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All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

The accuracy of dynamic attitude propagation

Propagating attitude by integrating Euler's equation for rigid body motion has long been suggested for the Earth Radiation Budget Satellite (ERBS) but until now has not been implemented. Because of limited Sun visibility, propagation is necessary for yaw determination. With the deterioration of the gyros, dynamic propagation has become more attractive. Angular rates are derived from integrating Euler's equation with a stepsize of 1 second, using torques computed from telemetered control system data. The environmental torque model was quite basic. It included gravity gradient and unshadowed aerodynamic torques. Knowledge of control torques is critical to the accuracy of dynamic modeling. Due to their coarseness and sparsity, control actuator telemetry were smoothed before integration. The dynamic model was incorporated into existing ERBS attitude determination software. Modeled rates were then used for attitude propagation in the standard ERBS fine-attitude algorithm. In spite of the simplicity of the approach, the dynamically propagated attitude matched the attitude propagated with good gyros well for roll and yaw but diverged up to 3 degrees for pitch because of the very low resolution in pitch momentum wheel telemetry. When control anomalies significantly perturb the nominal attitude, the effect of telemetry granularity is reduced and the dynamically propagated attitudes are accurate on all three axes.

Harvie, E.↗
NASA NTRS1990

A star pattern recognition algorithm for autonomous attitude determination

The star-pattern recognition algorithm presented allows the advanced Full-sky Autonomous Star Tracker (FAST) device, such as the projected ASTROS II system of the Mariner Mark II planetary spacecraft, to reliably ascertain attitude about all three axes. An ASTROS II-based FAST, possessing an 11.5 x 11.5 deg field of view and 8-arcsec accuracy, can when integrated with an all-sky data base of 4100 guide stars determine its attitude in about 1 sec, with a success rate close to 100 percent. The present recognition algorithm can also be used for automating the acquisition of celestial targets by astronomy telescopes, autonomously updating the attitude of gyro-based attitude control systems, and automating ground-based attitude reconstruction.

Van Bezooijen, R. W. H.↗
NASA NTRS1978

Approximate algorithms for fast optimal attitude computation

Fast accurate algorithms are presented for computing an optimal attitude which minimizes a quadratic loss function. These algorithms compute an optimal rotation which carries a set of reference vectors into a set of corresponding observation vectors. Simplifications of these algorithms are obtained for the case of small rotation angles. Applications to the Magsat mission are discussed.

Shuster, M. D.↗
NASA NTRS1978

HEAO attitude reference design

The paper deals with the precision onboard attitude reference implemented as part of the attitude control and determination subsystem for the three High Energy Astronomy Observatories (HEAO-A, HEAO-B, and HEAO-C) in the HEAO scientific spacecraft program. The first observatory (HEAO-A, designated HEAO-1 when in orbit) was launched successfully into near-earth orbit on August 12, 1977. The HEAO attitude reference, analysis techniques for performance prediction, and flight results from the HEAO-1 observatory during its first months of operation. The HEAO-B design is specifically described and analyzed in terms of gyro processing, kinematic integration, ground update algorithm, and star tracker update algorithm. Attitude reference performance estimates are also discussed. It is shown that the orbital performance of the attitude reference correlates very well with the developmental predictions, thereby validating the analytical techniques used during the development. This validation provides a firm basis from which to extrapolate to other applications and related design concepts.

Hoffman, D. P.↗
NASA NTRS1993

Attitude determination using vector observations: A fast optimal matrix algorithm

The attitude matrix minimizing Wahba's loss function is computed directly by a method that is competitive with the fastest known algorithm for finding this optimal estimate. The method also provides an estimate of the attitude error covariance matrix. Analysis of the special case of two vector observations identifies those cases for which the TRIAD or algebraic method minimizes Wahba's loss function.

Markley, F. Landis↗
NASA NTRS1993

Attitude determination using vector observations - A fast optimal matrix algorithm

The attitude matrix minimizing Wahba's loss function is computed directly by a method that is competitive with the fastest known algorithm for finding this optimal estimate. The method also provides an estimate of the attitude error covariance matrix. Analysis of the special case of two vector observations identifies those cases for which the TRIAD or algebraic method minimizes Wahba's loss function.

