ISA Transactions 49 (2010) 249–256 Contents lists available at ScienceDirect ISA Transactions journal homepage: www.elsevier.com/locate/isatrans Pico satellite attitude estimation via Robust Unscented Kalman Filter in the presence of measurement faults Halil Ersin Soken ∗ , Chingiz Hajiyev Istanbul Technical University, Istanbul, Turkey article info Article history: Received 27 July 2009 Received in revised form 5 February 2010 Accepted 9 April 2010 Available online 10 May 2010 Keywords: Attitude estimation Robust Kalman filtering Scale factor Measurement faults abstract In the normal operation conditions of a pico satellite, a conventional Unscented Kalman Filter (UKF) gives sufficiently good estimation results. However, if the measurements are not reliable because of any kind of malfunction in the estimation system, UKF gives inaccurate results and diverges by time. This study introduces Robust Unscented Kalman Filter (RUKF) algorithms with the filter gain correction for the case of measurement malfunctions. By the use of defined variables named as measurement noise scale factor, the faulty measurements are taken into consideration with a small weight, and the estimations are corrected without affecting the characteristics of the accurate ones. Two different RUKF algorithms, one with single scale factor and one with multiple scale factors, are proposed and applied for the attitude estimation process of a pico satellite. The results of these algorithms are compared for different types of measurement faults in different estimation scenarios and recommendations about their applications are given. © 2010 ISA. Published by Elsevier Ltd. All rights reserved. 1. Introduction Since they were proposed, Kalman filters have been widely used as an attitude determination technique [1], and different Kalman filter types have been developed for that purpose. As a known fact; the attitude estimation problem of a pico satellite cannot be solved by linear Kalman filters because of the inherent nonlinear dynamics and kinematics. In such cases an Extended Kalman Filter (EKF) may be used instead. By using EKF, it is possible to estimate attitude parameters of a satellite which has three onboard magnetometers as the only measurement sensors [2]. However, the mandatory linearization phase of EKF procedures may cause the filter to diverge and usually Jacobian calculations required for this phase are cumbersome and time-consuming [3,4]. The Unscented Kalman Filter (UKF) is a relatively new Kalman filtering technique that generalizes the Kalman filter for both linear and nonlinear systems and in the case of nonlinear dynamics, UKF may afford considerably more accurate estimation results than the former observer design methodologies such as Extended Kalman Filters. UKF is based on the fact that; approximation of a nonlinear distribution is easier than the approximation of a nonlinear function or transformation [5]. UKF introduces sigma points to catch higher order statistics of the system, and by securing higher order information of the system, it satisfies both ∗ Corresponding address: Faculty of Aeronautics and Astronautics, Istanbul Technical University, 34469 Maslak Istanbul, Turkey. Tel.: +90 537 402 80 76; fax: +90 212 285 2926. E-mail address: ersin_soken@yahoo.com (H.E. Soken). better estimation accuracy and convergence characteristics [6]. Besides, as the estimation characteristic of the UKF is not affected by the level of nonlinearity, it can be preferred for the systems which have highly nonlinear dynamics and measurements models such as spacecraft [7]. On the other hand, UKF has no capability to adapt itself to the changing conditions of the measurement system. Malfunctions such as abnormal measurements, increase in the background noise etc. affect instantaneous filter outputs and processes may result in the failure of the filter. In order to avoid such conditions, the filter must be operated robustly. UKF can be made adaptive and hence insensitive to the priori measurements or system uncertainties by using various different techniques. Multiple Model Based Adaptive Estimation (MMAE), Innovation Based Adaptive Estimation (IAE) and Residual Based Adaptive Estimation (RAE) are three basic approaches to adaptive Kalman filtering. In the first approach, more than one filter runs parallel under different models in order to satisfy the filter’s true statistical information. However, that can be only achieved if the sensor/actuator faults are known. Also, this approach requires several parallel Kalman filters to run, and the processing time may increase in such a condition [8]. In IAE or RAE methods, adaptation is applied directly to the covariance matrices of the measurement and/or system noises in accordance with the differentiation of the residual or innovation sequence. To realize these methods, the innovation or residual vectors must be known for m epoch and that causes an increment in the storage burden, as well as the requirement to know the width of the moving window [9]. Besides, in order to estimate the covariance matrix of the measurement noise based on the innovation or residual vector, the number, type 0019-0578/$ – see front matter © 2010 ISA. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.isatra.2010.04.001