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The attitude algorithms applied to strapdown inertial platforms are discussed. A review of six attitude transformation algorithms and the realizations of these algorithms by digital differential analyzers are presented. The number of digital differential analyzers for each algorithm is either smaller than or equal to that obtained by others.
Digital computer simulation of two strapdown system attitude algorithms by response to angular input rates
Digital differential analyzer (DDA) realization of the direction cosine, Euler angle, and quaternion algorithms. It is shown that, for any one of the three attitude algorithms, 27 DDAs are needed. This number is considerably smaller than those obtained by others for the cases of Euler angle and quaternion algorithms.
In this paper, a new and efficient algorithm is developed for attitude determination from vector observations. The new algorithm, called the Predictive Attitude Determination (PAD) algorithm, is derived from a general nonlinear predictive filter approach. Traditional deterministic algorithms are shown to be suboptimal for anisotropic measurement errors. The major advantage of the PAD algorithm is that it can be easily applied to the case where anisotropic measurement errors exist. Also, an analytical expression is derived for the steady-state attitude error covariance, which is shown to be equivalent to the optimal covariance derived from maximum likelihood techniques. Simulation studies indicate that the new algorithm is able to accurately determine the attitude of a spacecraft, even for radically anisotropic measurement errors.
Algorithms for onboard attitude control of the Solar Maximum Mission (SMM) are discussed and test results are presented. The algorithms include: despin and sun acquisition, control of pitch and yaw (sun pointing) to 5 arc-sec accuracy and roll (around the sun line) to 0.1 deg, time-optimal and constant-rate slew sequences, attitude maintenance during orbit night and sun reacquisition at orbit dawn, momentum unloading, and gyro drift calibration. The tests were performed on the SMM Software Development and Validation Facility at the NASA Goddard Space Flight Center with a FORTRAN prototype version of the onboard software.
A G-RAC attitude-control algorithm is used to minimize maneuver execution error in a spacecraft with a flexible appendage when said spacecraft must induce translational momentum by firing (in open loop) large thrusters along a desired direction for a given period of time. The controller is dynamic with two integrators and requires measurement of only the angular position and velocity of the spacecraft. The global stability of the closed-loop system is guaranteed without having access to the states describing the dynamics of the appendage and with severe saturation in the available torque. Spacecraft apply open-loop thruster firings to induce a desired translational momentum with an extended appendage. This control algorithm will assist this maneuver by stabilizing the attitude dynamics around a desired orientation, and consequently minimize the maneuver execution errors.
This paper categorizes the qualitative behavior of the Command and Control Segment (CCS) differential correction algorithm as applied to attitude estimation using simultaneous spin axis sun angle and Earth cord length measurements. The categories of interest are the domains of convergence, divergence, and their boundaries. Three series of plots are discussed that show the dependence of the estimation algorithm on the vehicle radius, the sun/Earth angle, and the spacecraft attitude. Common qualitative dynamics to all three series are tabulated and discussed. Out-of-limits conditions for the estimation algorithm are identified and discussed.
TRIAD is a well known simple algorithm that generates the attitude matrix between two coordinate systems when the components of two abstract vectors are given in the two systems. TRIAD however, is sensitive to the order in which the algorithm handles the vectors, such that the resulting attitude matrix is influenced more by the vector processed first. In this work we present a new algorithm, which we call Optimized TRIAD, that blends in a specified manner the two matrices generated by TRIAD when processing one vector first, and then when processing the other vector first. On the average, Optimized TRIAD yields a matrix which is better than either one of the two matrices in that is ti the closest to the correct matrix. This result is demonstrated through simulation.
This paper presents an onboard closed loop attitude reorientation algorithm for a dual-spin spacecraft, Galileo. The basic concept for the design uses the despun stator as a reference and fires a sequence of fixed duration thruster pulses to precess the angular momentum vector to its commanded orientation. The error signals used to despin the stator and to perform the turn are derived from the stator error quaternion which is computed using gyro outputs. Constraints considered in the design include gyro rate saturation, plume impingement effects, system parameter variations, as well as software reliability and flexibility. The performance of the algorithm was predicted by analysis and confirmed by computer simulation results. It was concluded that a reorientation accuracy of better than 1 milliradian with a nutation angle of less than 1 degree during the turn can be achieved.
