author = "Garcia, Roberta Veloso and Pardal, C. Paula M. and Kuga, 
                         H{\'e}lio Koiti",
          affiliation = "{Universidade de S{\~a}o Paulo (USP)} and {Universidade de 
                         S{\~a}o Paulo (USP)} and {Instituto Nacional de Pesquisas 
                         Espaciais (INPE)}",
                title = "Nonlinear filtering for sequential spacecraft attitude estimation 
                         with real data: cubature kalman filter, unscented kalman filter 
                         and extended kalman filter",
                 year = "2018",
         organization = "Cospar Scientific Assembly, 42.",
             abstract = "The purpose of this work is to analyze the performance of the 
                         Cubature Kalman Filter, Unscented Kalman Filter and Extended 
                         Kalman Filter estimators in the attitude estimation problem when 
                         submitted to real attitude sensors data. The Extended Kalman 
                         Filter (EKF) is the most used nonlinear filtering algorithm for 
                         the attitude estimation in real time. The EKF is the nonlinear 
                         version of the Kalman Filter which linearizes about an estimate of 
                         the current mean and covariance. However, when the filter is 
                         subjected to poor conditions, the linearization of the system may 
                         not be efficient and lead to an estimation of low accuracy and 
                         divergence of the filter. The Unscented Kalman Filter (UKF) is an 
                         algorithm that was developed in order to avoid the linearizations 
                         required by the EKF. Basically, the UKF uses a set of points 
                         chosen deterministically, called sigma-points, to capture the 
                         probability distribution and generalizes to nonlinear system 
                         without the burdensome analytic derivation as in the EKF. More 
                         recently, the Cubature Kalman Filter (CKF) was proposed as an 
                         alternative estimation algorithm for general nonlinear systems. 
                         The CKF, which builds on the numerical-integration perspective of 
                         Gaussian filters, employs a third-degree spherical-radical 
                         cubature rule to compute Gaussianweighted integrals, 
                         derivative-free nonlinear filtering algorithm with improved 
                         performance over the UKF in terms of estimation accuracy, 
                         numerical stability and computational costs. In this work, the 
                         application uses the real measurement data for orbit and attitude 
                         of the CBERS-2 (China Brazil Earth Resources Satellite) satellite. 
                         The attitude dynamical model is described by nonlinear equations 
                         involving the Euler angles. The attitude sensors available are two 
                         DSS (Digital Sun Sensors), two IRES (Infra-Red Earth Sensor), and 
                         one triad of mechanical gyros. The analyzes are based on the 
                         robustness of the filter, in relation to the precision, 
                         computational cost and convergence speed in attitude estimation. 
                         As the use of real data makes it impossible to compare the 
                         estimated results with the real attitude of the satellite, then 
                         the results obtained via EKF are taken as reference for comparison 
                         with the UKF and CKF. The results in this work show that, for the 
                         case studied in this article, the filters are very competitive and 
                         present advantages and disadvantages that should be evaluated 
                         according to the need of each problem.",
  conference-location = "Pasadena, California",
      conference-year = "14-22 July",
             language = "en",
        urlaccessdate = "23 jan. 2021"