is commonly used to solve this problem. Triads of accelerometers and magnetometers are used to measure gravity and local magnetic field vectors in sensor coordinates. In the QUEST algorithm, local magnetic field measurements affect not only the estimation of yaw but also that of roll and pitch. Due to the deviations in the direction of the magnetic field vector between locations, it is not desirable to use magnetic data in calculations that are related to the determination of roll and pitch. This paper presents a geometrically intuitive 3-degree-of-freedom (3-DOF) orientation estimation algorithm with physical meaning [which is called the factored quaternion algorithm (FQA)], which restricts the use of magnetic data to the determination of the rotation about the vertical axis. The algorithm produces a quaternion output to represent the orientation. Through a derivation based on half-angle formulas and due to the use of quaternions, the computational cost of evaluating trigonometric functions is avoided. Experimental results demonstrate that the proposed algorithm has an overall accuracy that is essentially identical to that of the QUEST algorithm and is computationally more efficient. Additionally, magnetic variations cause only azimuth errors in FQA attitude estimation. A singularity avoidance method is introduced, which allows the algorithm to track through all orientations.

Inertial and magnetic posture tracking for inserting humans into networked virtual environments

Rigid body orientation can be determined without the aid of a generated source using nine-axis MARG (Magnetic field, Angular Rate, and Gravity) sensor unit containing three orthogonally mounted angular rate sensors, three orthogonal linear accelerometers and three orthogonal magnetometers. This paper describes a quaternion-based complementary filter algorithm for processing the output data from such a sensor. The filter forms the basis for a system designed to determine the posture of an articulated body in real-time. In the system the orientation relative to an Earth-fixed reference frame of each limb segment is individually determined through the use of an attached MARG sensor. The orientations are used to set the posture of an articulated body model. Details of the fabrication of a prototype MARG sensor are presented. Calibration algorithms for the sensors and the human body model are also presented. Experimental results demonstrate the effectiveness of the tracking system and verify the correctness of the underlying theory.

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

Testing and evaluation of an integrated GPS/INS system for small AUV navigation

A Small Autonomous Underwater Vehicle Navigation System (SANS) is being developed at the Naval Postgraduate School. The SANS is an integrated Global Positioning System/Inertial Navigation System (GPS/INS) navigation system composed of low-cost and small-size components. It is designed to demonstrate the feasibility of using a low-cost strap-down inertial measurement unit (IMU) to navigate between intermittent GPS fixes. The present hardware consists of a GPS/DGPS receiver, IMU, compass, water speed sensor, water depth sensor, and a data processing computer. The software is based on a 12-state complementary filter that combines measurement data from all sensors to derive a vehicle position/orientation estimate. This paper describes hardware and software design and testing results of the SANS. It is shown that results from tilt table testing and bench testing provide an effective means for tuning filter gains. Ground vehicle testing verifies the overall functioning of the SANS and exhibits an encouraging degree of accuracy.

Estimation of Human Foot Motion During Normal Walking Using Inertial and Magnetic Sensor Measurements

A foot motion filtering algorithm is presented for estimating foot kinematics relative to an earth-fixed reference frame during normal walking motion. Algorithm input data are obtained from a foot-mounted inertial/magnetic measurement unit. The sensor unit contains a three-axis accelerometer, a three-axis angular rate sensor, and a three-axis magnetometer. The algorithm outputs are the foot kinematic parameters, which include foot orientation, position, velocity, acceleration, and gait phase. The foot motion filtering algorithm incorporates novel methods for orientation estimation, gait detection, and position estimation. Accurate foot orientation estimates are obtained during both static and dynamic motion using an adaptive-gain complementary filter. Reliable gait detection is accomplished using a simple finite state machine that transitions between states based on angular rate measurements. Accurate position estimates are obtained by integrating acceleration data, which has been corrected for drift using zero velocity updates. Algorithm performance is examined using both simulations and real-world experiments. The simulations include a simple but effective model of the human gait cycle. The simulation and experimental results indicate that a position estimation error of less than 1% of the total distance traveled is achievable using commonly available commercial sensor modules.

Design and implementation of MARG sensors for 3-DOF orientation measurement of rigid bodies

This presents the latest design and implementation of the magnetic, angular rate, and gravity (MARG) sensor module. The MARG sensor module is designed for measuring 3-DOF orientations in real time without singularities. Each MARG sensor contains orthogonally mounted triads of micromachined rate sensors, accelerometers, and magnetometers for a total of nine sensor components. With an integrated microcontroller, the overall factor is less than one cubic inch. Digital data output rate is 100 Hz. To simplify calibration procedures and filtering algorithms, it is important that the response of the individual sensor components is linear within the typical operating regions. Experiments were conducted utilizing a precision tilt table and results indicate that all the sensor components are linear. A simple hand calibration method that requires no specialized equipment is also described. It was validated by experiments that indicate hand calibration produces results that are nearly equivalent to those obtained following precision tilt table calibration.

An improved quaternion-based Kalman filter for real-time tracking of rigid body orientation

This paper presents an improved Kalman filter for real-time tracking of human body motions. An earlier version of the filter was presented at IROS 2001. Since then, the filter has been substantially improved. Real-time tracking of rigid body orientation is accomplished using the MARG (magnetic, angular rate, and gravity) sensors. A MARG sensor measures the three-dimensional local magnetic field, three-dimensional angular rate, and three-dimensional acceleration. A Kalman filter is designed to process measurements provided by the MARG sensors, and to produce real-time orientation represented in quaternions. There are many design decisions as related to choice of state vectors, output equations, process model, etc. The filter design presented in this paper utilizes the Gauss-Newton method for parameter optimization in conjunction with Kalman filtering. The use of the Gauss-Newton method, particularly the reduced-order implementation introduced in the paper, significantly simplifies the Kalman filter design, and reduces computational requirements.

Limitations of Attitude Estimnation Algorithms for Inertial/Magnetic Sensor Modules

This paper discuss the theory of orientation estimation algorithms designed for inertial/magnetic sensor modules and briefly describe three types of sensor modules. Specifically, the modules discussed are the InterSense InertiaCube, the MicroStrain 3DM-G, and the MARG III. The MARG III was designed by the authors and manufactured by McKinney Technology. Basic background on the ambient magnetic field of the Earth and how it is distorted by ferrous objects and electrically powered devices is then provided. Methods of calibrating magnetic field variations are then discussed.