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All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Attitude Accuracy Study for the Earth Observing System (EOS) AM-1 Spacecraft

Earth Observing System (EOS) spacecraft will take measurements of the Earth's clouds, oceans, atmosphere, land, and radiation balance. These EOS spacecraft are part of the National Aeronautics and Space Administration's Mission to Planet Earth, and consist of several series of satellites, with each series specializing in a particular class of observations. This paper focuses on the EOS AM-1 spacecraft, which is the first of three satellites constituting the EOS AM series (morning equatorial crossing) and the initial spacecraft of the EOS program. EOS AM-1 has a stringent onboard attitude knowledge requirement, of 36/41/44 arc seconds (3 sigma) in yaw/roll/pitch, respectively. During normal mission operations, attitude is determined onboard using an extended Kalman sequential filter via measurements from two charge coupled device (CCD) star trackers, one Fine Sun Sensor, and an Inertial Rate Unit. The attitude determination error analysis system (ADEAS) was used to model the spacecraft and mission profile, and in a worst case scenario with only one star tracker in operation, the attitude uncertainty was 9.7/ll.5/12.2 arc seconds (3 sigma) in yaw/roll/pitch. The quoted result assumed the spacecraft was in nominal attitude, using only the 1-rotation per orbit motion of the spacecraft about the pitch axis for calibration of the gyro biases. Deviations from the nominal attitude would show greater attitude uncertainties, unless calibration maneuvers which roll and/or yaw the spacecraft have been performed. This permits computation of the gyro misalignments, and the attitude knowledge requirement would remain satisfied.

Lesikar, James D., II↗
NASA NTRS1993

Linearization of Attitude-Control Error Dynamics

Direction cosines and quaternions are useful for representing rigid-body attitude because they exhibit no kinematic singularities. Each utilizes more variables than the minimum three degrees of freedom required to specify attitude. Therefore, application of a nonlinear inversion procedure to either formulation introduces singularities. Furthermore, in designing an attitude-control system, it is not appropriate to express attitude error as a difference of direction cosines (or quaternions). One should employ a measure of attitude error that not only is minimal but preserves orthogonal rotation properties as well. This note applies an inversion procedure to an appropriate measure of attitude error, so that the singularity occurs when the error reaches +/- 180 deg. This approach leads to the realization of a new model-follower attitude-control system that exhibits exact linear attitude-error dynamics.

Bach, Ralph↗
NASA NTRS1978

Precision attitude determination for multimission spacecraft

Attitude determination algorithms for a multimission spacecraft are derived and their performance analyzed. The attitude determination system is composed of a strapdown Inertial Reference Unit (IRU), two fixed head star trackers, and an onboard computer. IRU data is processed to maintain real-time knowledge of spacecraft attitude relative to an inertial reference frame. Star tracker data is processed using Kalman filtering techniques to estimate and correct the attitude determination errors and the gyro drift compensation errors. The results of a star availability analysis for stellar, solar and earth pointing missions are presented. Linear covariance analysis techniques are used to evaluate nominal attitude determination performance, the effects of sensor measurement accuracy variations, the effects of errors in knowledge of sensor measurement accuracy, and the effects of star tracker misalignment errors. Results of a nonlinear simulation analysis of attitude determination performance are also presented. These analyses show that precision attitude determination for stellar, solar and earth pointing missions is achieved.

Murrell, J. W.↗
NASA NTRS1981

Spacecraft attitude calibration/verification baseline study

A baseline study for a generalized spacecraft attitude calibration/verification system is presented. It can be used to define software specifications for three major functions required by a mission: the pre-launch parameter observability and data collection strategy study; the in-flight sensor calibration; and the post-calibration attitude accuracy verification. Analytical considerations are given for both single-axis and three-axis spacecrafts. The three-axis attitudes considered include the inertial-pointing attitudes, the reference-pointing attitudes, and attitudes undergoing specific maneuvers. The attitude sensors and hardware considered include the Earth horizon sensors, the plane-field Sun sensors, the coarse and fine two-axis digital Sun sensors, the three-axis magnetometers, the fixed-head star trackers, and the inertial reference gyros.

