This paper considers the problem of obtaining good attitude estimates from measurements obtained from typical low cost inertial measurement units. The outputs of such systems are characterized by high noise levels and time varying additive biases. We formulate the filtering problem as deterministic observer kinematics posed directly on the special orthogonal group SO (3) driven by reconstructed attitude and angular velocity measurements. Lyapunov analysis results for the proposed observers are derived that ensure almost global stability of the observer error. The approach taken leads to an observer that we term the direct complementary filter. By exploiting the geometry of the special orthogonal group a related observer, termed the passive complementary filter, is derived that decouples the gyro measurements from the reconstructed attitude in the observer inputs. Both the direct and passive filters can be extended to estimate gyro bias online. The passive filter is further developed to provide a formulation in terms of the measurement error that avoids any algebraic reconstruction of the attitude. This leads to an observer on SO(3), termed the explicit complementary filter, that requires only accelerometer and gyro outputs; is suitable for implementation on embedded hardware; and provides good attitude estimates as well as estimating the gyro biases online. The performance of the observers are demonstrated with a set of experiments performed on a robotic test-bed and a radio controlled unmanned aerial vehicle.

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Nonlinear Complementary Filters on the Special Orthogonal Group

Digital Control Of Dynamic Systems This well-respected, market-leading text discusses the use of digital computers in the real-time control of dynamic systems. The emphasis is on the design of digital controls that achieve good dynamic response and small errors while using signals that are sampled in time and quantized in amplitude. Digital Control of Dynamic Systems (3rd Edition): Franklin ... This well-respected, market-leading text discusses the use of digital computers in the real-time control of dynamic systems. The emphasis is on the design of digital controls that achieve good dynamic response and small errors while using signals that are sampled in time and quantized in amplitude. Digital Control of Dynamic Systems: Gene F. Franklin ... Digital Control of Dynamic Systems, 2nd Edition. Gene F. Franklin, Stanford University. J. David Powell, Stanford University Digital Control of Dynamic Systems, 2nd Edition Pearson This well-respected work discusses the use of digital computers in the real-time control of dynamic systems. The emphasis is on the design of digital controls that achieve good dynamic response and small errors while using signals that are sampled in time and quantized in amplitude. MATLAB statements and problems are thoroughly and carefully integrated throughout the book to offer readers a complete design picture. Digital Control of Dynamic Systems, 3rd Edition ... Digital control of dynamic systems | Gene F. Franklin, J. David Powell, Michael L. Workman | download | B–OK. Download books for free. Find books Digital control of dynamic systems | Gene F. Franklin, J ... Abstract This well-respected work discusses the use of digital computers in the real-time control of dynamic systems. The emphasis is on the design of digital controls that achieve good dynamic... (PDF) Digital Control of Dynamic Systems Digital Control of Dynamic Systems, Addison.pdf There is document Digital Control of Dynamic Systems, Addison.pdfavailable here for reading and downloading. Use the download button below or simple online reader. The file extension PDFand ranks to the Documentscategory. Digital Control of Dynamic Systems, Addison.pdf Download ... Automatic control is the science that develops techniques to steer, guide, control dynamic systems. These systems are built by humans and must perform a specific task. Examples of such dynamic systems are found in biology, physics, robotics, finance, etc. Digital Control means that the control laws are implemented in a digital device, such as a microcontroller or a microprocessor. Introduction to Digital Control of Dynamic Systems And ... The discussions are clear, nomenclature is not hard to follow and there are plenty of worked examples. The book covers discretization effects and design by emulation (i.e. design of continuous-time control system followed by discretization before implementation) which are not to be found on every book on digital control. Amazon.com: Customer reviews: Digital Control of Dynamic ... Find helpful customer reviews and review ratings for Digital Control of Dynamic Systems (3rd Edition) at Amazon.com. Read honest and unbiased product reviews from our users. Amazon.com: Customer reviews: Digital Control of Dynamic ... 1.1.2 Digital control Digital control systems employ a computer as a fundamental component in the controller. The computer typically receives a measurement of the controlled variable, also often receives the reference input, and produces its output using an algorithm. Introduction to Applied Digital Control From the Back Cover This well-respected, marketleading text discusses the use of digital computers in the real-time control of dynamic systems. The emphasis is on the design of digital controls that achieve good dynamic response and small errors while using signals that are sampled in time and quantized in amplitude. Digital Control of Dynamic Systems (3rd Edition) Test Bank `Among the advantages of digital logic for control are the increased flexibility `of the control programs and the decision-making or logic capability of digital `systems, which can be combined with the dynamic control function to meet `other system requirements. `The digital controls studied in this book are for closed-loop (feedback) Every day, eBookDaily adds three new free Kindle books to several different genres, such as Nonfiction, Business & Investing, Mystery & Thriller, Romance, Teens & Young Adult, Children's Books, and others.

http://ieeexplore.ieee.org/iel6/29/26151/01163502.pdf

Digital control of dynamic systems

In this paper, a quaternion based extended Kalman filter (EKF) is developed for determining the orientation of a rigid body from the outputs of a sensor which is configured as the integration of a tri-axis gyro and an aiding system mechanized using a tri-axis accelerometer and a tri-axis magnetometer. The suggested applications are for studies in the field of human movement. In the proposed EKF, the quaternion associated with the body rotation is included in the state vector together with the bias of the aiding system sensors. Moreover, in addition to the in-line procedure of sensor bias compensation, the measurement noise covariance matrix is adapted, to guard against the effects which body motion and temporary magnetic disturbance may have on the reliability of measurements of gravity and earth's magnetic field, respectively. By computer simulations and experimental validation with human hand orientation motion signals, improvements in the accuracy of orientation estimates are demonstrated for the proposed EKF, as compared with filter implementations where either the in-line calibration procedure, the adaptive mechanism for weighting the measurements of the aiding system sensors, or both are not implemented.

