On Inherent Information Redundancy in Vector Measuring Attitude Determination Methods

Paper number

IAC-05-C1.P.03

Author

Dr. Alfred Ng, Canadian Space Agency, Canada

Coauthor

Mr. Narendra Gollu, Concordia University, Canada

Coauthor

Dr. Yuri Kim, Canadian Space Agency, Canada

Year

2005

Abstract

For any spacecraft attitude control systems design, a successful choice of an appropriate Attitude Determination Method (ADM) is very important to meet mission requirements. A variety of deterministic and statistical methods based on a set of physical vectors measured by attitude sensors have been developed and published over the years. It is a well-known fact that at least two non-collinear vectors are necessary to derive whole set of rigid body attitude parameters. The minimal independent set of them is three independent Euler angles in certain order of rotations.  The most common deterministic method to obtain a spacecraft attitude with two measured vectors is an algebraic Triad Method [1], which allows the derivation of the directional cosines matrix between spacecraft body frame and the desired reference frame. Three Euler angles can be obtained from the matrix. It should be noted that despite every measured vector provides a capability to derive two Euler angles, the Triad Method ignores the redundancy in information and combines the measured information in a certain singular way generating a singular deterministic solution. There are stochastically optimal estimation methods such as Least-Square, Quest and Kalman-Filtering methods that combine vectors measured redundant information on a statistical basis. Some assumptions about statistics of measured sensor errors and, sometimes about the minimum magnitude of the angles determined are required in order to apply these methods.

In this article, the authors would like to bring the attention to vector measuring device inherent redundancy problem. This article presents a new Dyad Method that is deterministic and allows a pair of sensors measuring two non-collinear vectors, independently two Euler angles from each as well as the third one from other sensor. The procedure can be symmetrically reversed applying it to the same sensor pair but in the reverse order. Two sets of Euler angles are eventually obtained that can be weighted with a least square rule. The result is with respect to special coordinate frames and special order of rotation. The method may have significant advantages in some cases when sensor data outage temporary occurs. The efficiency of this method is proven by presenting the analysis and simulation in comparison with traditional Triad Method. The features and prospective applications are discussed. 

[1] 	Shuster, M.D. \& Oh, S.D., "Three-Axis Attitude Determination from Vector Observations," J. Guidance \& Control, Vol. 4, No. 1, 1981, pp. 70–77.

Abstract document

IAC-05-C1.P.03.pdf

Manuscript document

IAC-05-C1.P.03.pdf (🔒 authorized access only).

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