Journal of Electrical Engineering & Technology Vol. 7, No. 1, pp. 132~140, 2012 http://dx.doi.org/10.5370/JEET.2012.7.1.132 132 Aerodynamic Derivatives Identification Using a Non-Conservative Robust Kalman Filter Han Sung Lee*, Won-sang Ra † , Jang Gyu Lee*, Yongkyu Song** and Ick-Ho Whang*** Abstract – A non-conservative robust Kalman filter (NCRKF) is applied to flight data to identify the aerodynamic derivatives of an unmanned autonomous vehicle (UAV). The NCRKF is formulated using UAV lateral motion data and then compared with results from the conventional Kalman filter (KF) and the recursive least square (RLS) method. A superior performance for the NCRKF is demonstrated by simulation and real flight data. The NCRKF is especially effective in large uncertainties in vehicle modeling and in measuring flight data. Thus, it is expected to be useful in missile and aircraft parameter identification. Keywords: Non-conservative robust Kalman filter, Aerodynamic derivatives identification, EKF, RLS 1. Introduction Aerodynamic derivatives are an important parameter in the formulation of the dynamic equations of a vehicle in flight. They are functions of the shape of the aircraft, the control input, and the Mach number [1, 2]. To identify aerodynamic derivatives from flight data as precisely as possible, various estimation methods have been applied in the past [3-6]. These methods can be categorized into two groups of research. One formulates the aerodynamic derivatives in a linear form and estimates them using either the least square (LS) method or by the KF [7, 8]. The other method formulates the aerodynamic derivatives as augmented states, resulting in a nonlinear filtering problem. An extended Kalman filter (EKF) or a maximum likelihood (ML) method is usually employed in this problem [9-14]. The EKF and the ML methods are generally known to provide better results than the recursive least square (RLS) and the Kalman filter (KF) methods, assuming that the system and the measurements are reasonably well modeled. However, in aerodynamic derivatives identification from flight data, obtaining an acceptable model is not easy because of various uncertainties inherent in forming the dynamic equations and in the telemetering of the flight data. Based on our experience, an EKF is very sensitive to system noise covariance. A time-consuming search for the best system noise covariance, to design a filter, is thereby unavoidable. Therefore, a robust identification technique, using something other than the EKF and the ML methods, is desirable. To avoid the limitations of a non-linear filter, a linear regression model is derived from this model. By doing this, an imperfect system noise covariance tuning is eliminated. For this regression, the aerodynamic derivatives are assumed to be constant. Therefore, the first order derivative of each state is zero. The LS method has been used previously as identification technique for this model. However, the LS method provides an unbiased estimation under the assumption that the noise distribution is Gaussian. Unfortunately, the Gaussian assumption does not hold in the aerodynamic derivatives identification problem. To overcome the non-Gaussian distribution problem, we propose to employ a non-conservative robust Kalman filter (NCRKF) [15-17]. The NCRKF is derived by rejecting additive noise terms in the measurement matrix to compensate for the limits of the LS and the KF methods regarding this problem. The NCRKF was formulated to identify the aerodynamic derivatives in the lateral motion equations of an unmanned autonomous vehicle (UAV). Only the lateral motion equation was selected for simplicity. The resulting NCRKF was then compared with the RLS and the KF results to demonstrate that it performs better under inevitable modeling uncertainties. As a result, we found the NCRKF more suitable for aerodynamic derivatives identification from flight data. 2. NCRKF Formulation for UAV Lateral Motion 2.1 Dynamic equations for UAV lateral motion Linearized lateral dynamic equations around the trim of a UAV can be expressed as [18] † Corresponding Author: School of Mechanical and Control Engineering, Handong Global University, Korea (wonsang@handong.edu). * School of Electrical Engineering, Seoul National University, Korea (ppklhs1, jgl@snu.ac.kr). ** School of Aerospace and Mechanical Engineering, Korea Aerospace University, Korea (yksong@hau.ac.kr). *** Department of Guidance and Control, Agency for Defense Development, P.O. Box 35-11, Korea (ickho@nate.com). Received: April 12, 2011; Accepted: May 25, 2011