Fisher Information Based Analysis of Deterministic Relative Attitude Observability in Planar Vehicle Formations Christopher K. Nebelecky * , John L. Crassidis † University at Buffalo, State University of New York, Amherst, NY 14260-4400 Baro Hyun ‡ University of Michigan, Ann Arbor, Michigan 48109-2140 Yang Cheng § Mississippi State University, Mississippi State, MS 39762 This paper examines the problem of relative attitude observability for formations of three, four and five vehicle formations. The analysis is rooted in within the principles of maximum likelihood estimation insomuch as the metric for observability is the resulting Fisher information matrix for the small attitude errors. For formations of three and four vehicles it is shown that the relative attitudes are not observable by proving that the Fisher information matrix is singular for these cases. For formations of five vehicles, the observability relies on the number of LOS vector pairs available within the formation. It is shown that a minimum number of 8 LOS vector pairs is necessary for the attitudes to be observable, with all configurations of less LOS vector pairs yielding a singular Fisher information matrix. I. Introduction Attitude determination involves the calculation of the orientation between two orthogonal reference frames. While attitude determination doesn’t fall under any one specific discipline, it has been the space community that has had the most interest in the attitude determination problem. The ability to successfully accomplish a spacecraft’s mission is often directly related to the ability to determine its attitude to within some tolerable level. Without accurate and dependable attitude knowledge a spacecraft risks losing power, communications links and the ability to perform maneuvers, for example. A particularly interesting and important division of attitude determination is that of relative attitude determination. While all attitude determination is in some sense relative, here relative is defined as being between two vehicles, i.e. the relative attitude between two spacecraft is the orientation of one spacecraft’s body coordinate frame with respect to the other spacecraft’s body coordinate frame rather then with respect to some inertial or intermediate coordinate frame. The need for accurate relative attitude information is essential for a variety of applications with formation flying and rendezvous being just a few examples. Relative attitude determination can be performed using both filtering and single point methods. These methods, in some way, involve comparison of multiple line-of-sight (LOS) vector observations expressed in one coordinate frame to those same vectors expressed in another coordinate frame. Filtering methods combine these LOS observations with the system dynamics in order to estimate the relative attitudes in real- time. Extended Kalman filters have been successfully used in estimating the relative position and attitude * Graduate Student, Department of Mechanical & Aerospace Engineering. E-mail: ckn@buffalo.edu. Student Member AIAA. † Professor, Department of Mechanical & Aerospace Engineering. E-mail: johnc@buffalo.edu. Associate Fellow AIAA. ‡ Postdoctoral Research Fellow. E-mail: bhyun@umich.edu. § Assistant Professor, Department of Aerospace Engineering. Email: cheng@ae.msstate.edu, Associate Fellow AIAA. 1 of 16 American Institute of Aeronautics and Astronautics AIAA/AAS Astrodynamics Specialist Conference 13 - 16 August 2012, Minneapolis, Minnesota AIAA 2012-4513 Copyright © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Downloaded by John Crassidis on November 6, 2012 | http://arc.aiaa.org | DOI: 10.2514/6.2012-4513