Main themes |
The object of this course is to lead to a good understanding of stochastic processes, their most commonly used models and their properties, as well as the derivation of some of the most commonly used estimators for such processes : Wiener and Kalman filters, predictors and smoothers.
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Aims |
At the end of this course, the students will be able to : - Have a good understanding of and familiarity with random variables and stochastic processes ; - Characterize and use stable processes and their spectral properties; - Use the major estimators, and characterize their performences ; - Synthetize predictors, filters and smoothers, in both Wiener or Kalman frameworks.
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Content |
The course is subdivided into four parts/chapters: -Probabilities, random variables, moments, change of variables. -Stochastic processes, independence, stability, ergodicity, spectral representation, classical models of stochastic processes. -Estimation (for random variables) : biais, variance, bounds, convergence, asymptotic properties, classical estimators. -Estimation (for random processes) : filtering, prediction, smoothing, Wiener and Kalman estimators. -Learning will be based on courses interlaced with practical exercise sessions (exercises done in class or in the computer room using MATLAB). In addition, the training includes a project to be realized by groups of 2 or 3 students.
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