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- Politecnico di Milano
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- Computer Engineering
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- Model Identification and Data Analysis
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Study material for Model Identification and Data Analysis, shared by the Studwiz community and reviewed by moderators.
Model Identification and Data AnalysisBy topic
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Model Identification Notes of the course by prof. S. Garatti @ Politecnico di Milano VERONIKA GULEV A 2019-2020 1. Stochastic Processes and Stochastic Dynamical Models 2 1.1. Stochastic Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2. Model Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3. Operational Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4. Frequency Domain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.5. Different Representations of ARMA models . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.6. Canonical Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2. Theory of Prediction 13 2.1. General Prediction Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2. Optimal Linear Prediction From Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3. Optimal Linear Prediction From Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4. Optimal Prediction Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.5. Prediction of Non-Zero Mean ARMA Process . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.6. Prediction of ARMAX Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3. Model Identification 20 3.1. Parametric Model Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.2. Prediction Error Minimization (PEM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.3. Identification of ARX Models: Least Squares Method (LS) . . . . . . . . . . . . . . . . . . . 22…
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