This report presents an algorithm that incorporates real-time data from two infrared cameras and computes the attitude parameters of the Spacecraft Control Laboratory Experiment (SCOLE), a laboratory apparatus representing an offset-feed antenna attached to the Space Shuttle by a flexible mast. The algorithm utilizes camera position information of three miniature LEDs, mounted on the SCOLE platform, permitting arbitrary camera placement and an on-line attitude extraction. The continuous nature of the algorithm allows identification of the placement of the two cameras with respect to some initial position of the three reference LEDs, followed by on-line six degrees of freedom attitude tracking, regardless of the attitude time history. The report provides a description of the algorithm in the camera identification mode as well as the mode of target tracking. Experimental data from a reduced-size SCOLE-like laboratory model, reflecting the performance of the camera identification and tracking processes, are presented.
Three-axis attitude determination is equivalent to finding a coordinate transformation matrix which transforms a set of reference vectors fixed in inertial space to a set of measurement vectors fixed in the spacecraft. The attitude determination problem can be expressed as a constrained optimization problem. The constraint is that a coordinate transformation matrix must be proper, real, and orthogonal. A transformation matrix can be thought of as optimal in the least-squares sense if it maps the measurement vectors to the reference vectors with minimal 2-norm errors and meets the above constraint. This constrained optimization problem is known as Wahba's problem. Several algorithms which solve Wahba's problem exactly have been developed and used. These algorithms, while steadily improving, are all rather complicated. Furthermore, they involve such numerically unstable or sensitive operations as matrix determinant, matrix adjoint, and Newton-Raphson iterations. This paper describes an algorithm which minimizes Wahba's loss function, but without the constraint. When the constraint is ignored, the problem can be solved by a straightforward, numerically stable least-squares algorithm such as QR decomposition. Even though the algorithm does not explicitly take the constraint into account, it still yields a nearly orthogonal matrix for most practical cases; orthogonality only becomes corrupted when the sensor measurements are very noisy, on the same order of magnitude as the attitude rotations. The algorithm can be simplified if the attitude rotations are small enough so that the approximation sin(theta) approximately equals theta holds. We then compare the computational requirements for several well-known algorithms. For the general large-angle case, the QR least-squares algorithm is competitive with all other know algorithms and faster than most. If attitude rotations are small, the least-squares algorithm can be modified to run faster, and this modified algorithm is faster than all but a similarly specialized version of the QUEST algorithm. We also introduce a novel measurement averaging technique which reduces the n-measurement case to the two measurement case for our particular application, a star tracker and earth sensor mounted on an earth-pointed geosynchronous communications satellite. Using this technique, many n-measurement problems reduce to less than or equal to 3 measurements; this reduces the amount of required calculation without significant degradation in accuracy. Finally, we present the results of some tests which compare the least-squares algorithm with the QUEST and FOAM algorithms in the two-measurement case. For our example case, all three algorithms performed with similar accuracy.
The Microwave Anisotropy Probe (MAP) is a follow-on to the Differential Microwave Radiometer (DMR) instrument on the Cosmic Background Explorer (COBE) spacecraft. The MAP spacecraft will perform its mission, studying the early origins of the universe, in a Lissajous orbit around the Earth-Sun L(sub 2) Lagrange point. Due to limited mass, power, and financial resources, a traditional reliability concept involving fully redundant components was not feasible. This paper will discuss the redundancy philosophy used on MAP, describe the hardware redundancy selected (and why), and present backup modes and algorithms that were designed in lieu of additional attitude control hardware redundancy to improve the odds of mission success. Three of these modes have been implemented in the spacecraft flight software. The first onboard mode allows the MAP Kalman filter to be used with digital sun sensor (DSS) derived rates, in case of the failure of one of MAP's two two-axis inertial reference units. Similarly, the second onboard mode allows a star tracker only mode, using attitude and derived rate from one or both of MAP's star trackers for onboard attitude determination and control. The last backup mode onboard allows a sun-line angle offset to be commanded that will allow solar radiation pressure to be used for momentum management and orbit stationkeeping. In addition to the backup modes implemented on the spacecraft, two backup algorithms have been developed in the event of less likely contingencies. One of these is an algorithm for implementing an alternative scan pattern to MAP's nominal dual-spin science mode using only one or two reaction wheels and thrusters. Finally, an algorithm has been developed that uses thruster one shots while in science mode for momentum management. This algorithm has been developed in case system momentum builds up faster than anticipated, to allow adequate momentum management while minimizing interruptions to science. In this paper, each mode and algorithm will be discussed, and simulation results presented.
