The course presents methods and tools to enable students to to formulate and solve model identification and data analysis problems and to design and implement state estimation systems, with specific reference to Aerospace Engineering. More precisely the following topics are studied: parameter estimation and output error model identification; fundamental data analysis problems; Bayesian estimation and learning; state estimation; black-box model identification; case studies in Aerospace Engineering.

Lectures and exercise sessions will allow students to: 

• Acquire a more advanced knowledge of probability, statistics, estimation and learning theory.
• Formulate and solve model identification problems.
• Familiarise with data analysis problems such as principal component analysis and data classification.
• Design and implement state estimators for, e.g., aircraft and spacecraft attitude determination and navigation.

Part 1: introduction to estimation and learning in aerospace.

- Overview of estimation and learning problems in aerospace: sensor calibration, parameter estimation, model identification, state estimation, navigation, fault detection, fault tolerant control.

- Introduction to the theory of estimation and learning.

- Introduction to model identification: problem statement; grey vs black box models; linear vs nonlinear models; the notions of structural and experimental identifiability.

- The model identification process: from experiment design to model validation.

 Part 2: parameter estimation and output error model identification

- Estimation theory: the maximum likelihood method.

- Density estimation: Gaussian and Gaussian mixture models.

- Least squares estimation; recursive least squares and least mean squares as supervised learning.

- Time-domain output error identification of nonlinear state space models.

- Time-domain and frequency-domain output error identification of linear state space models.

 Part 3: data analysis problems

- Dimensionality reduction and principal component analysis.

- Data classification and support vector machines.

 Part 4: Bayesian estimation and learning; state estimation

- Estimation theory: introduction to Bayesian estimation and learning.

- Optimal state estimation for linear systems: the Kalman filter.

- Time-domain equation error identification of linear state space models.

- The Extended Kalman filter; overview of more general state estimation schemes.

 Part 5: black-box linear model identification

- Problem statement: structure selection vs parameter estimation.

- MIMO black-box modelling: predictor-based subspace identification.

 Part 6: case studies

- Identification of control-oriented models for helicopter and multirotor flight mechanics.

- Attitude determination for aircraft and spacecraft: the Multiplicative Extended Kalman filter.

- Experimental parameter and state estimation for the longitudinal dynamics of a multirotor UAV.

 Students are required to know the basic principles of probability and statistics and of linear systems theory, both for continuous-time and discrete-time systems.

The students will be able to choose between an oral exam and a project which will be presented during the course. In both cases the evaluation will be also based on the clarity of the presentation. During the exam the students shall demonstrate that:

• they have acquired a working knowledge of probability and statistics.
• They understand maximum likelihood and Bayesian estimation and learning theory.
• They are able to formulate and solve data analysis and model identification problems.
• They can design and implement state estimators for, e.g., aircraft and spacecraft attitude determination and navigation.

(in preparation)

978-1563478321