Chen, L. C.↗
NASA NTRS1988

Attitude determination and parameter estimation using vector observations

Procedures for attitude determination based on Wahba's loss function are generalized to include the estimation of parameters other than the attitude, such as sensor biases. Optimization with respect to the attitude requires either the singular value decomposition of a 3x3 matrix or finding the maximum eigenvalue and corresponding eigenvector of a 4x4 symmetric matrix, but does not require an a priori estimate of the attitude. Optimization with respect to the other parameters employs an iterative approach, which does require an a priori estimate of these parameters. Conventional state estimation methods require a priori estimates of both the parameters and the attitude, while the algorithms presented in this paper always compute the exact optimal attitude for given values of the parameters. The proposed method is shown to give the correct solution of an example problem. An expression for the covariance of the attitude and parameter estimates is derived.

Markley, F. Landis↗
NASA NTRS1988

Three-axis attitude determination via Kalman filtering of magnetometer data

A three-axis Magnetometer/Kalman Filter attitude determination system for a spacecraft in low-altitude Earth orbit is developed, analyzed, and simulation tested. The motivation for developing this system is to achieve light weight and low cost for an attitude determination system. The extended Kalman filter estimates the attitude, attitude rates, and constant disturbance torques. Accuracy near that of the International Geomagnetic Reference Field model is achieved. Covariance computation and simulation testing demonstrate the filter's accuracy. One test case, a gravity-gradient stabilized spacecraft with a pitch momentum wheel and a magnetically-anchored damper, is a real satellite on which this attitude determination system will be used. The application to a nadir pointing satellite and the estimation of disturbance torques represent the significant extensions contributed by this paper. Beyond its usefulness purely for attitude determination, this system could be used as part of a low-cost three-axis attitude stabilization system.

Martel, Francois↗
NASA NTRS1989

Attitude determination and parameter estimation using vector observations - Theory

Procedures for attitude determination based on Wahba's loss function are generalized to include the estimation of parameters other than the attitude, such as sensor biases. Optimization with respect to the attitude is carried out using the q-method, which does not require an a priori estimate of the attitude. Optimization with respect to the other parameters employs an iterative approach, which does require an a priori estimate of these parameters. Conventional state estimation methods require a priori estimates of both the parameters and the attitude, while the algorithm presented in this paper always computes the exact optimal attitude for given values of the parameters. Expressions for the covariance of the attitude and parameter estimates are derived.

Markley, F. Landis↗
NASA NTRS1991

The impact of initial and recurrent cockpit resource management training on attitudes

It is noted that previous analyses of the boomerang effect (attitude change as a result of training in the direction opposite of that intended) in aviation training environments were limited in that each subscale of the cockpit management attitudes questionnaire (CMAQ) was examined independently. This study develops and utilizes a new algorithm for grouping subjects such that a global attitude change score is derived from the attitude change scores on each CMAQ subscale. By evaluating global attitude change in addition to the more specific attitude change on each subscale, it might be possible to better comprehend the effects of crew resource management training on pilot attitudes.

Irwin, Cheryl M.↗
NASA NTRS1993

Torque equilibrium attitudes for the Space Station

All spacecraft orbiting in a low earth orbit (LEO) experience external torques due to environmental effects. Examples of these torques include those induced by aerodynamic, gravity-gradient, and solar forces. It is the gravity-gradient and aerodynamic torques that produce the greatest disturbances to the attitude of a spacecraft in LEO, and large asymmetric spacecraft, such as the space station, are affected to a greater degree because the magnitude of the torques will, in general, be larger in proportion to the moments of inertia. If left unchecked, these torques would cause the attitude of the space station to oscillate in a complex manner and the resulting motion would destroy the micro-gravity environment as well as prohibit the orbiter from docking. The application of control torques will maintain the proper attitude, but the controllers have limited momentum capacity. When any controller reaches its limit, propellant must then be used while the device is reset to a zero or negatively-biased momentum state. Consequently, the rate at which momentum is accumulated is a significant factor in the amount of propellant used and the frequency of resupply necessary to operate the station. A torque profile in which the area curve for a positive torque is not equal to the area under the curve for a negative torque is 'biased,' and the consequent momentum build-up about that axis is defined as secular momentum because it continues to grow with time. Conversely, when the areas are equal, the momentum is cyclic and bounded. A Torque Equilibrium Attitude (TEA) is thus defined as an attitude at which the external torques 'balance' each other as much as possible, and which will result in lower momentum growth in the controllers. Ideally, the positive and negative external moments experienced by a spacecraft at the TEA would exactly cancel each other out and small cyclic control torques would be required only for precise attitude control. Over time, the only momentum build-up in the controllers would be due to electro-mechanical losses within the device. However, the atmospheric torques are proportional to the density of the atmosphere and the density varies with the orbital position, time of day, time of year, and the solar cycle. In addition, there are unmodeled disturbances and uncertainties in the mass and inertias. Therefore, there is no constant attitude that will completely balance the environmental torques and the dynamic TEA cannot be solved in closed form. The objective of this research was to determine a method to calculate a dynamic TEA such that the rate of momentum build-up in the controllers would be minimized and to implement this method in the MATRIX(x) simulation software by Integrated Systems, Inc.

