Engineering topics

Markley, F. Landis

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

At least 37 records · Page 2

NASA NTRS2007

Kalman Filter for Spinning Spacecraft Attitude Estimation

This paper presents a Kalman filter using a seven-component attitude state vector comprising the angular momentum components in an inertial reference frame, the angular momentum components in the body frame, and a rotation angle. The relatively slow variation of these parameters makes this parameterization advantageous for spinning spacecraft attitude estimation. The filter accounts for the constraint that the magnitude of the angular momentum vector is the same in the inertial and body frames by employing a reduced six-component error state. Four variants of the filter, defined by different choices for the reduced error state, are tested against a quaternion-based filter using simulated data for the THEMIS mission. Three of these variants choose three of the components of the error state to be the infinitesimal attitude error angles, facilitating the computation of measurement sensitivity matrices and causing the usual 3x3 attitude covariance matrix to be a submatrix of the 6x6 covariance of the error state. These variants differ in their choice for the other three components of the error state. The variant employing the infinitesimal attitude error angles and the angular momentum components in an inertial reference frame as the error state shows the best combination of robustness and efficiency in the simulations. Attitude estimation results using THEMIS flight data are also presented.

Markley, F. Landis↗

NASA NTRS2007

Quaternion Averaging

Many applications require an algorithm that averages quaternions in an optimal manner. For example, when combining the quaternion outputs of multiple star trackers having this output capability, it is desirable to properly average the quaternions without recomputing the attitude from the the raw star tracker data. Other applications requiring some sort of optimal quaternion averaging include particle filtering and multiple-model adaptive estimation, where weighted quaternions are used to determine the quaternion estimate. For spacecraft attitude estimation applications, derives an optimal averaging scheme to compute the average of a set of weighted attitude matrices using the singular value decomposition method. Focusing on a 4-dimensional quaternion Gaussian distribution on the unit hypersphere, provides an approach to computing the average quaternion by minimizing a quaternion cost function that is equivalent to the attitude matrix cost function Motivated by and extending its results, this Note derives an algorithm that deterniines an optimal average quaternion from a set of scalar- or matrix-weighted quaternions. Rirthermore, a sufficient condition for the uniqueness of the average quaternion, and the equivalence of the mininiization problem, stated herein, to maximum likelihood estimation, are shown.

Markley, F. Landis↗

NASA NTRS2006

I Love My Attitude Problem

This viewgraph presentation provides a survey of modern methods for attitude estimation. Two algorithms are discussed: Kalman Filters and Wahba's Problem. Several spacecraft Attitude Determination And Control Subsystem (ADACS) are discussed including: Solar Maximum Mission (SMM), Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX), Hubble Space Telescope (HST), Tropical Rainfall Measuring Mission (TRMM), and Wilkinson Microwave Anisotropy Probe (WMAP). Also included is a discussion about Zero Gyro Sunpoint (ZGSP), and the WMAP Attitude Anomaly.

Markley, F. Landis↗

NASA NTRS2006

HUMBLE PROBLEMS

Harold Morton introduced a talk by saying that when you wind up an old professor, he tends to talk for a microcentury. I will attempt to keep my comments to that canonical time span. Having failed to find some unifying theme for this talk, I decided to just ramble through my career with a focus on the algorithms, spacecraft, and people I've had the privilege and pleasure to work with. The algorithms, and certainly the spacecraft, are not all mine. The people are some of those whose ideas that have most influenced and inspired my career. The organization of the paper is largely chronological, but I do not hesitate to jump forward or backward in time when the material demands it. The coverage is broad but necessarily shallow; the interested reader can find more detail in the references

Markley, F. Landis↗

NASA NTRS2006

Kalman Filtering of Angular-Momentum-Based Attitude Parameters

This paper presents an extended Kalman filter using an attitude parameterization that is advantageous for attitude estimation of spinning spacecraft. The parameters are the angular momentum components in an inertial reference frame, the angular momentum components in the body frame, and a rotation angle. To avoid the singularity of the 7x7 covariance of this state vector arising from the constraint that the magnitude of the angular momentum vector is the same in the inertial and body frames, the Kalman filter employs the nonsingular 6x6 covariance of a reduced error state. Three of the components of this six-component error state are the usual infinitesimal attitude error angles, so the usual 3x3 attitude covariance matrix is a submatrix of the 6x6 covariance. The performance of the resulting filter is compared with that of a quaternion-based filter.

