Robust Kalman filtering for small satellite attitude estimation in the presence of measurement faults Halil Ersin Soken a,n , Chingiz Hajiyev b , Shin-ichiro Sakai c a The Graduate University for Advanced Studies (Sokendai), Department of Space and Astronautical Science, JAXA/ISAS Campus, Yoshinodai 3-1-1, Sagamihara, Kanagawa, Japan b Istanbul Technical University, Faculty of Aeronautics and Astronautics, 34469 Maslak Istanbul, Turkey c Japan Aerospace Exploration Agency (JAXA), Institute of Space and Astronautical Science (ISAS) Yoshinodai 3-1-1, Sagamihara, Kanagawa, Japan article info Article history: Received 5 July 2013 Received in revised form 11 November 2013 Accepted 9 December 2013 Recommended by Nikolas Kazantzis Available online 22 December 2013 Keywords: Robust Kalman filtering REKF RUKF Measurement fault Attitude estimation Small satellite abstract In normal working conditions it is possible to achieve sufficient attitude estimation accuracy for a satellite using regular Kalman filter algorithm. On the other hand, when there is a fault in the measurements, the Kalman filter fails in providing the required accuracy and may even collapse over time. In this paper, a Robust Kalman filtering method is proposed for the attitude estimation problem. By using the proposed method both the Extended Kalman Filter and Unscented Kalman Filter are modified and the new algorithms, which are robust against measurement malfunctions, are called Robust Extended Kalman Filter and Robust Unscented Kalman Filter, respectively. A multiple scale factor based adaptation scheme is preferred for adapting the filters so only the data of the faulty sensor is scaled and any unnecessary information loss is prevented. The proposed algorithms are demonstrated for attitude estimation of a small satellite and performances of these two robust Kalman filters are compared in case of different measurement faults. The application of the algorithm is discussed for small satellite missions where the attitude accuracy depends on a limited number of measurements. & 2013 European Control Association. Published by Elsevier Ltd. All rights reserved. 1. Introduction The Extended Kalman Filter (EKF) is a nonliear version of Kalman Filter (KF) which has been widely preferred for various applications including attitude estimation [15]. The Unscented Kalman Filter (UKF) algorithm is a recent filtering method which has many advantages over the well known EKF. The essence of the UKF is the fact that; a nonlinear distribution can be approximated more easily than a nonlinear function or transformation [11]. The UKF avoids the linearization step of the EKF by introducing sigma points to catch higher order statistic of the system. As a result, it satisfies both better estimation accuracy and convergence speed [27]. The UKF is more robust against noise, bias and [17] and initial attitude estimation errors [3]. In literature there are many examples where the UKF is used for attitude estimation. In [3] the attitude and gyro biases are estimated via the UKF and in [24] a dual-state parameter estima- tion routine is presented as a part of attitude determination system of a small satellite. Moreover, Vinther et al. [28] introduces an UKF based inexpensive cubesat attitude estimation method where also the magnetometer biases are estimated and in [9] the UKF is used for in-orbit magnetic disturbance estimation and compensation. One main problem for both the EKF and UKF, when they are used for spacecraft attitude estimation, is that they are not robust against faults. Such faults in the measurements affect the estima- tion accuracy and may make the attitude estimator diverge in the long term. Hence the KF algorithm that is used as the attitude estimator must be built robust using an adaptive approach [26]. In literature the adaptation methods for the linear KF are discussed by many researchers. The method proposed by Mehra [19,20] can be shown as the forerunning study in this area. The Multiple Model Based Adaptive Estimation (MMAE), Innovation Based Adaptive Estimation (IAE) and Residual Based Adaptive Estimation (RAE) are some of the techniques which may be given as examples of more recent studies [22]. Estimation of the process and measurement noise covariances is further discussed in [30,23,4]. In [30] noise covariance matrices of a discrete–time linear system is estimated via an algorithm named 3-OM. In [23] the noise covariances are computed in a single step using the autocovariance least-squares method. Lastly, [4] gives a survey of the recent studies about the covariance estimation. Another approach is scaling the noise covariance matrices rather than estimating them [1]. Multiplying the process or measurement noise covariance matrix with a time-dependent scale factor [5,7] is a method that is used for correcting the gain of the Kalman filter and can be applied when the information Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ejcon European Journal of Control 0947-3580/$ - see front matter & 2013 European Control Association. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ejcon.2013.12.002 n Corresponding author. Tel./fax: þ81 42 759 8311. E-mail addresses: ersin_soken@ac.jaxa.jp, ersin_soken@yahoo.com (H.E. Soken), cingiz@itu.edu.tr (C. Hajiyev), sakai@isas.jaxa.jp (S.-i. Sakai). European Journal of Control 20 (2014) 64–72