Thompson, Roger C.↗
NASA NTRS1995

Evaluation and modeling of autonomous attitude thrust control for the Geostation Operational Environmental Satellite (GOES)-8 orbit determination

The Geostationary Operational Environmental Satellite (GOES)-8 experienced a series of orbital perturbations from autonomous attitude control thrusting before perigee raising maneuvers. These perturbations influenced differential correction orbital state solutions determined by the Goddard Space Flight Center (GSFC) Goddard Trajectory Determination System (GTDS). The maneuvers induced significant variations in the converged state vector for solutions using increasingly longer tracking data spans. These solutions were used for planning perigee maneuvers as well as initial estimates for orbit solutions used to evaluate the effectiveness of the perigee raising maneuvers. This paper discusses models for the incorporation of attitude thrust effects into the orbit determination process. Results from definitive attitude solutions are modeled as impulsive thrusts in orbit determination solutions created for GOES-8 mission support. Due to the attitude orientation of GOES-8, analysis results are presented that attempt to absorb the effects of attitude thrusting by including a solution for the coefficient of reflectivity, C(R). Models to represent the attitude maneuvers are tested against orbit determination solutions generated during real-time support of the GOES-8 mission. The modeling techniques discussed in this investigation offer benefits to the remaining missions in the GOES NEXT series. Similar missions with large autonomous attitude control thrusting, such as the Solar and Heliospheric Observatory (SOHO) spacecraft and the INTELSAT series, may also benefit from these results.

Forcey, W.↗
NASA NTRS1995

Modal Correction Method For Dynamically Induced Errors In Wind-Tunnel Model Attitude Measurements

This paper describes a method for correcting the dynamically induced bias errors in wind tunnel model attitude measurements using measured modal properties of the model system. At NASA Langley Research Center, the predominant instrumentation used to measure model attitude is a servo-accelerometer device that senses the model attitude with respect to the local vertical. Under smooth wind tunnel operating conditions, this inertial device can measure the model attitude with an accuracy of 0.01 degree. During wind tunnel tests when the model is responding at high dynamic amplitudes, the inertial device also senses the centrifugal acceleration associated with model vibration. This centrifugal acceleration results in a bias error in the model attitude measurement. A study of the response of a cantilevered model system to a simulated dynamic environment shows significant bias error in the model attitude measurement can occur and is vibration mode and amplitude dependent. For each vibration mode contributing to the bias error, the error is estimated from the measured modal properties and tangential accelerations at the model attitude device. Linear superposition is used to combine the bias estimates for individual modes to determine the overall bias error as a function of time. The modal correction model predicts the bias error to a high degree of accuracy for the vibration modes characterized in the simulated dynamic environment.

Buehrle, R. D.↗
NASA NTRS1996

An Evaluation of Attitude-Independent Magnetometer-Bias Determination Methods

Although several algorithms now exist for determining three-axis magnetometer (TAM) biases without the use of attitude data, there are few studies on the effectiveness of these methods, especially in comparison with attitude dependent methods. This paper presents the results of a comparison of three attitude independent methods and an attitude dependent method for computing TAM biases. The comparisons are based on in-flight data from the Extreme Ultraviolet Explorer (EUVE), the Upper Atmosphere Research Satellite (UARS), and the Compton Gamma Ray Observatory (GRO). The effectiveness of an algorithm is measured by the accuracy of attitudes computed using biases determined with that algorithm. The attitude accuracies are determined by comparison with known, extremely accurate, star-tracker-based attitudes. In addition, the effect of knowledge of calibration parameters other than the biases on the effectiveness of all bias determination methods is examined.