The results of the study of the Communications Technology Satellite (CTS) attitude acquisition procedures are described. Models of spacecraft hardware and dynamics are also included.
This paper presents a single frame algorithm for the spin-axis orientation-determination of spinning spacecraft that encounters no ambiguity problems, as well as a simple Kalman filter for continuously estimating the full attitude of a spinning spacecraft. The later algorithm is comprised of two low order decoupled Kalman filters; one estimates the spin axis orientation, and the other estimates the spin rate and the spin (phase) angle. The filters are ambiguity free and do not rely on the spacecraft dynamics. They were successfully tested using data obtained from one of the ST5 satellites.
Accurate spacecraft attitudes may only be obtained if the primary attitude sensors are well calibrated. Launch shock, relaxation of gravitational stresses and similar effects often produce large enough alignment shifts so that on-orbit alignment calibration is necessary if attitude accuracy requirements are to be met. A variety of attitude sensor alignment algorithms have been developed to meet the need for on-orbit calibration. Two new algorithms are presented here: ALICAL and ALIQUEST. Each of these has advantages in particular circumstances. ALICAL is an attitude independent algorithm that uses near simultaneous measurements from two or more sensors to produce accurate sensor alignments. For each set of simultaneous observations the attitude is overdetermined. The information content of the extra degrees of freedom can be combined over numerous sets to provide the sensor alignments. ALIQUEST is an attitude dependent algorithm that combines sensor and attitude data into a loss function that has the same mathematical form as the Wahba problem. Alignments can then be determined using any of the algorithms (such as the QUEST quaternion estimator) that have been developed to solve the Wahba problem for attitude. Results from the use of these methods on active missions are presented.
Previous high fidelity onboard attitude algorithms estimated only the spacecraft attitude and gyro bias. The desire to promote spacecraft and ground autonomy and improvements in onboard computing power has spurred development of more sophisticated calibration algorithms. Namely, there is a desire to provide for sensor calibration through calibration parameter estimation onboard the spacecraft as well as autonomous estimation on the ground. Gyro calibration is a particularly challenging area of research. There are a variety of gyro devices available for any prospective mission ranging from inexpensive low fidelity gyros with potentially unstable scale factors to much more expensive extremely stable high fidelity units. Much research has been devoted to designing dedicated estimators such as particular Extended Kalman Filter (EKF) algorithms or Square Root Information Filters. This paper builds upon previous attitude, rate, and specialized gyro parameter estimation work performed with Pseudo Linear Kalman Filter (PSELIKA). The PSELIKA advantage is the use of the standard linear Kalman Filter algorithm. A PSELIKA algorithm for an orthogonal gyro set which includes estimates of attitude, rate, gyro misalignments, gyro scale factors, and gyro bias is developed and tested using simulated and flight data. The measurements PSELIKA uses include gyro and quaternion tracker data.
A new algorithm is developed for inflight magnetometer bias determination without knowledge of the attitude. This algorithm combines the fast convergence of a heuristic algorithm currently in use with the correct treatment of the statistics and without discarding data. The algorithm performance is examined using simulated data and compared with previous algorithms.
Gyro test package, dynamic test facility and real time attitude algorithm to investigate operational capabilities of strapdown inertial attitude package