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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., Published in IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, v61 n7 p2059- 2072, Jul 2012.

There are three major thrusts to this thesis. The first was to design and build a device to measure ground speed for testing the position estimating capabilities of the Small Autonomous Navigation System (SANS) filter. The ground tests consisted by placing the SANS unit on a golf cart and maneuvering it along a known track. The speed sensing device uses a bicycle wheel attached to the golf cart along with an appropriate time to speed software conversion. The next problem was to determine if the existing paddle wheel in use would be accurate enough for the SANS to conduct underway tests. To perform this, a mechanism had to be built to channel water and measure its speed while allowing the paddle wheel to be in the flow. Finally, the electronic compass was found to have heading dependent errors, thus a test was designed to determine its deviation. This was performed by swinging the compass using a transit aligned with its axis. This established a deviation table that was inserted into the SANS code, further refining its directional capabilities. As a final test for determining the effectiveness of the calibrated inputs, tests were conducted that showed that the SANS filter is capable of obtaining 3 meter accuracy with no Global Positioning Update for an excess of two minutes. This is well beyond the initial goals set for the system, http://archive.org/details/calbrationndeval109458043, Lieutenant, United States Navy, Approved for public release; distribution is unlimited.

A foot motion filtering algorithm is presented for es- timating 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 inte- grating 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.

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., Published in the Journal of IEEE Transactions on Instrumentation and Measurement, v57 n3 p638-650, March 2008.

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.

This article describes several experiments designed to examine small-scale magnetic interference caused by typical objects and how this interference can be expected to affect the accuracy of orientation estimates produced using data from inertial/magnetic sensor modules. The results provide insight into the limitations of inertial/magnetic sensor module orientation tracking. They indicate that while errors due to local variations in a common room environment caused by individual objects can be significant, in most cases they can be avoided by maintaining a separation of approximately 1 m from the source of interference. The interference caused by combined sources in a noisy indoor environment can, however, be quite complex. The results also indicate that inertial/magnetic sensor modules can be used to track link orientation of a mechanical arm relative to an Earth-fixed reference frame., Published in the Journal of IEEE Robotics and Automation Magazine, p76-87, September 2007.

Inertial/Magnetic tracking is based on the use of sensors containing three orthogonally mounted angular rate sensors, three orthogonal linear accelerometers and three orthogonal magnetometers to determine independently the orientation of each link of an articulated rigid body. Inertial/magnetic orientation tracking could be applied to a broad range of problems which require real-time tracking of an articulated structure without being continuously dependent upon an artificially generated source. This research focuses on the goal of developing and demonstrating wireless full body tracking using MARG sensor modules. During the period of this report, six manuscripts were submitted for peer-reviewed publication. Of these six, five have been accepted. These include three journal publications and two conference papers. In additions, scientific advances have been made in the following areas: * Study of the Magnetic Effects on Inertial/Magnetic Sensor Modules * Development of a singularity free Factored Quaternion Algorithm * Development of an advanced Kalman Filter for Inertial/Magnetic Body Tracking *Initial development in using inertial/magnetic sensors for position tracking., The original document contains color images.

Limitations of Attitude Estimation Algorithms for Inertial/Magnetic Sensor Modules

Numerous applications require a self-contained personal navigation system that works in indoor and outdoor environments, does not require any infrastructure support, and is not susceptible to jamming. Posture tracking with an array of inertial/magnetic sensors attached to individual human limb segments has been successfully demonstrated. The "sourceless" nature of this technique makes possible full body posture tracking in an area of unlimited size with no supporting infrastructure. Such sensor modules contain three orthogonally mounted angular rate sensors, three orthogonal linear accelerometers and three orthogonal magnetometers. This paper describes a method for using accelerometer data combined with orientation estimates from the same modules to calculate position during walking and running. The periodic nature of these motions includes short periods of zero foot velocity when the foot is in contact with the ground. This pattern allows for precise drift error correction. Relative position is calculated through double integration of drift corrected accelerometer data. Preliminary experimental results for various types of motion including walking, side stepping, and running.

