Probabilistic Determination Algorithm for Detumbling and Angular Rate Convergence using a Three-Axis Magnetometer

Abstract

This paper proposes an algorithm to determine the convergence of angular rate by using B-dot measurements from a 3-axis magnetometer based on a probabilistic approach. The probability distribution of the sum of the square of B-dot is analytically derived when the CubeSat has a zero angular rate. The probability distribution when the CubeSat has a non-zero angular rate is derived based on simulations. In addition, by choosing two probability distributions and setting a threshold between them, the convergence probability of the angular rate is calculated using Bayes’ theorem assuming that CubeSat obtains consecutive magnetic measurements in real-time. Finally, the proposed algorithm is verified through Monte Carlo simulations and detailed discussions are presented along with comparisons with previous research and methods.