Linear Covariance Techniques for Closed-Loop Attitude Determination and Control Analysis

Abstract

Listen

Translate article

During the 2011-2012 winter semester, graduate students in the Department of Aerospace Engineering, Technion were asked to reproduce the results of an attitude estimation paper by Prof. Itzhack Bar-Itzhack, “True Covariance Simulation of the EUVE Update Filter”, as a homework assignment for a special topics course on linear covariance analysis. The students reproduced both the expected filter errors and the true filter errors as reported by Bar-Itzhack using covariance analysis. Bar Itzhack’s work was then extended to determine the closed-loop pointing/control errors, again using linear covariance techniques. The control problem included star-tracker and gyro errors, magnetic torquer actuation errors, random disturbance moments, a suboptimal Kalman filter with model replacement, and a simple proportional-derivative control law. Using an augmented state formulation, covariance techniques were used to determine the variances of the expected and true attitude estimation errors, the variances of the true pointing errors of the closed-loop system, and the variance of the required control effort. Results were verified by nonlinear Monte Carlo analysis. The linear covariance analysis proved to be a very useful and fast analysis tool for the preliminary design of attitude determination and control systems.