Thu, 21 Aug 2008 15:16:44 BST CiteULike: bsilverthorn kalman_filters http://www.citeulike.org/user/bsilverthorn/tag/kalman_filters CiteULike.org en-gb Copyright © 2004-2008 citeulike.org http://www.citeulike.org/user/bsilverthorn/article/3126328 <i>Industrial Electronics, 2007. ISIE 2007. IEEE International Symposium on (2007), pp. 66-71.</i><br /><br />A novel approach to the straightforward implementation of unscented filtering in a unit quaternion space is proposed for spacecraft attitude estimation. A method of weighted mean computation for quaternions is derived in a rotational space, leading to a quaternion with a unit norm. Quaternion multiplication, which allows a quaternion in the filter to lie in the unit quaternion space, is then used for predicted covariance computations and quaternion updates. In this study, quaternion process noise, which increases the uncertainty in attitude orientation, is either modeled as the vector part of the quaternion or as a rotation vector. Simulation results indicate that the proposed approach successfully estimates spacecraft attitude. Unscented Filtering in a Unit Quaternion Space for Spacecraft Attitude Estimation Yee-Jin Cheon Jong-Hwan Kim doi:10.1109/ISIE.2007.4374575 Industrial Electronics, 2007. ISIE 2007. IEEE International Symposium on (2007), pp. 66-71. 2008-08-15T21:17:16-00:00 2007 Industrial Electronics, 2007. ISIE 2007. IEEE International Symposium on 66 71 bayes_filtering kalman_filters pose_estimation quaternions spacecraft unscented_kalman http://www.citeulike.org/user/bsilverthorn/article/2727317 <i>Acoustics, Speech, and Signal Processing, 2001. Proceedings. (ICASSP '01). 2001 IEEE International Conference on, Vol. 6 (2001), pp. 3461-3464.</i><br /><br />Over the last 20-30 years, the extended Kalman filter (EKF) has become the algorithm of choice in numerous nonlinear estimation and machine learning applications. These include estimating the state of a nonlinear dynamic system as well estimating parameters for nonlinear system identification (eg, learning the weights of a neural network). The EKF applies the standard linear Kalman filter methodology to a linearization of the true nonlinear system. This approach is sub-optimal, and can easily lead to divergence. Julier et al. (1997), proposed the unscented Kalman filter (UKF) as a derivative-free alternative to the extended Kalman filter in the framework of state estimation. This was extended to parameter estimation by Wan and Van der Merwe et al., (2000). The UKF consistently outperforms the EKF in terms of prediction and estimation error, at an equal computational complexity of (OL³)^l for general state-space problems. When the EKF is applied to parameter estimation, the special form of the state-space equations allows for an O(L²) implementation. This paper introduces the square-root unscented Kalman filter (SR-UKF) which is also O(L³) for general state estimation and O(L²) for parameter estimation (note the original formulation of the UKF for parameter-estimation was O(L³)). In addition, the square-root forms have the added benefit of numerical stability and guaranteed positive semi-definiteness of the state covariances The square-root unscented Kalman filter for state and parameter-estimation Rudoplh van der Merwe Eric Wan doi:10.1109/ICASSP.2001.940586 Acoustics, Speech, and Signal Processing, 2001. Proceedings. (ICASSP '01). 2001 IEEE International Conference on, Vol. 6 (2001), pp. 3461-3464. 2008-04-28T05:01:55-00:00 2001 Acoustics, Speech, and Signal Processing, 2001. Proceedings. (ICASSP '01). 2001 IEEE International Conference on 6 3461 3464 bayes_filtering kalman_filters pose_estimation unscented_kalman http://www.citeulike.org/user/bsilverthorn/article/3124262 <i>American Control Conference, 2002. Proceedings of the 2002, Vol. 6 (2002), pp. 4555-4559.</i><br /><br />This paper describes a generalisation of the unscented transformation (UT) which allows sigma points to be scaled to an arbitrary dimension. The UT is a method for predicting means and covariances in nonlinear systems. A set of samples are deterministically chosen which match the mean and covariance of a (not necessarily Gaussian-distributed) probability distribution. These samples can be scaled by an arbitrary constant. The method guarantees that the mean and covariance second order accuracy in mean and covariance, giving the same performance as a second order truncated filter but without the need to calculate any Jacobians or Hessians. The impacts of scaling issues are illustrated by considering conversions from polar to Cartesian coordinates with large angular uncertainties. The Scaled Unscented Transformation Simon Julier doi:10.1109/ACC.2002.1025369 American Control Conference, 2002. Proceedings of the 2002, Vol. 6 (2002), pp. 4555-4559. 2008-08-14T17:26:18-00:00 2002 American Control Conference, 2002. Proceedings of the 2002 6 4555 4559 bayes_filtering kalman_filters unscented_kalman http://www.citeulike.org/user/bsilverthorn/article/3116050 <i>Information Fusion, 2003. Proceedings of the Sixth International Conference of, Vol. 1 (2003), pp. 47-54.</i> A Quaternion-based Unscented Kalman Filter for Orientation Tracking Edgar Kraft Information Fusion, 2003. Proceedings of the Sixth International Conference of, Vol. 1 (2003), pp. 47-54. 2008-08-13T18:46:34-00:00 2003 Information Fusion, 2003. Proceedings of the Sixth International Conference of 1 47 54 kalman_filters pose_estimation quaternions unscented_kalman http://www.citeulike.org/user/bsilverthorn/article/3112551 <i>Journal of Guidance, Control, and Dynamics, Vol. 26, No. 4. (2003), pp. 536-542.</i> Unscented Filtering for Spacecraft Attitude Estimation John Crassidis FL Markley Journal of Guidance, Control, and Dynamics, Vol. 26, No. 4. (2003), pp. 536-542. 2008-08-12T18:27:06-00:00 2003 Journal of Guidance, Control, and Dynamics 26 4 536 542 kalman_filters pose_estimation quaternions spacecraft unscented_kalman http://www.citeulike.org/user/bsilverthorn/article/2675803 <i>Journal of Basic Engineering, Vol. 82, No. 1. (1960), pp. 35-45.</i> A new approach to linear filtering and prediction problems Rudolf Kalman Journal of Basic Engineering, Vol. 82, No. 1. (1960), pp. 35-45. 2008-04-16T01:26:04-00:00 1960 Journal of Basic Engineering 82 1 35 45 kalman_filters