Application of Vectorized Attitude Determination Using Global Positioning System Signals

In this paper, an analysis of two techniques for finding a point-by-point (deterministic) attitude solution of a vehicle using Global Positioning System phase difference measurements is preformed. These techniques transform a general loss function into a more numerically efficient form. One technique determines three-dimensional vectors in the body coordinate system, and the other in the reference coordinate system. Covariance relationships for both vectorized approaches show that they produce suboptimal estimates of the attitude unless the baseline or sightlines are proportional to an orthonormal set, in which case they produce optimal estimates. Both vectorized techniques are tested on a hardware dynamic simulator. Results from this study are useful to determine the circumstances for which vector transformation yields the more accurate results. Introduction The utilization of phase difference measurements from Global Positioning System (GPS) receivers provides a novel approach for three-axis attitude determination and/or estimation. These measurements have been successfully used to determine the attitude of both aircraft and spacecraft. Recently, much attention has been placed on spacecraft-based applications. One of the first space-based GPS .Copyright © 1998 by John L. Crassidis. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. experiments for attitude determination was flown on the RADCAL (RADar CALibration) spacecraft. To obtain maximum GPS visibility, and to reduce signal interference due to multipath reflection, GPS patch antennas were placed on the top surface of the spacecraft bus. Although the antenna baselines were short for attitude determination, accuracies between 0.5 to 1.0 degrees (root-mean-square) were achieved. In this paper, the problem of finding the attitude from GPS phase difference measurements using deterministic approaches is addressed. Error sources, such as integer ambiguity, are not investigated. These errors are assumed to be accounted for before the attitude determination problem is solved. The most common GPS attitude determination scheme minimizes a loss function constituting the sum weighted two-norm residuals between the measured and determined phase difference quantities. A suboptimal solution involves transforming the general loss function into a form that can be minimized without iterative intense methods. One such technique, shown in Ref. [6], transforms the general loss function into a form identical to Wahba’s problem. Therefore, fast algorithms such as QUEST and FOAM can then be used to determine the attitude. Cohen [1] showed that the solution based on Wahba’s problem is almost an order of magnitude faster than a conventional nonlinear least-squares algorithm. The vectorized approach in Ref. [6] involves a two step process. The first step involves finding the sightline vectors in the body coordinate system. At least three non-coplanar baselines must exist to perform this transformation. If this is not the case, the AIAA-98-4390