Real-time tracking of the orientation or attitude of rigid bodies has wide applications in robotics [1], helicopters [2], teleoperation, augmented reality, and virtual reality [3].

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.

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., Published in the Journal of IEEE Transactions on Robotics, v22 n6 p1216-1227, December 2006.

One embodiment the invention includes a method of determining an orientation of a sensor. The method includes measuring a local magnetic field vector and a local gravity vector and using those measurements to determine the orientation of the sensor. Embodiments can include measuring the magnetic field vector and the local gravity vector using quatemion coordinates. Another embodiment includes measuring a local magnetic field vector, a local gravity vector, and the angular velocity of the sensor. These three vectors are processed to determine the orientation of the sensor. In one embodiment the three vectors can all be measured in quatemion coordinates. Another method embodiment includes detennining a local gravity vector by providing a acceleration detector, moving the detector from a start point to an end point over a time period, and summing acceleration measurements over the time period. The local gravity vector is calculated using the summed acceleration measurements.

A human body motion tracking system based on use of the MARG (Magnetic, Angular Rate, and Gravity) sensors has been under development at the Naval Postgraduate School and Miami University. The design of a quaternion- based Kalman filter for processing the MARG sensor data was described in [1]. This paper presents the real-time implementation and testing results of the quaternion-based Kalman filter. Experimental results validate the Kalman filter design, and show the feasibility of the MARG sensors for real- time human body motion tracking.

Rigid body orientation can be estimated in a sourceless manner through the use of small three degree of freedom sensor modules containing orthogonally mounted triads of micromachined angular rate sensors accelerometers, and magnetometers. With proper filter design, drift errors can be eliminated However, variations in the direction of the local magnetic field reference vector can cause errors in the estimated orientation. The experimental work described in this paper attempts to quantify these errors with an eye toward the development of corrective algorithms. To determine the types and magnitudes of errors that can be expected, three different types of inertial/magnetic sensor modules were subjected to controlled changes in the direction and magnitude of the local magnetic field. The amount of magnetic variation caused by several common objects was also measured in order to gain insight into the magnitude of errors that can be expected during operation in a typical environment. The experiments indicate that variations in the direction of the local magnetic field lead to errors only in azimuth estimation when using inertial/magnetic sensor modules. In a common roam environment, errors due to local variations caused by objects such as electrical heaters CRT monitors, and metal furniture can be expected to be no more than 16 degrees. In most causes these errors can be avoided by maintaining a separation of approximately two feet from the source of interference., Presented at the Proceedings of the 2004 IEEE International Conference on Robotics and Automation held in New Orleans, April 2004.

Real-time tracking of human body motion has applications in tele-operation, synthetic reality and others. A motion tracking system based on use of the MARG sensor has been under development at Naval Postgraduate School and Miami University. The Magnetic, Angular Rate and Gravity (MARG) sensor modules use B combination of three orthogonal magnetometers, three orthogonal angular rate sensors, and three orthogonal accelerometers to measure 3-D orientation of individual limb segments in order to determine posture. This paper presents the latest results of the MARG human body motion tracking system. The design and implementation of a Control Interface Unit (CIU), a real-time 3-D human avatar called Andy, and a concurrent client-server program are discussed. Experimental testing and evaluation of the overall MARG system is also presented. The system is able to track multiple human limbs in real time. The captured human motion data can be visualized over the Internet by multiple clients using the 3-D avatar., Presented at the Proceedings of the 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems held in Sendai, Japan on 28 September - 2 October 2004.

