Filtering Techniques
(Academic Year 2019-2020)
This page contains material about the Filtering Techniques part (3 cfu, 24 hours) of the
course Data and Decision Analysis.
Instructor
Andrea Garulli
News
How the exam works
In order to pass this part of the exam, students have to do a project work and an oral exam.
The project work is an homework which requires the use of software tools for solving estimation problems involving dynamic systems. It takes approximately one/two weeks and the students can choose to do it alone or in couples.
The oral exam includes a discussion of the project and questions on all the topics treated during the course.
Students are strongly encouraged to ask for the project at the end of the course and to complete the oral exam within the summer session (June-July). Students willing to take the exam in subsequent sessions must ask for the project at least two weeks before the oral exam.
Students do not have to register in segreteriaonline for taking the exam (the dates in segreteriaonline concern the Decision analysis part, taught by Antonello Giannitrapani).
Bibliography and prerequisites
Main textbook
T. Soderstrom, Discrete-time Stochastic Systems, Springer London Ltd, 2nd ed., 2002. Library code: 269 - 269a.
Other reference textbooks
F. L. Lewis, Optimal Estimation, John Wiley, 1986.
E. W. Kamen and J. K. Su, Introduction to Optimal Estimation, Springer, 1999.
Prerequisites
Basic notions of probability calculus and dynamic systems. Fundamentals of Matlab programming.
Contents
0. Preliminaries. Probability distributions. Mean and covariance. Conditional probability. Gaussian variables. Confidence intervals. Stochastic processes.
Ref.: [Soderstrom, 2.1-2.4, 3.1-3.3].
Classes: Class 0.1; Class 0.2 Class 0.3.
1. State estimation for dynamic systems. Non stationary stochastic
systems. The state estimation problem and the Kalman filter. Asymptotic
properties of the Kalman filter. Recursive system identification.
Ref.: [Soderstrom, 3.3; 4.2; 6.1-6.3; 6.7].
Classes: Class 1.1; Class 1.2; Class
1.3.
Lab sessions: Lab_session_7;
data_labsession7.mat;
labsession7_solution.m;
code_2015_05_20.m.
2. Nonlinear filtering. State estimation in nonlinear stochastic
systems. The Extended Kalman Filter. Advanced nonlinear filtering
techniques: unscented filter; sequential Monte Carlo methods.
Ref.: [Soderstrom, 9.1-9.5. S. Julier and J. Uhlmann, "Unscented
filtering and nonlinear estimation", Proc. of the IEEE, 92(3), pag.
401-422, 2004].
Classes: Class 2.1; Class 2.2.
Lab sessions: Lab_session_8;
data1_labsession8.mat;
data2_labsession8.mat;
labsession8_solution.m;
code_2015_05_25.m.
Additional material: unscented_transform_example.m; particle_filter_example.m.
Useful stuff
Please report errors or problems to: garulli at
ing.unisi.it
Thanks!