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

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

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

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

Generalization of the Euler angles.

Abstract It is shown that the Euler angles can be generalized to axes other than members of an orthonormal triad. As rst shown by Davenport, the three generalized Euler axes, hereafter: Davenport axes, must still satisfy the constraint that the rst two and the last two axes be mutually perpendicular if these axes are to dene a universal set of attitude parameters. which represent the attitude, in particular, the attitude of a rigid body. Here, n 1 , n 2 , and n 3 are selected from the set {1,2,3 }, wherê In general, we denote column vectors by bold sans serif letters. A caret here denotes a unit column vector. The primes denote that the column vectors are each representations with respect to a dierent abstract basis (as seen by an inertial observer). In this case, the basis is the current basis of the body-xed coordinate system, which changes (from an inertial point of view) as the body rotates

Deterministic three-axis attitude determination,” The

Abstract The general problem of determining the attitude deterministically, that is, directly without the optimization of a cost function, from measurements of arc lengths and directions is examined. While there is no continuous degeneracy for the solutions to this problem, because effectively three data are given, nonetheless, the attitude solution still has generally a discrete degeneracy which can be removed only by the addition of further data. The only case escaping the discrete degeneracy has an over-determined solution. Specific algorithms are developed for all cases, and the nature of the degeneracy is explored in detail

Spin-Axis Attitude Estimation Du spinnst doch! Du hast doch'n Knall! Du spinnst doch! Du spinnst doch total! 3 Die Prinzen (1993)

Abstract Spin-axis attitude estimation is examined in a manner analogous to the study of three-axis attitude estimation. Measurement modeling issues are given careful consideration, as are those of representation, frame, and constraint. Three approaches to spin-axis attitude estimation are presented and compared numerically. A thorough covariance analysis of all algorithms is performed

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