Real-time tracking of human body motion has applications in tele-operation, synthetic reality and others. A motion tracking system based on use of the MARG senson has been under development at Naval Postgraduate School and Miami University. The Magnetic, Angular Rate, and Gravity (MARG) sensor modules use B combination of three orthogonal magnetometers, three orthogonal angular rate sensors, and tbree orthogonal accelerometers to measure 3-D orientation of individual limb segments in order to determine posture. This paper presents the latest results of the MARG human body motion tracUng system. The design and implementation of a Control Interface Unit (CIU), a real-time 3-D human avatar called “Andy,” and a concurrent client-server program are discussed. Experimental testing and evaluation of the overall MARG system is also presented. The system is able to track multiple human limbs in real time. Tbe captured human motion data can be visualired over the Internet by multiple clients usiog the 3-0 avatar.

Rigid body orientation can be estimated in a “sourceless manner” through the use of small three degree of freedom sensor modules containing orthogonally mounted triads of micromachined angular rate sensors, accelerometers, and magnetometers. With proper filter design, drift errors can be eliminated. However, variations in the direction of the local magnetic field reference vector can cause errors in the estimated orientation. The experimental work described in this paper attempts to quantify these errors with an eye toward the development of corrective algorithms. To determine the types and magnitudes of errors that can be expected, three different types of inertiaVmagnetic sensor modules were subjected to controlled changes in the direction and magnitude of the local magnetic field. The amount of magnetic variation caused by several common objects was also measured in order to gain insight into the magnitude of errors that can be expected during operation in a typical environment. The experiments indicate that variations in the direction of the local magnetic field lead to errors only in azimuth estimation when using inertidmagnetic sensor modules. In a common roam environment, errors due to local variations caused by objects such as electrical heaters, CRT monitors, and metal furniture can be expected to be no more than 16 degrees. In most causes these errors can be avoided by maintaining a separation of approximately two feet from the source of interference.

One embodiment the invention comprises a method of determining an orientation of a sensor. The method includes measuring a local magnetic field vector and a local gravity vector and using those measurements to determine the orientation of the sensor. Embodiments can include measuring the magnetic field vector and the local gravity vector using quaternion coordinates. Another embodiment comprises measuring a local magnetic field vector, a local gravity vector, and the angular velocity of the sensor. These three vectors are processed to determine the orientation of the sensor. In one embodiment the three vectors can all be measured in quaternion coordinates. Another method embodiment comprises determining a local gravity vector by providing a acceleration detector, moving the detector from a start point to an end point over a time period, and summing acceleration measurements over the time period. The local gravity vector is calculated using the summed acceleration measurements. A system embodiment of the present invention includes a body having mounted thereon at least one sensor. The at least one sensor is configured to output orientation inform a - tion to at least one processing unit that inputs the orientation information into a synthetic environment. The system also can include a display for displaying the orientation of the body with respect to the synthetic environment.

This paper 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 form 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., Presented at the Proceedings of the 2003 IEEE International Conference on Robotics and Automation held in Taipei, Taiwan on 14-19 September 2003.

Human body posture can be tracked in real-time using small inexpensive inertial/magnetic sensor modules to measure the orientation of individual limb segments. To perform this task inertial/magnetic sensors generally contain: three orthogonally mounted angular rate sensors, three orthogonally mounted accelerometers, and three orthogonally mounted magnetometers. These sensors must be small and light enough to be securely attached to major limb segments and avoid user encumbrance. Sensor data must be processed by an efficient filtering algorithm that is able to produce accurate orientation estimates without singularities in all attitudes and does not require still periods to correct for drift. This paper discusses the design of a sourceless body tracking system with an emphasis on sensor and efficient filter design. Various methods for mitigating small transient orientation errors due to variability in the direction of the local magnetic field vector are also described.

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.

This paper presents the latest design and implementation of the Magnetic, Angular Rate, and Gravity (MRG) sensor module. The MRG sensor module is designed for measuring 3-DOF orientations in real time without singularities. Each MRG 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 form factor is less than one cubic inch. Digital data output rate i . ~1 00 Hz. To simp/!@ calibration procedures and filtering algorithms, it is important that the response ojthr individual sensor componenrs 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.