Markley, F. L.↗
NASA NTRS1990

On-board attitude determination and control algorithms for SAMPEX

Algorithms for onboard attitude determination and control of the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX) were developed. The algorithms include spacecraft ephemeris and geomagnetic field models, attitude determination with 2 degree accuracy, control of pitch axis pointing to the sun and yaw axis pointing away from the Earth to achieve control of pitch axis within 5 degrees of sunline, momentum unloading, and nutation damping. The closed loop simulations were performed on a VAX 8830 using a prototype version of the on-board software.

Flatley, Thomas W.↗
NASA NTRS1981

Efficient algorithms for single-axis attitude estimation

The computationally efficient algorithms determine attitude from the measurement of art lengths and dihedral angles. The dependence of these algorithms on the solution of trigonometric equations was reduced. Both single time and batch estimators are presented along with the covariance analysis of each algorithm.

Shuster, M. D.↗
NASA NTRS1996

REQUEST: A Recursive QUEST Algorithm for Sequential Attitude Determination

In order to find the attitude of a spacecraft with respect to a reference coordinate system, vector measurements are taken. The vectors are pairs of measurements of the same generalized vector, taken in the spacecraft body coordinates, as well as in the reference coordinate system. We are interested in finding the best estimate of the transformation between these coordinate system.s The algorithm called QUEST yields that estimate where attitude is expressed by a quarternion. Quest is an efficient algorithm which provides a least squares fit of the quaternion of rotation to the vector measurements. Quest however, is a single time point (single frame) batch algorithm, thus measurements that were taken at previous time points are discarded. The algorithm presented in this work provides a recursive routine which considers all past measurements. The algorithm is based on on the fact that the, so called, K matrix, one of whose eigenvectors is the sought quaternion, is linerly related to the measured pairs, and on the ability to propagate K. The extraction of the appropriate eigenvector is done according to the classical QUEST algorithm. This stage, however, can be eliminated, and the computation simplified, if a standard eigenvalue-eigenvector solver algorithm is used. The development of the recursive algorithm is presented and illustrated via a numerical example.

Bar-Itzhack, Itzhack Y.↗
NASA NTRS1986

Determining Calibration Constants for Attitude Measurements

Algorithm based on method of least squares determines calibration constants of seismic instruments for precise attitude measurements. Algorithm programed and run successfully on commercially available desk-top computer. Simplifies determinations of accelerometer calibration constants, and used in field to verify accelerometer stability.

Tcheng, P.↗
NASA NTRS1988

Determining Spacecraft Attitude For Planetary Mapping

New algorithm calculates attitude with accuracy to spare. Report describes algorithm for use in determining attitude of spacecraft from incremental-angle output of strapdown gyroscope and star-scanner measurements. Highlights detail of underlying theories and strategies. Presents results of simulation to demonstrate capability of algorithm, and discusses possible applications.

Huang, Whitak H.↗
NASA NTRS1993

Testing of the on-board attitude determination and control algorithms for SAMPEX

Algorithms for on-board attitude determination and control of the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX) have been expanded to include a constant gain Kalman filter for the spacecraft angular momentum, pulse width modulation for the reaction wheel command, an algorithm to avoid pointing the Heavy Ion Large Telescope (HILT) instrument boresight along the spacecraft velocity vector, and the addition of digital sun sensor (DSS) failure detection logic. These improved algorithms were tested in a closed-loop environment for three orbit geometries, one with the sun perpendicular to the orbit plane, and two with the sun near the orbit plane - at Autumnal Equinox and at Winter Solstice. The closed-loop simulator was enhanced and used as a truth model for the control systems' performance evaluation and sensor/actuator contingency analysis. The simulations were performed on a VAX 8830 using a prototype version of the on-board software.