Markley, F. Landis↗

NASA NTRS2006

The Space Technology-7 Disturbance Reduction System Precision Control Flight Validation Experiment Control System Design

As originally proposed, the Space Technology-7 Disturbance Reduction System (DRS) project, managed out of the Jet Propulsion Laboratory, was designed to validate technologies required for future missions such as the Laser Interferometer Space Antenna (LISA). The two technologies to be demonstrated by DRS were Gravitational Reference Sensors (GRSs) and Colloidal MicroNewton Thrusters (CMNTs). Control algorithms being designed by the Dynamic Control System (DCS) team at the Goddard Space Flight Center would control the spacecraft so that it flew about a freely-floating GRS test mass, keeping it centered within its housing. For programmatic reasons, the GRSs were descoped from DRS. The primary goals of the new mission are to validate the performance of the CMNTs and to demonstrate precise spacecraft position control. DRS will fly as a part of the European Space Agency (ESA) LISA Pathfinder (LPF) spacecraft along with a similar ESA experiment, the LISA Technology Package (LTP). With no GRS, the DCS attitude and drag-free control systems make use of the sensor being developed by ESA as a part of the LTP. The control system is designed to maintain the spacecraft s position with respect to the test mass, to within 10 nm/the square root of Hz over the DRS science frequency band of 1 to 30 mHz.

O'Donnell, James R.↗

NASA NTRS2006

Mated Flight Control Issues for Space Exploration Systems

Several unique issues related to mated flight control have been broadly identified. These issues include redundancies in subsystems, controllability, command and control authority distribution, information flow across elements, and changes and variability in system characteristics due to variable mated configurations during operations. Architectural options for mated flight control are discussed in the context of evolving space systems.

Lim, Kyong B.↗

NASA NTRS2005

ATTITUDE FILTERING ON SO(3)

A new method is presented for the simultaneous estimation of the attitude of a spacecraft and an N-vector of bias parameters. This method uses a probability distribution function defined on the Cartesian product of SO(3), the group of rotation matrices, and the Euclidean space W N .The Fokker-Planck equation propagates the probability distribution function between measurements, and Bayes s formula incorporates measurement update information. This approach avoids all the issues of singular attitude representations or singular covariance matrices encountered in extended Kalman filters. In addition, the filter has a consistent initialization for a completely unknown initial attitude, owing to the fact that SO(3) is a compact space.

Markley, F. Landis↗

NASA NTRS2005

Nonlinear Attitude Filtering Methods

The extended Kalman filter (EKF) is the workhorse of real-time spacecraft attitude estimation. Since the group SO3 of rotation matrices has dimension three, most attitude determination EKFs use lower- dimensional attitude parameterizations than the nine-parameter attitude matrix itself. The fact that all three- parameter representations of SO3 are singular or discontinuous for certain attitudes has led to extended discussions of constraints and attitude representations in EKFs. The most successful EKF uses a nonsingular parameterization for the global attitude, which necessarily has more than three parameters, while employing a three-component representation for the attitude errors. This filter has become known as the Multiplicative Extended Kalman Filter. These issues are now well understood, however, and the EKF has performed admirably in the vast majority of attitude determination applications. Nevertheless, poor performance or even divergence arising from the linearization implicit in the EKF has led to the development of nonlinear filters, most recently sigma point or unscented filters and particle filters.

Markley, F. Landis↗

NASA NTRS2005

Attitude Estimation for Large Field-of-View Sensors

The QUEST measurement noise model for unit vector observations has been widely used in spacecraft attitude estimation for more than twenty years. It was derived under the approximation that the noise lies in the tangent plane of the respective unit vector and is axially symmetrically distributed about the vector. For large field-of-view sensors, however, this approximation may be poor, especially when the measurement falls near the edge of the field of view. In this paper a new measurement noise model is derived based on a realistic noise distribution in the focal-plane of a large field-of-view sensor, which shows significant differences from the QUEST model for unit vector observations far away from the sensor boresight. An extended Kalman filter for attitude estimation is then designed with the new measurement noise model. Simulation results show that with the new measurement model the extended Kalman filter achieves better estimation performance using large field-of-view sensor observations.

Cheng, Yang↗

NASA NTRS2004

A Universal Formula for Extracting the Euler Angles

Recently, the authors completed a study of the Davenport angles, which are a generalization of the Euler angles for which the initial and final Euler axes need not be either mutually parallel or mutually perpendicular or even along the coordinate axes. During the conduct of that study, those authors discovered a relationship which can be used to compute straightforwardly the Euler angles characterizing a proper-orthogonal direction-cosine matrix for an arbitrary Euler-axis set satisfying n(sub 1) x n(sub 2) = 0 and n(sub 3) x n(sub 1) = 0, which is also satisfied by the more usual Euler angles we encounter commonly in the practice of Astronautics. Rather than leave that relationship hidden in an article with very different focus from the present Engineering note, we present it and the universal algorithm derived from it for extracting the Euler angles from the direction-cosine matrix here. We also offer literal "code" for performing the operations, numerical examples, and general considerations about the extraction of Euler angles which are not universally known, particularly, the treatment of statistical error.