This thesis proposes the design of an improved Magnetic, Angular Rate, Gravity (MARG) Body Tracking System. The current MARG Body Tracking System is limited to tracking three limb-segments. The MARG sensors are physically connected to a desktop computer by cables. In this thesis, a multiplexing circuit was implemented to allow tracking of 15 limb-segments. Processing was moved from a desktop computer to a wearable computer and wireless communication was implemented using an IEEE 802.1 lb spread, spectrum wireless LAN. The resultant system is able to track the entire human body and is untethered. The range of the system is the same as that of the wireless LAN which can be extended with the use of repeaters. This thesis work will ultimately allow human insertion into virtual environments for training and other applications.

Current motion tracking technologies fail to provide accurate wide area tracking of multiple users without interference and occlusion problems. This research proposes to overcome current limitations using nine-axis magnetic/angular/rate/gravity (MARG) sensors combined with a quaternion-based complementary filter algorithm capable of continuously correcting for drift and following angular motion through all orientations without singularities. Primarily, this research involves the development of a prototype tracking system to demonstrate the feasibility of MARG sensor body motion tracking Mathematical analysis and computer simulation are used to validate the correctness of the complementary filter algorithm The implemented human body model utilizes the world-coordinate reference frame orientation data provided in quaternion form by the complementary filter and orients each limb segment independently. Calibration of the model and the inertial sensors is accomplished using simple but effective algorithms. Physical experiments demonstrate the utility of the proposed system by tracking of human limbs in real-time using multiple MARG sensors. The system is "sourceless" and does not suffer from range restrictions and interference problems. This new technology overcomes the limitations of motion tracking technologies currently in use. It has the potential to provide wide area tracking of multiple users in virtual environment and augmented reality applications., Sponsored in part by the Navy Modeling and Simulation Office, Washington, DC.

The filter represents rotations using quaternions rather than Euler angles, which eliminates the long-standing problem of singularities associated with those angles. 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 in turn integrated to obtain quaternions. The outputs of the model are values of three-dimensional angular rates, three-dimensional linear accelerations, and three-dimensional magnetic field vector. Gauss-Newton iteration is utilized to find the best quaternion that relates the measured linear accelerations and earth magnetic field in the body coordinate frame to calculated values in the earth coordinate frame. The quaternion obtained from the optimization algorithm is used as part of the observations for the Kalman filter. As a result, the measurement equations become linear. A new approach to attitude estimation is introduced in this thesis. The computational requirements related to the extended Kalman filter developed using this approach are significantly reduced, making it possible to estimate attitude in real-time. Extensive static and dynamic simulation of the filter using Matlab proved it to be robust. 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 attitude.

At the Naval Postgraduate School (NPS), a small AUV navigation system (SANS) was developed for research in support of shallow-water mine countermeasures and coastal environmental monitoring The objective of this thesis is to test and evaluate the SANS performance after tuning the filter gains through a series of testing procedures. The new version of SANS (SANS III) used new hardware components which were smaller, cheaper, and more reliable. A PC/l O4 computer provided more computing power and, increased the reliability and compatibility of the system. Implementing an asynchronous Kalman filter in the position and velocity estimation part of the navigation subsystem improved the navigation accuracy significantly. To determine and evaluate the overall system performance, ground vehicle testing was conducted. Test results showed that the SANS III was able to navigate within + 15 feet of Global Positioning track with no Global Positioning update for three minutes.

A small AUV navigation system (SANS) has been developed at the Naval Postgraduate School. The SANS is an integrated GPS/INS navigation system composed of low-cost, small-size components. It is designed to demonstrate the feasibility of using a low-cost inertial measurement unit to navigate between intermittent GPS fixes. This paper reports recent improvements to the SANS hardware, latest testing results after compensating heading-dependent derivations in the TCM-2 compass measurements, and development of an asynchronous Kalman filter for improved position estimation