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Master Aerospace Engineering
System Identification of Aerospace Vehicles
Dr.ir. C.C. de Visser
Dr. Q. Chu
Dr.ir. E. van Kampen
Dr.ir. D.M. Pool
Contact Hours / Week x/x/x/x
Different, to be announced
Expected prior knowledge
A global overview of the complete system identification cycle applied to aerospace vehicles, from sensor data
acquisition and state estimation to aircraft aerodynamic model identification and validation. Introduction to
sensor data acquisition and management, state and parameter estimation, and the “two-step” method for
aerodynamic model identification. Finally an overview is give of advanced modelling techniques.
2. State estimation.
Introduction to the essential role of the Kalman Filter (KF) in aircraft state estimation. The extension of
the standard KF to nonlinear systems will be introduced in the form of the Extended Kalman Filter/Smoother
(EKF/EKS), and iterated extended Kalman filter (IEKF). Applications of the Kalman filters in aerospace
navigation, attitude determination, on-board sensor calibration, sensor integration, and data fusion will be
3. Parameter estimation.
Introduction to the process of parameter estimation and its role in creating accurate aerodynamic models of
aircraft. Introduction to four of the most widely used parameter estimation techniques; Least squares (LS),
Weighted Least squares (WLS), Total Least Squares (TLS), and Maximum Likelihood (ML) parameter estimation.
Additionally, recursive parameter estimation methods like Recursive Least Squares (RLS) will be introduced.
4. Advanced optimization techniques.
Some problems cannot be solved adequately with standard linear optimization techniques. In that case, a
nonlinear optimization method must be used. In this part of the course, a powerful global nonlinear optimization
technique based on interval analysis will be introduced.
5. Advanced modelling methods: Neural Networks.
Neural Networks are a class of black-box function approximators that can be used to model nonlinear systems like
Micro Air Vehicles and high performance aircraft. The application of neural networks to aircraft system identification
is discussed, and it will be shown how neural networks can be used inside a framework for parameter estimation.
6. Advanced modelling methods: Multivariate Splines.
Multivariate Simplex B-Splines are a powerful type of white-box function approximators that can be used to create
accurate models of aircraft with highly nonlinear aerodynamics such as MAV’s and high performance aircraft. A number
of unique methods for assessing the quality of the created models are discussed, and pointers towards future research
7. Demonstration: Aircraft system identification with multivariate splines.
An in-depth demonstration will be given of the process of Aircraft system identification with multivariate splines
using real flight test data from the Cessna Citation II laboratory aircraft. The goal is not only to create an accurate
flight dynamics model of the Citation II, but also to apply various model validation techniques to assess the quality
of the created model.
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
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
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.
After completing the course, students will have a thorough understanding of the theoretical elements of
aircraft system identification. Students will be able to apply these elements to go from real CFD, wind
tunnel, and flight test data to an accurate aerodynamic model that can be used in simulator or flight
control system applications.
Literature and Study Materials
• Q.P. Chu, ‘Modern flight test technologies and system identification’, lecture notes, Faculty of Aerospace
Engineering, Delft University of technology.
• C.C. de Visser, ‘Global Nonlinear Model Identification with Multivariate Splines’, PhD thesis,
Faculty of Aerospace Engineering, Delft University of technology.
• V. Klein and E. A. Morelli, Aircraft System Identification, AIAA, 2006.
• J.A. Mulder, J.K.Sridhar, J.Breeman, ‘Nonlinear Analysis and Manoeuvre Design’,
‘Identification of Dynamic Systems, Applications to Aircraft’, AGARD AG-300,
Vol. 3, Part. 2, , May 1994
• R.E. Maine, K.W.Iliff, AGARD Flight Test Techniques Series on
‘Identification of Dynamic Systems, Applications to Aircraft’,
AGARD AG-300, Vol. 3, Part. 1, , December 1986 .
• Eric Walter and Luc Pronzato, Identification of parametric models, Springer, ISBN 3-540-76119-5.