Quaternion-based extended Kalman filter for determining orientation by inertial and magnetic sensing

Location sharing and tracking using mobile phones or other wireless devices

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.

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

The design of inexpensive multi-sensor attitude determination systems is discussed. The systems discussed fuse information from a triad of solid state rate gyros with an aiding system mechanized using GPS or magnetometers and accelerometers. Euler angle and quaternion-based sensor fusion algorithms are developed. Methods for gain scheduling and estimator pole placement are presented. Using simulation and flight test results, it is shown that quaternion-based algorithms simplify gain scheduling and improve transient response.

Design of multi-sensor attitude determination systems

Attitude determination systems that use inexpensive sensors and are based on computationally efficient and robust algorithms are indispensable for real-time vehicle navigation, guidance and control applications. This paper describes an attitude determination system that is based on two vector measurements of non-zero, non-colinear vectors. The algorithm is based on a quaternion formulation of Wahba's (1966) problem, whereby the error quaternion (q/sub e/) becomes the observed state and can be cast into a standard linear measurement equation. Using the Earth's magnetic field and gravity as the two measured quantities, a low-cost attitude determination system is proposed. An iterated least-squares solution to the attitude determination problem is tested on simulated static cases, and shown to be globally convergent. A time-varying Kalman filter implementation of the same formulation is tested on simulated data and experimental data from a maneuvering aircraft. The time-varying Kalman filter implementation of this algorithm is exercised on simulated and real data collected from an inexpensive triad of accelerometers and magnetometers. The accelerometers in conjunction with the derivative of GPS velocity provided a measure of the gravitation field vector and the magnetometers measured the Earth's magnetic field vector. Tracking errors on experimental data are shown to be less than 1 degree mean and standard deviation of approximately 11 degrees in yaw, and 3 degrees in pitch and roll. Best case performance of the system during maneuvering is shown to improve standard deviations to approximately 3 degrees in yaw, and 1.5 degrees in pitch and roll.

/pdf/a-gyro-free-quaternion-based-attitude-determination-system-3b4hc57k4z.pdf

A gyro-free quaternion-based attitude determination system suitable for implementation using low cost sensors

An inexpensive Attitude Heading Reference System (AHRS) for general aviation applications is developed by fusing low cost ($20-$1000) automotive grade inertial sensors with GPS. The inertial sensor suit consists of three orthogonally mounted solid state rate gyros. GPS is used for attitude determination in a triple antenna ultra short baseline configuration. A complementary filter is used to combine the information from the inertial sensors with the attitude information derived from GPS. The inertial sensors provide attitude information at a sufficiently high bandwidth to drive an inexpensive glass-cockpit type display for pilot-in-the-loop control. The low bandwidth GPS attitude is used to calibrate the rate gyro biases on-line. Data collected during laboratory testing is used to construct error models for the inertial sensors. Analysis based on these models shows that the system can coast through momentary GPS outages lasting 2 minutes with attitude errors less than 6 degrees. Actual performance observed during ground and flight tests with GPS off was found to be substantially better than that predicted by manufacturer supplied specification sheets. Based on this, it is concluded that off-line calibration combined with GPS based in-flight calibration can dramatically improve the performance of inexpensive automotive grade inertial sensors. Data collected from flight tests indicate that some of the automotive grade inertial sensors (180 deg/hr) can perform near the low end of tactical grade (10 deg/hr) sensors for short periods of time after being calibrated on-line by GPS.

A low-cost GPS/inertial attitude heading reference system (AHRS) for general aviation applications

Possible configurations for a general aviation autonomous navigation system are studied. Doubtless, an advanced GPS receiver is a "must have" system component. GPS has had some outages due to unintentional interference or even intentional jamming and aircraft should be able to navigate through such an event. Natural candidates for GPS backup are inertial sensors, magnetic compass, and air-speed sensors. All these sensors can be calibrated during GPS availability. Moreover, for dead reckoning systems, wind velocity can be estimated as well. This paper presents an original statistical model for wind variations that matches actual data very well. Using this model and a parametric family of inertial measurement sensors, horizontal position errors during a GPS outage are compared for a variety of configurations: a dead reckoning system, stand alone inertial sensors and inertial sensors integrated with the dead reckoning system.

The role of dead reckoning and inertial sensors in future general aviation navigation

Stanford University has developed a low-cost prototype synthetic vision system and flight tested it onboard general aviation aircraft. The display aids pilots by providing an 'out the window' view, making visualization of the desired flight path a simple task. Predictor symbology provides guidance on straight and curved paths presented in a 'tunnel- in-the-sky' format. Based on commodity PC hardware to achieve low cost, the Tunnel Display system uses differential GPS (typically from Stanford prototype Wide Area Augmentation System hardware) for positioning and GPS-aided inertial sensors for attitude determination. The display has been flown onboard Piper Dakota and Beechcraft Queen Air aircraft at several different locations. This paper describes the system, its development, and flight trials culminating with tests in Alaska during the summer of 1998. Operational experience demonstrated the Tunnel Display's ability to increase flight- path following accuracy and situational awareness while easing the task instrument flying.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

J.D. Powell

Papers

Design of multi-sensor attitude determination systems

A gyro-free quaternion-based attitude determination system suitable for implementation using low cost sensors

A low-cost GPS/inertial attitude heading reference system (AHRS) for general aviation applications

The role of dead reckoning and inertial sensors in future general aviation navigation

Alaskan flight trials of a synthetic vision system for instrument landings of a piston twin aircraft