Comp. Appl. Math. https://doi.org/10.1007/s40314-018-0576-8 Unscented Kalman filter and smoothing applied to attitude estimation of artificial satellites Roberta Veloso Garcia 1 · Hélio Koiti Kuga 2 · William Reis Silva 2 · Maria Cecília Zanardi 3 Received: 21 March 2017 / Revised: 4 January 2018 / Accepted: 11 January 2018 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018 Abstract This article uses the state smoothing methodology applied to nonlinear systems to refine the attitude of artificial satellites. In this paper, simulated data of telemetry and ephemeris of a satellite with the specifications of China Brazil Earth Resources Satellite are considered and the dynamic system is described by the set of kinematic equations in terms of the Euler angles and the bias vector of gyroscope. The estimator used to determine the forward estimates in time is the Unscented Kalman filter, while the Rauch–Tung–Striebel fixed interval estimator makes the estimate backward time. The results show that, although the time of the estimation process is slightly increased, the smoother presents estimated attitude and bias closer to the real values than the estimated values when using only the Unscented Kalman filter. Therefore, the smoother can be considered as a technique that provides refined measurements of the attitude and bias of the gyroscope that may serve to calibrate the Kalman filter for next estimates. Keywords Rauch–Tung–Striebel smoother · Unscented Kalman filter · Attitude estimation · Euler angles Mathematics Subject Classification 60G25 · 60-xx · 60G-xx · 60G-25 Communicated by Guest Editors of S.I.: Celestial Mechanics and Control. B Roberta Veloso Garcia robertagarcia@usp.br 1 Lorena School of Engineering, Sao Paulo University, Estrada Municipal do Campinho, s/n, Lorena, SP CEP: 12.602-810, Brazil 2 Technological Institute of Aeronautics, Pr. Marechal Eduardo Gomes, 50, Vila das Acácias, São José dos Campos, SP CEP: 12.228-900, Brazil 3 Federal University of ABC, Av. dos Estados, 5001, Bairro Bangu, Santo André, SP CEP: 09210-580, Brazil 123