Validation and optimization of the GSAMQ analytical propagator for spin-stabilized satellite: Validação e otimização do propagador analítico GSAMQ para satélite spin-stabilizado

The aim of this paper is to validate the analytical propagator through simulations comparing the results with the real data and to optimize the work's source code so that it is processed faster. This work analyzes the use of the quadrupole model in the Earth's magnetic field when an analytical propagator calculates eddy current and residual magnetic torques in spin-stabilized satellites. For that, the components of the gravity gradient torque, the solar radiation torque and aerodynamics torque are also included. The simulations are carried out for a predetermined period and use data from the SCD1 Brazilian satellite, provided by the National Institute for Space Research (INPE). The results are then compared with the real data to validate the propagator. The propagator with the quadrupole model is called GSAMQ and uses the mean deviations of the magnitude of the spin velocity, and the angles of right ascension and declination of the spin axis as evaluation parameters. A statistical approach is included in this analysis and shows the model's accuracy

UNSCENTED KALMAN FILTERS AND EXTENDED H FILTER FOR SPACECRAFT ATTITUDE ESTIMATION USING QUATERNIONS

In this work, the attitude determination and the gyros drift estimation using the Uncented Kalman Filter (UKF) and the Second-Order Extended H Filter (SOEH F) for nonlinear systems will be described. The extended H filter provides a rigorous method for dealing with systems that have model and noise uncertainties. Thus, extended H filter is simply a robust version of the extended Kalman filter because to add tolerance to unmodeled noise and dynamics. The Unscented Kalman Filter transforms a set of points (cloud) through known nonlinear equations and combines the results to estimate the mean and covariance of the state. The points (called sigma-points) are carefully selected on the basis of a specific criterion. The application uses the simulated measurement data for orbit and attitude of the CBERS-2 (China Brazil Earth Resources Satellite). The attitude model is described by quaternions and the attitude sensors available are two DSS (Digital Sun Sensors), two IRES (Infra-Red Earth Sensor), and one triad of mechanical gyros.The results in this work show that one can reach accuracies in attitude determination within the prescribed requirements, besides providing estimates of the gyro drifts which can be further used to enhance the gyro error model. Keywords: Unscented Kalman Filter, Extended H Filter, Attitude Estimation, Gyro Calibration, Nonlinear Syste

ENFOQUE CTSA E O ENSINO DE ROBÓTICA NAS ATIVIDADES DO PROJETO ASTROEM III: O EXPERIMENTO ROBOMIND E ROBÔ LEGO MINDSTORMS NXT

Este trabalho tem como objetivo apresentar as atividades relacionadas ao Ensino de Robótica, desenvolvidas pelo Projeto Astroem III com enfoque CTSA. Para tanto, apresentaremos os experimentos realizados com o Robomind e o Lego Mindstorms NXT com grupos de alunos do Ensino Médio de duas escolas da rede pública estadual do Grande ABC. Os resultados demonstram que as atividades relacionadas à Robótica Educativa tornam as aulas mais atrativas, atualizadas e contextualizadas, possibilitando uma reflexão sobre o avanço científico e tecnológico e seus impactos para a sociedade e para o meio ambiente

Influence of geomagnetic field models on analytical propagator for SPIN stabilized satellites / Influência de modelos de campo geomagnético em analíticos propagador de satélites estabilizados com SPIN

 This work explores the impacts of using dipole or quadrupole models for Earth’s magnetic field when an analytical propagator calculates residual and eddy current torques on spin-stabilized satellites. Comprising the gravity gradient, solar radiation pressure, aerodynamic, and the aforementioned torques, the propagators used data from Brazilian satellites SCD1 and SCD2, provided by the National Institute for Space Research (INPE). Ranging about two decades in total, the selected simulation periods had their respective initial data propagated by both programs and then compared with actual data from the satellites, both updating the simulation with new daily data and not. The first propagator, called GSAM, which uses the dipole model to calculate the magnetic torques, was used to screen for simulation periods due to its swift running time. The second propagator uses the quadrupole model and is called GSAMQ. The mean deviations for the spin velocity, right ascension and declination angles were compared for both satellites, which showed that the programs better predict the spatial orientation of satellite SCD2 over SCD1, especially GSAMQ. It is also demonstrated that the programs’ precision heavily relies on the initial data, suggesting that a statistical approach of GSAMQ’s performance could shed more light on its accuracy.Analytical Propagators, Artificial Satellites, Environmental Torques, Satellite Attitude

