Engineering topics

Markley, F. Landis

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

At least 55 records · Page 3

NASA NTRS2002

The Microwave Anisotropy Probe (MAP) Mission

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 star trackers, a digital sun sensor, twelve coarse sun sensors, three reaction wheel assemblies, and a propulsion system. 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 NTRS2001

Maximum Torque and Momentum Envelopes for Reaction Wheel Arrays

Spacecraft reaction wheel maneuvers are limited by the maximum torque and/or angular momentum which the wheels can provide. For an n-wheel configuration, the torque or momentum envelope can be obtained by projecting the n-dimensional hypercube, representing the domain boundary of individual wheel torques or momenta, into three dimensional space via the 3xn matrix of wheel axes. In this paper, the properties of the projected hypercube are discussed, and algorithms are proposed for determining this maximal torque or momentum envelope for general wheel configurations. Practical implementation strategies for specific wheel configurations are also considered.

Reynolds, R. G.↗

NASA NTRS2001

Attitude Representations for Kalman Filtering

The four-component quaternion has the lowest dimensionality possible for a globally nonsingular attitude representation, it represents the attitude matrix as a homogeneous quadratic function, and its dynamic propagation equation is bilinear in the quaternion and the angular velocity. The quaternion is required to obey a unit norm constraint, though, so Kalman filters often employ a quaternion for the global attitude estimate and a three-component representation for small errors about the estimate. We consider these mixed attitude representations for both a first-order Extended Kalman filter and a second-order filter, as well for quaternion-norm-preserving attitude propagation.

Markley, F. Landis↗

NASA NTRS2001

Fast Quaternion Attitude Estimation from Two Vector Measurements

Many spacecraft attitude determination methods use exactly two vector measurements. The two vectors are typically the unit vector to the Sun and the Earth's magnetic field vector for coarse "sun-mag" attitude determination or unit vectors to two stars tracked by two star trackers for fine attitude determination. Existing closed-form attitude estimates based on Wahba's optimality criterion for two arbitrarily weighted observations are somewhat slow to evaluate. This paper presents two new fast quaternion attitude estimation algorithms using two vector observations, one optimal and one suboptimal. The suboptimal method gives the same estimate as the TRIAD algorithm, at reduced computational cost. Simulations show that the TRIAD estimate is almost as accurate as the optimal estimate in representative test scenarios.

Markley, F. Landis↗

NASA NTRS2000

New Developments in Quaternion Estimation from Vector Observations

This paper contains a critical comparison of estimators minimizing Wahba's loss function. Some new results are presented for the QUaternion ESTimator (QUEST) and EStimators of the Optimal Quaternion (ESOQ and ESOQ2) to avoid the computational burden of sequential rotations in these algorithms. None of these methods is as robust in principle as Davenport's q method or the Singular Value Decomposition (SVD) method, which are significantly slower. Robustness is only an issue for measurements with widely differing accuracies, so the fastest estimators, the modified ESOQ and ESOQ2, are well suited to sensors that track multiple stars with comparable accuracies. More robust forms of ESOQ and ESOQ2 are developed that are intermediate in speed.

Markley, F. Landis↗

NASA NTRS2000

Analytic Steady-State Accuracy of a Spacecraft Attitude Estimator

This paper extends Farrenkopf's analysis of a single-axis spacecraft attitude estimator using gyro and angle sensor data to include the angle output white noise of a rate-integrating gyro. Analytic expressions are derived for the steady-state pre-update and post-update angle and drift bias variances and for the state update equations. It is shown that only part of the state update resulting from the angle sensor measurement is propagated to future times.

Markley, F. Landis↗

NASA NTRS2000

Spacecraft Attitude Determination Methods

This document is presentation in viewgraph form, which outlines the methods of determining spacecraft attitude. The presentation reviews several parameterizations relating to spacecraft attitude, such as Euler's Theorem, Rodriques parameters, and Euler-Rodriques parameters or Quaternion. Onboard attitude determination is the norm, using either single frame or filtering methods. The presentation reviews several mathematical representations of attitude. The mechanisms for determining attitude on board the Hubble Space Telescope, the Tropical Rainfall and Measuring Mission and the Solar Anomalous and Magnetospheric Particle Explorer are reviewed. Wahba's problem, Procrustes Problem, and some solutions are also summarized.

