Stochastic processes : Estimation and prediction [ LINMA1731 ]

• FSAB1106 (or equivalent training in signals and systems)
• FSAB1105 (or equivalent training in probabilities and statistics)

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.

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 performances ;
• Synthetize predictors, filters and smoothers, in both Wiener or Kalman frameworks.

• Project during the course semester
• Exam

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.

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.

Course notes, written by the two lecturers, are available.