Batch and filter approaches to spacecraft sensor alignment estimation

Two Kalman-filter formulations are presented for the estimation of spacecraft sensor misalignments from inflight data. In the first the sensor misalignments are part of the filter state variable; in the second the state vector contains only dynamical variables, but the sensitivities of the filter innovations to the misalignments are calculated within the Kalman filter. This procedure permits the misalignments to be estimated in batch mode as well as a much smaller dimension for the Kalman filter state vector. This results not only in a significantly smaller computational burden but also in a smaller sensitivity of the misalignment estimates to outliers in the data. Numerical simulations of the filter performance are presented

Spin stabilized satellite's attitude analytical prediction

An analytical approach for spin stabilized attitude propagation is presented, considering the coupled effect of the aerodynamic torque and the gravity gradient torque. A spherical coordination system fixed in the satellite is used to locate the satellite spin axis in relation to the terrestrial equatorial system. The spin axis direction is specified by its right ascension and the declination angles and the equation of motion are described by these two angles and the magnitude of the spin velocity. An analytical averaging method is applied to obtain the mean torques over an orbital period. To compute the average components of both aerodynamic torque and the gravity gradient torque in the satellite body frame reference system, an average time in the fast varying orbit element, the mean anomaly, is utilized. Afterwards, the inclusion of such torques on the rotational motion differential equations of spin stabilized satellites yields conditions to derive an analytical solution. The pointing deviation evolution, that is, the deviation between the actual spin axis and the computed spin axis, is also availed. In order to validate the analytical approach, the theory developed has been applied for spin stabilized Brazilian satellite SCD1, which are quite appropriated for verification and comparison of the data generated and processed by the Satellite Control Center of the Brazil National Research Institute (INPE). Numerical simulations performed with data of Brazilian Satellite SCD1 show the period that the analytical solution can be used to the attitude propagation, within the dispersion range of the attitude determination system performance of Satellite Control Center of the Brazilian Research Institute

Eficiência do Filtro de Kalman Unscented na estimação de atitude utilizando dados reais do satélite CBERS

The aim of this work is to compare the performance of the unscented Kalman filter (UKF) with the extended Kalman filter (EKF) in the attitude estimation nonlinear problems when the filters are subject to inaccurate initial conditions. For nonlinear systems the unscented Kalman filter uses a carefully selected set of sample points to more accurately map the probability distribution than the linearization of the standard extended Kalman filter, leading to faster convergence from inaccurate initial conditions in attitude estimation problems. In this study, the attitude of a satellite is estimated, simulating real time conditions using real data supplied by gyroscopes, infrared Earth sensors and digital Sun sensors. These sensors are on board the CBERS-2 satellite and the measurements were collected by the Satellite Control Centre of INPE. The satellite attitude is described by Euler angles, due to its easy geometric interpretation and the filter formulation is based on standard attitude-vector measurements using a gyro-based model for attitude propagation. Then by the degraded initial conditions it is possible to conclude that UKF is more efficient and accuracy than EKF. In relation with the process time, the UKF is competitive because although it demands a more time for the estimation process, the CPU time isn´t proportional to the generated sigma-points number. In the same way UKF can be applied in real time problem.Pages: 2241-224

Analytical prediction of the spin stabilized satellite's attitude using the solar radiation torque

The aim of this paper is to present an analytical solution for the spin motion equations of spin-stabilized satellite considering only the influence of solar radiation torque. The theory uses a cylindrical satellite on a circular orbit and considers that the satellite is always illuminated. The average components of this torque were determined over an orbital period. These components are substituted in the spin motion equations in order to get an analytical solution for the right ascension and declination of the satellite spin axis. The time evolution for the pointing deviation of the spin axis was also analyzed. These solutions were numerically implemented and compared with real data of the Brazilian Satellite of Data Collection - SCD1 an SCD2. The results show that the theory has consistency and can be applied to predict the spin motion of spin-stabilized artificial satellites

Um estudo da Libração Laplaciana

As quatro maiores luas de Júpiter – Io, Europa, Ganimedes e Calisto– são conhecidas como satélites galileanos, em homenagem ao físico eastrônomo italiano Galileo Galilem(1564-1642), que as descobriu emjaneiro de 1610. As três luasmais internas – Io, Europa e Ganimedes– possuem uma característica intrigante observada pelo astrônomo e matemático francês Pierre Simon Laplace (1749-1827): enquanto Io realiza quatro voltas ao redor de Júpiter, Europa realiza duas voltas e Ganimedes uma, o que define uma ressonância orbital na razão 4:2:1. Utilizando técnicas modernas de teoria de perturbações baseadas em séries de Lie, os autores deste livro apresentam um detalhado estudo analítico para um modelo matemático que descreva a dinâmica dos satélites galileanos. Uma solução analítica é apresentada para as variações de longo período para o movimento plano ao redor de um corpo central massivo de quatro corpos menores de massas comparáveis, com a condição de os períodos orbitais dos três primeiros corpos serem aproximadamente comensuráveis na razão 4:2:1