Gaussian Sum Filter Applied to Attitude Estimation for China-Brazil Earth Resources Satellite-4

The Gaussian Sum Filter (GSF) and the Particle Filter (PF) were applied in this work to attitude and gyros bias estimation using simulated orbit and attitude measurement data for CBERS-4 (China Brazil Earth Resources Satellite 4) recently in operation. For nonlinear systems, such as attitude dynamics, the posterior probability density function (pdf) may not be Gaussian though, which may lead to problems in the Extend Kalman Filter (EKF) and Unscented Kalman Filter (UKF). The fundamental concept in a GSF is to use a finite set of Gaussian distributions to estimate and to construct the pdf using Bayesian estimation approach. The goal for the GSF is approximates the predicted and posterior probabilities densities functions (pdfs) as a finite number of weighted sums of Gaussian densities distributions as has been proposed in the literature. The dynamic attitude model is described by quaternions and the available attitude sensors using for attitude estimation are two Digital Sun Sensors (DSS) with nonlinear functions of roll, pitch, and yaw attitude angles; two Infrared Earth Sensor (IRES) with direct measurements of roll and pitch angles; and a triad of mechanical gyroscopes that provide direct incremental angles or angular velocities. The results for attitude estimation show that it is possible to achieve precision in determining attitudes within the prescribed requirements using the GSF, with lower computational cost and with a smaller number of particles when compared to the standard particle filter.