Hashmall, J. A.↗
NASA NTRS1997

Predictive Attitude Estimation Using Global Positioning System Signals

In this paper, a new algorithm is developed for attitude estimation using Global Positioning System (GPS) signals. The new algorithm is based on a predictive filtering scheme designed for spacecraft without rate measuring devices. The major advantage of this new algorithm over traditional Kalman filter approaches is that the model error is not assumed to represented by an unbiased Gaussian noise process with known covariance, but instead is determined during the estimation process. This is achieved by simultaneously solving system optimality conditions and an output error constraint. This approach is well suited for GPS attitude estimation since some error sources that contribute to attitude inaccuracy, such as signal multipath, are known to be non-Gaussian processes. Also, the predictive filter scheme can use either GPS signals or vector observations or a combination of both for attitude estimation, so that performance characteristics can be maintained during periods of GPS attitude sensor outage. The performance of the new algorithm is tested using flight data from the REX-2 spacecraft. Results are shown using the predictive filter to estimate the attitude from both GPS signals and magnetometer measurements, and comparing that solution to a magnetometer-only based solution. Results using the new estimation algorithm indicate that GPS-based solutions are verified to within 2 degrees using the magnetometer cross-check for the REX-2 spacecraft. GPS attitude accuracy of better than 1 degree is expected per axis, but cannot be reliably proven due to inaccuracies in the magnetic field model.

Crassidis, John L.↗
NASA NTRS2003

Attitude Estimation or Quaternion Estimation?

The attitude of spacecraft is represented by a 3x3 orthogonal matrix with unity determinant, which belongs to the three-dimensional special orthogonal group SO(3). The fact that all three-parameter representations of SO(3) are singular or discontinuous for certain attitudes has led to the use of higher-dimensional nonsingular parameterizations, especially the four-component quaternion. In attitude estimation, we are faced with the alternatives of using an attitude representation that is either singular or redundant. Estimation procedures fall into three broad classes. The first estimates a three-dimensional representation of attitude deviations from a reference attitude parameterized by a higher-dimensional nonsingular parameterization. The deviations from the reference are assumed to be small enough to avoid any singularity or discontinuity of the three-dimensional parameterization. The second class, which estimates a higher-dimensional representation subject to enough constraints to leave only three degrees of freedom, is difficult to formulate and apply consistently. The third class estimates a representation of SO(3) with more than three dimensions, treating the parameters as independent. We refer to the most common member of this class as quaternion estimation, to contrast it with attitude estimation. We analyze the first and third of these approaches in the context of an extended Kalman filter with simplified kinematics and measurement models.

F Landis Markley↗
NASA NTRS2003

Towards Automating Spacecraft Attitude Sensor Calibration

With a view towards reducing cost and complexity for spacecraft early mission support at the NASA Goddard Space Flight Center (GSFC), efforts are being made to automate the attitude sensor calibration process. This paper addresses one of the major components needed by such a system. The beneficiaries of an improved calibration process are missions that demand moderate to high precision attitude knowledge or that need to perform accurate attitude slews. Improved slew accuracy reduces the time needed for re-acquisition of fine-pointing after each attitude maneuver, Rapid target acquisition can be very important for astronomical targeting or for off-nadir surface feature targeting by Earth-oriented spacecraft. The normal sequence of on-orbit calibration starts with alignment calibration of the star trackers and possibly the Sun sensor. Their relative alignment needs to be determined using a sufficiently large data set so their fields of view are adequately sampled. Next, the inertial reference unit (IRU) is calibrated for corrections to its alignment and scale factors. The IRU biases are estimated continuously by the onboard attitude control system, but the IRU alignment and scale factors are usually determined on the ground using a batch-processing method on a data set that includes several slews sufficient to give full observability of all the IRU calibration parameters. Finally, magnetometer biases, alignment, and its coupling to the magnetic torquers are determined in order io improve momentum management and occasionally for use in the attitude determination system. The detailed approach used for automating calibrations will depend on whether the automated system resides on the ground or on the spacecraft with an ultimate goal of autonomous calibration. Current efforts focus on a ground-based system driving subsystems that could run either on the ground or onboard. The distinction is that onboard calibration should process the data sequentially rather than in a single large batch since onboard computer data storage is limited. Very good batch- processing calibration utilities have been developed and used extensively at NASA/GSFC for mission support but no sequential calibration utilities are available. To meet this need, this paper presents the mathematical description of a sequential IRU calibration system. The system has been tested using flight data from the Rossi X-ray Timing Explorer (RXTE) during a series of attitude slews. The paper also discusses the current state of the overall automated system and describes plans for adding sequential alignment calibration and other additions that will reduce the amount of analyst time and input.