Markley, F. Landis↗

NASA NTRS1999

Attitude Determination Using Two Vector Measurements

Many spacecraft attitude determination methods use exactly two vector measurements. The two vectors are typically the unit vector to the Sun and the Earth's magnetic field vector for coarse "sun-mag" attitude determination or unit vectors to two stars tracked by two star trackers for fine attitude determination. TRIAD, the earliest published algorithm for determining spacecraft attitude from two vector measurements, has been widely used in both ground-based and onboard attitude determination. Later attitude determination methods have been based on Wahba's optimality criterion for n arbitrarily weighted observations. The solution of Wahba's problem is somewhat difficult in the general case, but there is a simple closed-form solution in the two-observation case. This solution reduces to the TRIAD solution for certain choices of measurement weights. This paper presents and compares these algorithms as well as sub-optimal algorithms proposed by Bar-Itzhack, Harman, and Reynolds. Some new results will be presented, but the paper is primarily a review and tutorial.

Markley, F. Landis↗

NASA NTRS1999

Nonlinear Fuzzy Hybrid Control of Spacecraft

This paper describes a new approach for intelligent control of a spacecraft with large angle maneuvers. This new approach, based on fuzzy logic, determines the required torque to achieve a robust, high performance attitude response. This scheme extends the robustness, performance and portability of the existing linear or nonlinear attitude controllers. Formulations are presented for attitude-control but can be extended to other applications. A simulation study, which uses the new control strategy to stabilize the motion of the Microwave Anisotropy Probe spacecraft in the presence of disturbances and saturations, demonstrates the merits of the proposed scheme.

Mason, Paul A. C.↗

NASA NTRS1999

Fast Integer Ambiguity Resolution for GPS Attitude Determination

In this paper, a new algorithm for GPS (Global Positioning System) integer ambiguity resolution is shown. The algorithm first incorporates an instantaneous (static) integer search to significantly reduce the search space using a geometric inequality. Then a batch-type loss function is used to check the remaining integers in order to determine the optimal integer. This batch function represents the GPS sightline vectors in the body frame as the sum of two vectors, one depending on the phase measurements and the other on the unknown integers. The new algorithm has several advantages: it does not require an a-priori estimate of the vehicle's attitude; it provides an inherent integrity check using a covariance-type expression; and it can resolve the integers even when coplanar baselines exist. The performance of the new algorithm is tested on a dynamic hardware simulator.

Lightsey, E. Glenn↗

NASA NTRS1999

30 Years of Wahba's Problem

This article discusses a problem proposed by Grace Wahba: Find the orthogonal matrix A with determinant +1 that minimizes the loss function L(A) is identical with the 1/2(summation from i( a(sub i) * absolute value of (b(sub i)- Ar(sub i))squared). where {b(sub i)} is a set of unit vectors measured in a spacecraft's body frame, {r(sub i)} e the corresponding unit vectors in a reference frame and {a(sub i) are non-negative weights). The orthogonal Procrustes problem is to find the orthogonal matrix A that is closest to B in the sense of the Fobenius norm, so that Wahba's Problem is equivalent to the orthogonal Procrustes problem with the provision that the determinant of A must be +1. The article reviews various solutions to this problem and the implementations of the various solutions.

Markley, F. Landis↗

NASA NTRS1999

How to Estimate Attitude from Vector Observations

The most robust estimators minimizing Wahba's loss function are Davenport's q method and the Singular Value Decomposition (SVD) method. The q method is faster than the SVD method with three or more measurements. The other algorithms are less robust since they solve the characteristic polynomial equation to find the maximum eigenvalue of Davenport's K matrix. They are only preferable when speed or processor power is an important consideration. Of these, Fast Optimal Attitude Matrix (FOAM) is the most robust and faster than the q method. Robustness is only an issue for measurements with widely differing accuracies, so the fastest algorithms, Quaternion ESTimator (QUEST), EStimator of the Optimal Quaternion (ESOQ), and ESOQ2, are well suited to star sensor applications.

Markley, F. Landis↗

NASA NTRS1999

Spacecraft Attitude Representations

The direction cosine matrix or attitude matrix is the most fundamental representation of the attitude, but it is very inefficient: It has six redundant parameters, it is difficult to enforce the six (orthogonality) constraints. the four-component quaternion representation is very convenient: it has only one redundant parameter, it is easy to enforce the normalization constraint, the attitude matrix is a homogeneous quadratic function of q, quaternion kinematics are bilinear in q and m. Euler angles are extensively used: they often have a physical interpretation, they provide a natural description of some spacecraft motions (COBE, MAP), but kinematics and attitude matrix involve trigonometric functions, "gimbal lock" for certain values of the angles. Other minimum (three-parameter) representations: Gibbs vector is infinite for 180 deg rotations, but useful for analysis, Modified Rodrigues Parameters are nonsingular, no trig functions, Rotation vector phi is nonsingular, but requires trig functions.

