Engineering topics

Markley, F. Landis

Publications and source records attributed to Markley, F. Landis.

At least 73 records · Page 4

NASA NTRS1997

A Predictive Attitude Determination Algorithm

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.

Markley, F. Landis↗

NASA NTRS1997

Efficient Sequential Attitude Estimation from Vector Observations

This paper presents a computationally efficient, sequential method for attitude matrix estimation using gyro and vector measurements. The method is based on a recently introduced, minimal-parameter third-order method for solving the orthogonal matrix differential equation in R(sup n). In the three-dimensional case, these third-order attitude parameters can be interpreted as temporal-integrals of the body-frame angular velocity components. A nonlinear algorithm is developed, which uses this minimal set of three parameters to estimate the nine-parameter direction-cosine matrix. Having an extremely simple kinematic equation, these parameters render the resulting estimator highly computationally efficient. An orthogonalization procedure, incorporated into the measurement processing stage, enhances the accuracy and stability of the resulting algorithm, yet retains reasonable simplicity. The performance of the estimator is demonstrated via a Monte Carlo simulation study.

Oshman, Yaakov↗

NASA NTRS1997

Vector Observation-Aided/Attitude-Rate Estimation Using Global Positioning System Signals

A sequential filtering algorithm is presented for attitude and attitude-rate estimation from Global Positioning System (GPS) differential carrier phase measurements. A third-order, minimal-parameter method for solving the attitude matrix kinematic equation is used to parameterize the filter's state, which renders the resulting estimator computationally efficient. Borrowing from tracking theory concepts, the angular acceleration is modeled as an exponentially autocorrelated stochastic process, thus avoiding the use of the uncertain spacecraft dynamic model. The new formulation facilitates the use of aiding vector observations in a unified filtering algorithm, which can enhance the method's robustness and accuracy. Numerical examples are used to demonstrate the performance of the method.

Oshman, Yaakov↗

NASA NTRS1996

Attitude Estimation Using Modified Rodrigues Parameters

In this paper, a Kalman filter formulation for attitude estimation is derived using the Modified Rodrigues Parameters. The extended Kalman filter uses a gyro-based model for attitude propagation. Two solutions are developed for the sensitivity matrix in the Kalman filter. One is based upon an additive error approach, and the other is based upon a multiplicative error approach. It is shown that the two solutions are in fact equivalent. The Kalman filter is then used to estimate the attitude of a simulated spacecraft. Results indicate that then new algorithm produces accurate attitude estimates by determining actual gyro biases.

Crassidis, John L.↗

NASA NTRS1996

Attitude Determination Improvements for GOES

In this paper, a summary of the basic simulation parameters and results of a new study for the Geostationary Operational Environmental Satellite (GOES) is shown. The study for GOES involves the simulation of minor modifications to the current spacecraft, so that the relative performance of these modifications can be analyzed. The first modification studies requires the placement of a baseline inertial reference unit, such as the Dry Rotor Inertial Reference Unit or the Hemispherical Resonator Gyro onto the spacecraft. The imager/sounder assembly is currently used to obtain landmark and/or star observations in order to compensate for spacecraft motion and external disturbances through ground processing. The study uses the imager/sounder assembly as another attitude sensor for on-board attitude determination. Also the addition of star trackers is used to provide precise attitude knowledge.

Crassidis, John L.↗

NASA NTRS1995

Kepler Equation solver

Kepler's Equation is solved over the entire range of elliptic motion by a fifth-order refinement of the solution of a cubic equation. This method is not iterative, and requires only four transcendental function evaluations: a square root, a cube root, and two trigonometric functions. The maximum relative error of the algorithm is less than one part in 10(exp 18), exceeding the capability of double-precision computer arithmetic. Roundoff errors in double-precision implementation of the algorithm are addressed, and procedures to avoid them are developed.

Markley, F. Landis↗

NASA NTRS1995

An MME-based attitude estimator using vector observations

In this paper, an optimal batch estimator and filter based on the Minimum Model Error (MME) approach is developed for three-axis stabilized spacecraft. Three different MME algorithms are developed. The first algorithm estimates the attitude of a spacecraft using rate measurements. The second algorithm estimates the attitude without using rate measurements. The absence of rate data may be a result of intentional design or from unexpected failure of existing gyros. The third algorithm determines input-torque modeling error trajectories. All of the algorithms developed in this paper use attitude sensors (e.g., three-axis magnetometers, sun sensors, star trackers, etc.). Results using these new algorithms indicate that an MME-based approach accurately estimates the attitude, rate, and input torque trajectories of an actual spacecraft.

Crassidis, John L.↗

NASA NTRS1995

SAMPEX special pointing mode

A new pointing mode has been developed for the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX) spacecraft. This pointing mode orients the instrument boresights perpendicular to the field lines of the Earth's magnetic field in regions of low field strength and parallel to the field lines in regions of high field strength, to allow better characterization of heavy ions trapped by the field. The new mode uses magnetometer signals and is algorithmically simpler than the previous control mode, but it requires increased momentum wheel activity. It was conceived, designed, tested, coded, uplinked to the spacecraft, and activated in less than seven months.

