**SC4040:** |
**Filtering & Identification** |

**ECTS:** |
6 |

**Responsible Instructor:** |
ir. E. van Solingen, Prof.dr.ir. M.H.G. Verhaegen |

**Contact Hours / Week x/x/x/x:** |
0/4/0/0 |

**Education Period:** |
2 |

**Start Education:** |
2 |

**Exam Period:** |
2, 3 |

**Course Language:** |
English |

**Expected prior knowledge:** |
BSc-degree in Engineering or Mathematics with basic knowledge of linear algebra, stochastic processes, signals and systems and control theory. |

**Course Contents:** |
The objective of this course is to show the use of linear algebra and its geometric interpretation in deriving computationally simple and easy to understand solutions to various system theoretical problems. Review of some topics from linear algebra, dynamical system theory and statistics, that are relevant for filtering and system identification. Kalman filtering as a weighted least squares problem. Prediction error and output error system identification as nonlinear least squares problems. Subspace identification based on basic linear algebra tools such as the QR factorization and the SVD. Discussion of some practical aspects in the system identification cycle. See also: http:/www.dcsc.tudelft.nl/~sc4040. |

**Study Goals:** |
At the end of the course the student should be able to: • Derive the solution of the weighted stochastic and deterministic linear least squares problem. • Proof the properties of unbiasedness and minimum variance of the weighted stochastic and deterministic linear least squares problem. • Use an observer to estimate the state sequence of a linear time invariant system. • Use the Kalman filter to estimate the state sequence of a linear time invariant system using knowledge of the system matrices, the system input and output measurements, and the covariance matrices of the uncertainty of these measurements. • Describe the difference between the predicted, filtered and smoothed state estimates. • Formulate and solve the Kalman filter problem as a weighted stochastic least squars problem. • Use the Kalman filter theory to estimate unknown inputs of a linear dynamical system in the presence of noise perturbations on the model. • Use the Kalman filter theory to design filters for detection (sensor, actuator or component) failures in a linear dynamical system in the presence of noise perturbations on the model. • Derive subspace identification methods for different noise models and relate the different subspace identification methods via the solution of a linear least squares problem. • Implement a least squares solution in matlab for elementary linear estimation and subspace identification problems. • Apply the filtering and identification methods to derive a mathematical model from real-life data sequences. In this application the students use the systematic identification cyclic approach to refine the model. |

**Education Method:** |
Lectures 0/4/0/0 |

**Literature and Study Materials:** |
Book Filtering and System Identification: A Least Squares Approach by Michel Verhaegen and Vincent Verdult. ISBN: 13-9780521875127 Deliverable by the Studentsociety Gezelschap Leeghwater. |

**Assessment:** |
Written exam (open book) and practical exercise. |

**Remarks:** |
The software package Matlab is needed to solve the practical exercise. |

**More Information:** |
http://www.dcsc.tudelft.nl/~sc4040 |