Shuster, Malcolm D.↗

NASA NTRS2003

Multiplicative Versus Additive Filtering for Spacecraft Attitude Determination

The absence of a globally nonsingular three-parameter representation of rotations forces attitude Kalman filters to estimate either a singular or a redundant attitude representation. We compare two filtering strategies using simplified kinematics and measurement models. Our favored strategy estimates a three-parameter representation of attitude deviations from a reference attitude specified 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. We point out some disadvantages of the other strategy, which directly estimates the four-parameter quaternion representation.

Markley, F. Landis↗

NASA NTRS2003

The Attitude Control System for the Wilkinson Microwave Anisotropy Probe

The Wilkinson Microwave Anisotropy Probe mission produces a map of the cosmic microwave background radiation over the entire celestial sphere by executing a fast spin and a slow precession of its spin axis about the Sun line to obtain a highly interconnected set of measurements. The spacecraft attitude is sensed and controlled using an inertial reference unit, two star trackers, a digital sun sensor, twelve coarse sun sensors, three reaction wheel assemblies, and a propulsion system. Sufficient attitude knowledge is provided to yield instrument pointing to a standard deviation (l sigma) of 1.3 arc-minutes per axis. In addition, the spacecraft acquires and holds the sunline at initial acquisition and in the event of a failure, and slews to the proper orbit adjust orientations and to the proper off-sunline attitude to start the compound spin. This paper presents an overview of the design of the attitude control system to carry out this mission and presents some early flight experience.

Markley, F. Landis↗

NASA NTRS2002

Generalization of the Euler Angles

It is shown that the Euler angles can be generalized to axes other than members of an orthonormal triad. As first shown by Davenport, the three generalized Euler axes, hereafter: Davenport axes, must still satisfy the constraint that the first two and the last two axes be mutually perpendicular if these axes are to define a universal set of attitude parameters. Expressions are given which relate the generalized Euler angles, hereafter: Davenport angles, to the 3-1-3 Euler angles of an associated direction-cosine matrix. The computation of the Davenport angles from the attitude matrix and their kinematic equation are presented. The present work offers a more direct development of the Davenport angles than Davenport's original publication and offers additional results.

Bauer, Frank H.↗

NASA NTRS2002

The Microwave Anisotropy Probe (MAP) Attitude Control System

The Microwave Anisotropy Probe mission is designed to produce a map of the cosmic microwave background radiation over the entire celestial sphere by executing a fast spin and a slow precession of its spin axis about the Sun line to obtain a highly interconnected set of measurements. The spacecraft attitude is sensed and controlled using an Inertial Reference Unit, two Autonomous Star Trackers, a Digital Sun Sensor, twelve Coarse Sun Sensors, three Reaction Wheel Assemblies, and a propulsion system. This paper describes the design of the attitude control system that carries out this mission and presents some early flight experience.

Markley, F. Landis↗

NASA NTRS2002

The Microwave Anisotropy Probe (MAP) Mission

Markley, F. Landis↗

NASA NTRS2002

Attitude Error Representations for Kalman Filtering

The quaternion has the lowest dimensionality possible for a globally nonsingular attitude representation. The quaternion must obey a unit norm constraint, though, which has led to the development of an extended Kalman filter using a quaternion for the global attitude estimate and a three-component representation for attitude errors. We consider various attitude error representations for this Multiplicative Extended Kalman Filter and its second-order extension.

Markley, F. Landis↗

NASA NTRS2002

Controller Design for the ST7 Disturbance Reduction System

The Space Technology 7 experiment will perform an on-orbit system-level validation of two specific Disturbance Reduction System technologies: a gravitational reference sensor employing a free-floating test mass and a set of micro-Newton colloidal thrusters. The Disturbance Reduction System is designed to maintain a spacecraft's position with respect to the free-floating test mass to less than 10 nm/ square root of Hz, over the frequency range 10(exp -3) Hz to 10(exp -2) Hz. This paper presents the design and analysis of the coupled drag-free and attitude control system that closes the loop between the gravitational reference sensor and the micro-Newton thrusters while incorporating star tracker data at low frequencies. The effects of actuation and measurement noise and disturbances on the spacecraft and test masses are evaluated in a seven-degree-of-freedom planar model incorporating two translational and one rotational degrees of freedom for the spacecraft and two translational degrees of freedom for each test mass.

Maghami, Peiman↗