Sedlak, Joseph↗
NASA NTRS1997

Enhanced Attitude Control Experiment for SSTI Lewis Spacecraft

The enhanced attitude control system experiment is a technology demonstration experiment on the NASA's small spacecraft technology initiative program's Lewis spacecraft to evaluate advanced attitude control strategies. The purpose of the enhanced attitude control system experiment is to evaluate the feasibility of designing and implementing robust multi-input/multi-output attitude control strategies for enhanced pointing performance of spacecraft to improve the quality of the measurements of the science instruments. Different control design strategies based on modern and robust control theories are being considered for the enhanced attitude control system experiment. This paper describes the experiment as well as the design and synthesis of a mixed H(sub 2)/H(sub infinity) controller for attitude control. The control synthesis uses a nonlinear programming technique to tune the controller parameters and impose robustness and performance constraints. Simulations are carried out to demonstrate the feasibility of the proposed attitude control design strategy. Introduction

Maghami, Peoman G.↗
NASA NTRS2005

Spinning Spacecraft Attitude Estimation Using Markley Variables: Filter Implementation And Results

Attitude estimation is often more difficult for spinning spacecraft than for three-axis stabilized platforms due to the need to follow rapidly-varying state vector elements and the lack of three-axis rate measurements from gyros. The estimation problem simplifies when torques are negligible and nutation has damped out, but the general case requires a sequential filter with dynamics propagation. This paper describes the implementation and test results for an extended Kalman filter for spinning spacecraft attitude and rate estimation based on a novel set of variables suggested in a paper by Markley [AAS93-3301 (referred to hereafter as Markley variables). Markley has demonstrated that the new set of variables provides a superior parameterization for numerical integration of the attitude dynamics for spinning or momentum-biased spacecraft. The advantage is that the Markley variables have fewer rapidly-varying elements than other representations such as the attitude quaternion and rate vector. A filter based on these variables was expected to show improved performance due to the more accurate numerical state propagation. However, for a variety of test cases, it has been found that the new filter, as currently implemented, does not perform significantly better than a quaternion-based filter that was developed and tested in parallel. This paper reviews the mathematical background for a filter based on Markley variables. It also describes some features of the implementation and presents test results. The test cases are based on a mission using magnetometer and Sun sensor data and gyro measurements on two axes normal to the spin axis. The orbit and attitude scenarios and spacecraft parameters are modeled after one of the THEMIS (Time History of Events and Macroscale Interactions during Substorms) probes. Several tests are presented that demonstrate the filter accuracy and convergence properties. The tests include torque-free motion with various nutation angles, large constant-torque attitude slews, sensor misalignments, large initial attitude and rate errors, and cases with low data frequency. It is found that the convergence is rapid, the radius of convergence is large, and the results are reasonably accurate even in the presence of unmodeled perturbations.

Sedlak, Joseph E.↗
NASA NTRS2002

Noise screen for attitude control system

An attitude control system comprising a controller and a noise screen device coupled to the controller. The controller is adapted to control an attitude of a vehicle carrying an actuator system that is adapted to pulse in metered bursts in order to generate a control torque to control the attitude of the vehicle in response to a control pulse. The noise screen device is adapted to generate a noise screen signal in response to the control pulse that is generated when an input attitude error signal exceeds a predetermined deadband attitude level. The noise screen signal comprises a decaying offset signal that when combined with the attitude error input signal results in a net attitude error input signal away from the predetermined deadband level to reduce further control pulse generation.

Rodden, John J.↗