Roberta Veloso Garcia

Unscented Kalman Filter Applied to the Spacecraft Attitude Estimation with Euler Angles

The aim of this work is to test an algorithm to estimate, in real time, the attitude of an artificial satellite using real data supplied by attitude sensors that are on board of the CBERS-2 satellite (China Brazil Earth Resources Satellite). The real-time estimator used in this work for attitude determination is the Unscented Kalman Filter. This filter is a new alternative to the extended Kalman filter usually applied to the estimation and control problems of attitude and orbit. This algorithm is capable of carrying out estimation of the states of nonlinear systems, without the necessity of linearization of the nonlinear functions present in the model. This estimation is possible due to a transformation that generates a set of vectors that, suffering a nonlinear transformation, preserves the same mean and covariance of the random variables before the transformation. The performance will be evaluated and analyzed through the comparison between the Unscented Kalman filter and the extended Kalman filter results, by using real onboard data.

Spin-Stabilized Spacecrafts: Analytical Attitude Propagation Using Magnetic Torques

An analytical approach for spin-stabilized satellites attitude propagation is presented, considering the influence of the residual magnetic torque and eddy currents torque. It is assumed two approaches to examine the influence of external torques acting during the motion of the satellite, with the Earths magnetic field described by the quadripole model. In the first approach is included only the residual magnetic torque in the motion equations, with the satellites in circular or elliptical orbit. In the second approach only the eddy currents torque is analyzed, with the satellite in circular orbit. The inclusion of these torques on the dynamic equations of spin stabilized satellites yields the conditions to derive an analytical solution. The solutions show that residual torque does not affect the spin velocity magnitude, contributing only for the precession and the drift of the spacecrafts spin axis and the eddy currents torque causes an exponential decay of the angular velocity magnitude. Numerical simulations performed with data of the Brazilian Satellites (SCD1 and SCD2) show the period that analytical solution can be used to the attitude propagation, within the dispersion range of the attitude determination system performance of Satellite Control Center of Brazil National Research Institute.

Least Squares Method for Attitude Determination Using the Real Data of CBERS-2 Satellite

his work is applied to the dynamics of rotational motion of artificial satellites, that is, itsorientation (attitude) with respect to an inertial reference system. The attitude determination involvesapproaches of nonlinear estimation techniques, which knowledge is essential to the safety and controlof the satellite and payload. Here one focuses on determining the attitude of a real satellite: CBERS-2(China Brazil Earth Resources Satellite). This satellite was launched in 2003 and were controlled andoperated in turns by China (Xi’an Control Center) and Brazil (Satellite Control Center). Its orbit isnear polar sun-synchronous with an altitude of 778km, crossing Equator at 10:30am in descendingdirection, frozen perigee at 90 degrees, and providing global coverage of the world every 26 days.The attitude dynamical model is described by nonlinear equations involving the Euler angles. Theattitude sensors available are two DSS (Digital Sun Sensor), two IRES (Infra-Red Earth Sensor), andone triad of mechanical gyros. The two IRES give direct measurements of roll and pitch angles with acertain level of error. The two DSS are nonlinear functions of roll, pitch, and yaw attitude angles. Thegyros furnish the angular measurements in the body frame reference system. Gyros are very importantsensors, as they provide direct incremental angles or angular velocities. They can sense instantaneousvariations of nominal velocities. An important feature is that it allows the replacement of complexmodels (different torques acting on the space environment) by using their measurements to turn thedynamical equations into simple kinematic equations. However gyros present several sources of errorof which the drift is the most troublesome. Such drifts yield along time an accumulation of errorswhich must be accounted for in the attitude determination process. Herein one proposes to estimatethe attitude and the drift of the gyros using the Least SquaresMethod. Results show that one can reachaccuracies in attitude determination within the prescribed requirements, besides providing estimatesof the gyro drifts which can be further used to enhance the gyro error model.

Efficiency of Solution Methods for Kepler’s Equation

This article discusses, in the case of eccentric orbits, some solution methods for Keplers equation, for instance: Newtons method, Halley method and the solution by Fourire-Bessel expansion. The efficiency of solution methods is evaluated according to the number of iterations that each method needs to lead to a solution within the specified tolerance. The solution using Fourier-Bessel series is not an iterative method, however, it was analyzed the number of terms required to achieve the accuracy of the prescribed solution.

Estimação de atitude com parâmetros modificados de rodrigues e dados reais do satélite CBERS-2B

A proposta deste trabalho e estudar o comportamento do Filtro de Kalman Unscented (FKU) utilizando os parâmetros modificados de Rodrigues (PMR), quando dados reais de sensores que estao a bordo do satelite CBERS-2B (China Brazil Earth Resources Satellite) alimentam o estimador.