Three-axis attitude determination from vector observations

TLDR

The paper discusses the mathematical relationship and relative merits of the TRIAD and QUEST algorithms, provides numerical examples, and emphasizes the advantage of computing covariance matrices in the body frame rather than the inertial frame. The study presents two computationally efficient algorithms for determining three‑axis attitude from two or more vector observations. The TRIAD algorithm offers a deterministic solution using two vector observations, while the QUEST algorithm optimally determines attitude by maximizing weighted overlap of any number of reference and observation vectors. Analytical expressions for the covariance matrices of the TRIAD and QUEST algorithms are derived, and the results—illustrated by numerical examples—are valuable for frequent single‑frame attitude computation and for evaluating launch‑window constraints or sensor configuration accuracies.

Abstract

Two computationally efficient algorithms are presented for determining three-axis attitude from two or more vector observations. The first of these, the TRIAD algorithm, provides a deterministic (i.e., nonoptimal) solution for the attitude based on two vector observations. The second, the QUEST algorithm, is an optimal algorithm which determines the attitude that achieves the best weighted overlap of an arbitrary number of reference and observation vectors. Analytical expressions are given for the covariance matrices for the two algorithms using a fairly realistic model for the measurement errors. The mathematical relationship of the two algorithms and their relative merits are discussed and numerical examples are given. The advantage of computing the covariance matrix in the body frame rather than in the inertial frame (e.g., in terms of Euler angles) is emphasized. These results are valuable when a single-frame attitude must be computed frequently. They will also be useful to the mission analyst or spacecraft engineer for the evaluation of launch-window constraints or of attitude accuracies for different attitude sensor configurations.