Covariance Analysis of Maximum Likelihood Attitude Estimation1

An attitude determination covariance measurement model for unit vector sensors with a wide field-of-view is analyzed and compared to the classic QUEST covariance model. The wide field-of-view model has been previously proposed as a more realistic alternative for sensors where measurement accuracy depends on angular distance from the boresight axis. Both QUEST and the wide field-of-view models are evaluated relative to a measurement model that uses the two-dimensional sensor focal plane measurements directly, rather than first converting them to unit vectors. The Cramér-Rao lower bound is derived for attitude determination based on such direct sensor measurements, and the wide field-of-view measurement model is shown to achieve this Cramér-Rao lower bound. Numerical simulations confirm that an extended Kalman filter based on the wide field-of-view model outperforms a filter based on the QUEST model, and also that the wide field-of-view 3σ bounds are effectively identical to those of a filter based on the direct two-dimensional sensor measurements. INTRODUCTION One of the requirements of most spacecraft missions is attitude determination. In this process, some combination of sensor measurements is used to determine the orientation of a spacecraft with respect to some chosen reference frame. Some attitude determination methods process a batch of measurements that apply at a specific instant in time. In particular, many strategies have been developed to find the optimal attitude by minimizing the Wahba problem cost function [1]. Other techniques estimate the attitude history of a dynamically-rotating spacecraft by applying an extended Kalman filter (EKF) or other filtering algorithms [2, 3, 4, 5]. For a survey of approaches to attitude determination, see Ref. [6]. Common sensors for attitude determination include three-axis magnetometers, Sun sensors, Earth-horizon sensors, star trackers and onboard GPS receivers [7]. In the context of filtering, these are often combined with gyroscopic rate measurements. Attitude determination strategies, both static and dynamic, require accurate mathematical models that relate each distinct type of measurement to the spacecraft attitude. Measurement models have two components. First, 1This paper is dedicated to the memory of Dr. Malcolm D. Shuster and the Acme Spacecraft Company. 2Postdoctoral Assistant, Department of Mechanical & Aerospace Engineering, University at Buffalo, State University of New York, Amherst, NY, 14260-4400. Email: [email protected]. 3Professor, Department of Mechanical & Aerospace Engineering, University at Buffalo, State University of New York, Amherst, NY, 14260-4400. Email: [email protected].