Mccullough, Jon D.↗
NASA NTRS2010

Spacecraft Attitude Tracking and Maneuver Using Combined Magnetic Actuators

The accuracy of spacecraft attitude control using magnetic actuators only is low and on the order of 0.4-5 degrees. The key reason is that the magnetic torque is two-dimensional and it is only in the plane perpendicular to the magnetic field vector. In this paper novel attitude control algorithms using the combination of magnetic actuators with Reaction Wheel Assembles (RWAs) or other types of actuators, such as thrusters, are presented. The combination of magnetic actuators with one or two RWAs aligned with different body axis expands the two-dimensional control torque to three-dimensional. The algorithms can guarantee the spacecraft attitude and rates to track the commanded attitude precisely. A design example is presented for Nadir pointing, pitch and yaw maneuvers. The results show that precise attitude tracking can be reached and the attitude control accuracy is comparable with RWAs based attitude control. The algorithms are also useful for the RWAs based attitude control. When there are only one or two workable RWAs due to RWA failures, the attitude control system can switch to the control algorithms for the combined magnetic actuators with the RWAs without going to the safe mode and the control accuracy can be maintained.

Zhou, Zhiqiang↗
NASA NTRS2012

Spacecraft Attitude Tracking and Maneuver Using Combined Magnetic Actuators

A paper describes attitude-control algorithms using the combination of magnetic actuators with reaction wheel assemblies (RWAs) or other types of actuators such as thrusters. The combination of magnetic actuators with one or two RWAs aligned with different body axis expands the two-dimensional control torque to three-dimensional. The algorithms can guarantee the spacecraft attitude and rates to track the commanded attitude precisely. A design example is presented for nadir-pointing, pitch, and yaw maneuvers. The results show that precise attitude tracking can be reached and the attitude- control accuracy is comparable with RWA-based attitude control. When there are only one or two workable RWAs due to RWA failures, the attitude-control system can switch to the control algorithms for the combined magnetic actuators with the RWAs without going to the safe mode, and the control accuracy can be maintained. The attitude-control algorithms of the combined actuators are derived, which can guarantee the spacecraft attitude and rates to track the commanded values precisely. Results show that precise attitude tracking can be reached, and the attitude-control accuracy is comparable with 3-axis wheel control.

Zhou, Zhiqiang↗
NASA NTRS1995

Use of nonlinear identification in robust attitude and attitude rate estimation for SAMPEX

A method is described for obtaining optimal attitude estimation/identification algorithms for spacecraft lacking attitude rate measurement devices (rate gyros), and then demonstrated using actual flight data from the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX) spacecraft. SAMPEX does not have on-board rate sensing, and relies on sun sensors and a three-axis magnetometer for attitude determination. The absence of rate data normally reduces both the total amount of data available and the sampling density (in time) by a substantial fraction. In addition, attitude data is occasionally unavailable (for example, during sun occultation). As a result, the sensitivity of the estimates to model uncertainty and to measurement noise increases. In order to maintain accuracy in the attitude estimates, there is an increased need for accurate models of the rotational dynamics. The Minimum Model Error(MME)/Least Square Correlation(LSC) algorithm accurately identifies an improved model for SAMPEX to be used during periods of complete data loss or extreme noise. The model correction is determined by estimating only one orbit(the identification pass) just prior to the assumed data loss(the prediction pass). The MME estimator correctly predicted the states during the identification phase, but more importantly determines the necessary model correction trajectory, d(t). The LSC algorithm is then used to find this trajectory's functional form, H(x(t)). The results show significant improvement of the new corrected model's attitude estimates as compared to the original uncorrected model's estimates. The possible functional form of the correction term is limited at this point in the study to functions strictly of the estimated states. The results, however, strongly suggest that functions based on the relative position of the satellite may also be possible candidates for future consideration.

Mook, D. Joseph↗
NASA NTRS1993

Computationally efficient algorithms for real-time attitude estimation

For many practical spacecraft applications, algorithms for determining spacecraft attitude must combine inputs from diverse sensors and provide redundancy in the event of sensor failure. A Kalman filter is suitable for this task, however, it may impose a computational burden which may be avoided by sub optimal methods. A suboptimal estimator is presented which was implemented successfully on the Delta Star spacecraft which performed a 9 month SDI flight experiment in 1989. This design sought to minimize algorithm complexity to accommodate the limitations of an 8K guidance computer. The algorithm used is interpreted in the framework of Kalman filtering and a derivation is given for the computation.

Pringle, Steven R.↗