Estimation
The construction of parametric models and the determination of estimates of the vector of parameters from experimental data is at the core of the activity of engineers and researchers who wish to analyze physical phenomena, build software sensors, detect faults in a system, simulate a process, evaluate a command… The objective of this course is to make students aware of the difficulties associated with the parametric modeling and identification process, difficulties they are often not aware of. The course will provide elements of answers to the following questions: How to build a model of a system? For a given model structure, will it be possible to determine the value of its parameters in a unique way? When two model structures are competing, will it be possible to distinguish them? Once the structure of the model has been chosen, taking into account the knowledge available a priori, which criterion should be chosen to estimate the model parameters? How are the optimal value of these parameters obtained? A set of parameters has been obtained, but is it really the only one possible? How to quantify the parameter estimation uncertainty? How should the data collection be organized to obtain the best accuracy ?
References
- S. M. Kay, Fundamentals of Statistical Processing, Volume I: Estimation Theory, Prentice Hall, 1993.
- E. Walter and L. Pronzato, Identification of Parametric Models: From Experimental Data, Springer, 1997.
- E. Walter, Numerical methods and optimization: a consumer guide, Springer, 2014.
- L. Ljung a