System Identification of Aerospace Vehicles

Accurate aerodynamic models play a crucial role in the design and operation of flight simulators and flight control systems. The creation of accurate aerodynamic models from CFD, wind tunnel, and flight test data has historically been a highly challenging task. This is a direct result of the nonlinear nature of aircraft (aero)dynamics and the fact that not all aircraft states can be measured directly. As a consequence, the aerospace vehicle parameter identification problem constitutes a joint parameter-state estimation problem. It is the aim of this course to provide the student with a complete overview of the system identification cycle as it is currently applied to aerospace systems, and to introduce the student to the current state of the art in the field of aerodynamic model identification.

The course consists of 7 parts covering the entire system identification cycle. In the first part of the course, the process of data acquisition using on-board sensors including accelerometers, gyroscopes, GPS and various air data sensors is discussed. It will be demonstrated that measurements made by real-world sensors are contaminated with noise, and are sometimes biased. Additionally, some aircraft states, like the true angle of attack, cannot be measured directly and must be reconstructed by combining sensor measurements. The second part of the course introduces the concept of state estimation in which prior physical knowledge of the system is used in a Kalman filter (KF) to estimate the true aircraft states from the measured states. Next to the ordinary Kalman filter, the Extended Kalman filter (EKF) and the Iterated extended Kalman filter (IEKF) will be introduced. In the third part of the course various methods for the estimation of model parameters will be discussed. It will be shown how the results from the state estimation are used in combination with a parameter estimator. This part not only focuses on offline batch parameter estimation methods like ordinary least squares (OLS), weighted least squares (WLS), total least squares (TLS), and maximum likelihood (ML) estimators, but also on recursive parameter estimation methods like recursive least squares (RLS) that can be used online. Special attention will be paid on the process of choosing a parameter estimator that is right for the job.

The fourth part of the course introduces an advanced global nonlinear optimization method based on interval analysis. In aerospace system identification, so-called non-convex and nonlinear optimization problems are often encountered. Such problems can be solved with global nonlinear optimization methods like interval analysis. The fifth and sixth part of the course focuses on two advanced model structures that can be used in combination with the earlier introduced parameter estimation methods. In the fifth part of the course the neural network black-box function approximator is introduced. It is shown how neural networks are used to approximate scattered multidimensional data. In the sixth part of the course a new method for aerodynamic model identification based on multivariate simplex B-splines is introduced. This method was recently developed at the Faculty of Aerospace Engineering of the TU-Delft, and has a number of advantages over existing methods. For example, the simplex B-splines have a transparent model structure, are general in any number of dimensions, and can be computed efficiently in real-time.

In the final part of the course, all theory introduced in the first six parts is used in a demonstration that uses real flight data from a real-life system like the Cessna Citation II laboratory aircraft, or a Micro Air Vehicle to identify a multivariate spline based aerodynamic model. The created model is validated using various techniques. Finally, pointers are given towards further research in the field of aerodynamic model validation.