Markley, F. Landis↗

NASA NTRS1995

A new angle on the Euler angles

We present a generalization of the Euler angles to axes beyond the twelve conventional sets. The generalized Euler axes must satisfy the constraint that the first and the third are orthogonal to the second; but the angle between the first and third is arbitrary, rather than being restricted to the values 0 and pi/2, as in the conventional sets. This is the broadest generalization of the Euler angles that provides a representation of an arbitrary rotation matrix. The kinematics of the generalized Euler angles and their relation to the attitude matrix are presented. As a side benefit, the equations for the generalized Euler angles are universal in that they incorporate the equations for the twelve conventional sets of Euler angles in a natural way.

Markley, F. Landis↗

NASA NTRS1995

Contingency designs for attitude determination of TRMM

In this paper, several attitude estimation designs are developed for the Tropical Rainfall Measurement Mission (TRMM) spacecraft. A contingency attitude determination mode is required in the event of a primary sensor failure. The final design utilizes a full sixth-order Kalman filter. However, due to initial software concerns, the need to investigate simpler designs was required. The algorithms presented in this paper can be utilized in place of a full Kalman filter, and require less computational burden. These algorithms are based on filtered deterministic approaches and simplified Kalman filter approaches. Comparative performances of all designs are shown by simulating the TRMM spacecraft in mission mode. Comparisons of the simulation results indicate that comparable accuracy with respect to a full Kalman filter design is possible.

Crassidis, John L.↗

NASA NTRS1994

Zero-Gyro safemode controller for the Hubble Space Telescope

A safehold mode has been implemented for Hubble Space Telescope that ensures a power-positive and thermally safe state without the use of rate gyros. This paper presents an overview of this zero-gyro sunpoint safemode, followed by details of the algorithm, the control system design, and results of simulations and of an on-orbit test of the algorithm.

ZERO-GYRO SAFEMODE CONTROLLER↗

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 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

H(sub infinity)-type filter for spacecraft attitude estimation

A nonlinear filtering theory from a deterministic point of view is presented and an application to attitude determination is considered. The approach that is taken in this paper is motivated largely by the H(sun infinity) control and estimation theory for linear systems which has been evolved within the last decade. Rather than formulating the estimation problem as a game played by two adversaries, as has been done in the linear case, we employ in this work some notions from the theory of dissipative systems as a vehicle for arriving at certain Hamilton-Jacobi inequality, which in turn, provides a solution to the filtering problem, whenever it is satisfied. Application of this method to a linear estimation problem and to the problem of estimating a spacecraft attitude quaternion and gyro drift bias vector are presented. In limiting cases, these give the Kalman filter and the extended Kalman filter, respectively. The main advantages of this approach over its probabilistic counterpart are that this approach does not require a prior knowledge of any statistics, and that in general it is more amenable to a quantitative assessment regarding approximations such as linearization, and that in certain cases this approach yields an exact solution to the nonlinear filtering.

Markley, F. Landis↗

NASA NTRS1993

New dynamic variables for rotating spacecraft

This paper introduces two new seven-parameter representations for spacecraft attitude dynamics modeling. The seven parameters are the three components of the total system angular momentum in the spacecraft body frame; the three components of the angular momentum in the inertial reference frame; and an angle variable. These obey a single constraint as do parameterizations that include a quaternion; in this case the constraint is the equality of the sum of the squares of the angular momentum components in the two frames. The two representations are nonsingular if the system angular momentum is non-zero and obeys certain orientation constraints. The new parameterizations of the attitude matrix, the equations of motion, and the relation of the solution of these equations to Euler angles for torque-free motion are developed and analyzed. The superiority of the new parameterizations for numerical integration is shown in a specific example.

Markley, F. Landis↗

NASA NTRS1991

Fast orbit propagator for graphical display

A simple analytic orbit propagator is presented which incorporates a mean-to-osculating transformation to generate a graphical display of the trajectories of earth-orbiting satellites. The first-order effects of the oblateness of the earth on the orbit are consistently included. The propagator encompasses a mean-to-osculating transformation on the semimajor axis, since large intrack errors can be generated by failing to observe the distinction between the mean and osculating values of this parameter.

Markley, F. Landis↗

NASA NTRS1990

Comparison of two on-orbit attitude sensor alignment methods

Compared here are two methods of on-orbit alignment of vector attitude sensors. The first method uses the angular difference between simultaneous measurements from two or more sensors. These angles are compared to the angular differences between the respective reference positions of the sensed objects. The alignments of the sensors are adjusted to minimize the difference between the two sets of angles. In the second method, the sensor alignment is part of a state vector that includes the attitude. The alignments are adjusted along with the attitude to minimize all observation residuals. It is shown that the latter method can result in much less alignment uncertainty when gyroscopes are used for attitude propagation during the alignment estimation. The additional information for this increased accuracy comes from knowledge of relative attitude obtained from the spacecraft gyroscopes. The theoretical calculations of this difference in accuracy are presented. Also presented are numerical estimates of the alignment uncertainties of the fixed-head star trackers on the Extreme Ultraviolet Explorer spacecraft using both methods.

Krack, Kenneth↗

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.↗