Engineering topics

Shuster, Malcolm D.

Publications and source records attributed to Shuster, Malcolm D..

8 records

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 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 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 NTRS1994

A new algorithm for attitude-independent magnetometer calibration

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.

Alonso, Roberto↗

NASA NTRS1993

Attitude analysis in Flatland: The plane truth

Many results in attitude analysis are still meaningful when the attitude is restricted to rotations about a single axis. Such a picture corresponds to attitude analysis in the Euclidean plane. The present report formalizes the representation of attitude in the plane and applies it to some well-known problems. In particular, we study the connection of the 'additive' and 'multiplicative' formulations of the differential corrector for the quaternion in its two-dimensional setting.

Shuster, Malcolm D.↗

NASA NTRS1991

New quests for better attitudes

During the past few years considerable insight was gained into the QUEST algorithm both as a maximum likelihood estimator and as a Kalman filter/smoother for systems devoid of dynamical noise. The new algorithms and software are described and analytical comparisons are made with the more conventional attitude Kalman filter. It is also described how they may be accommodated to noisy dynamical systems.

Shuster, Malcolm D.↗

NASA NTRS1990

Attitude sensor alignment calibration for the solar maximum mission

An earlier heuristic study of the fine attitude sensors for the Solar Maximum Mission (SMM) revealed a temperature dependence of the alignment about the yaw axis of the pair of fixed-head star trackers relative to the fine pointing Sun sensor. Here, new sensor alignment algorithms which better quantify the dependence of the alignments on the temperature are developed and applied to the SMM data. Comparison with the results from the previous study reveals the limitations of the heuristic approach. In addition, some of the basic assumptions made in the prelaunch analysis of the alignments of the SMM are examined. The results of this work have important consequences for future missions with stringent attitude requirements and where misalignment variations due to variations in the temperature will be significant.

Pitone, Daniel S.↗

NASA NTRS1988

Spacecraft alignment estimation

A numerically well-behaved factorized methodology is developed for estimating spacecraft sensor alignments from prelaunch and inflight data without the need to compute the spacecraft attitude or angular velocity. Such a methodology permits the estimation of sensor alignments (or other biases) in a framework free of unknown dynamical variables. In actual mission implementation such an algorithm is usually better behaved than one that must compute sensor alignments simultaneously with the spacecraft attitude, for example by means of a Kalman filter. In particular, such a methodology is less sensitive to data dropouts of long duration, and the derived measurement used in the attitude-independent algorithm usually makes data checking and editing of outliers much simpler than would be the case in the filter.

Shuster, Malcolm D.↗