Markley, F. Landis↗

NASA NTRS1998

Optimal integer resolution for attitude determination using global positioning system signals

In this paper, a new motion-based algorithm for GPS integer ambiguity resolution is derived. The first step of this algorithm converts the reference sightline vectors into body frame vectors. This is accomplished by an optimal vectorized transformation of the phase difference measurements. The result of this transformation leads to the conversion of the integer ambiguities to vectorized biases. This essentially converts the problem to the familiar magnetometer-bias determination problem, for which an optimal and efficient solution exists. Also, the formulation in this paper is re-derived to provide a sequential estimate, so that a suitable stopping condition can be found during the vehicle motion. The advantages of the new algorithm include: it does not require an a-priori estimate of the vehicle's attitude; it provides an inherent integrity check using a covariance-type expression; and it can sequentially estimate the ambiguities during the vehicle motion. The only disadvantage of the new algorithm is that it requires at least three non-coplanar baselines. The performance of the new algorithm is tested on a dynamic hardware simulator.

Crassidis, John L.↗

NASA NTRS1998

A Novel Sensor for Attitude Determination Using Global Positioning System Signals

An entirely new sensor approach for attitude determination using Global Positioning System (GPS) signals is developed. The concept involves the use of multiple GPS antenna elements arrayed on a single sensor head to provide maximum GPS space vehicle availability. A number of sensor element configurations are discussed. In addition to the navigation function, the array is used to find which GPS space vehicles are within the field-of-view of each antenna element. Attitude determination is performed by considering the sightline vectors of the found GPS space vehicles together with the fixed boresight vectors of the individual antenna elements. This approach has clear advantages over the standard differential carrier-phase approach. First, errors induced by multipath effects can be significantly reduced or eliminated altogether. Also, integer ambiguity resolution is not required, nor do line biases need to be determined through costly and cumbersome self-surveys. Furthermore, the new sensor does not require individual antennas to be physically separated to form interferometric baselines to determine attitude. Finally, development potential of the new sensor is limited only by antenna and receiver technology development unlike the physical limitations of the current interferometric attitude determination scheme. Simulation results indicate that accuracies of about 1 degree (3 omega) are possible.

Crassidis, John L.↗

NASA NTRS1998

Efficient and Optimal Attitude Determination Using Recursive Global Positioning System Signal Operations

In this paper, a new and efficient algorithm is developed for attitude determination from Global Positioning System signals. The new algorithm is derived from a generalized nonlinear predictive filter for nonlinear systems. This uses a one time-step ahead approach to propagate a simple kinematics model for attitude determination. The advantages of the new algorithm over previously developed methods include: it provides optimal attitudes even for coplanar baseline configurations; it guarantees convergence even for poor initial conditions; it is a non-iterative algorithm; and it is computationally efficient. These advantages clearly make the new algorithm well suited to on-board applications. The performance of the new algorithm is tested on a dynamic hardware simulator. Results indicate that the new algorithm accurately estimates the attitude of a moving vehicle, and provides robust attitude estimates even when other methods, such as a linearized least-squares approach, fail due to poor initial starting conditions.

Crassidis, John L.↗

NASA NTRS1998

Attitude Determination Using Two Vector Measurements

Many spacecraft attitude determination methods use exactly two vector measurements. The two vectors are typically the unit vector to the Sun and the Earth's magnetic field vector for coarse "sun-mag" attitude determination or unit vectors to two stars tracked by two star trackers for fine attitude determination. TRIAD, the earliest published algorithm for determining spacecraft attitude from two vector measurements, has been widely used in both ground-based and onboard attitude determination. Later attitude determination methods have been based on Wahba's optimality criterion for n arbitrarily weighted observations. The solution of Wahba's problem is somewhat difficult in the general case, but there is a simple closed-form solution in the two-observation case. This solution reduces to the TRIAD solution for certain choices of measurement weights. This paper presents and compares these algorithms as well as sub-optimal algorithms proposed by Bar-Itzhack, Harman, and Reynolds. Some new results will be presented, but the paper is primarily a review and tutorial.

Markley, F. Landis↗

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.↗