ELEC-E8107 - Stochastic models, estimation and control D, Lecture, 6.9.2022-7.12.2022
Kurssiasetusten perusteella kurssi on päättynyt 07.12.2022 Etsi kursseja: ELEC-E8107
Lecture 3, Sep 27: LINEAR DYNAMIC SYSTEMS WITH RANDOM INPUTS , STATE ESTIMATION IN DISCRETE TIME LINEAR DYNAMIC SYSTEMS = Kalman Filter
LINEAR DYNAMIC SYSTEMS WITH RANDOM INPUTS
• Gaussian pdf, mean and covariance
• Stochastic sequences, Markov property
• Discrete-time linear stochastic dynamic systems. Prediction, propagation of mean and covariance
• Continuous-time linear stochastic dynamic systems. Propagation of mean and covariance
STATE ESTIMATION IN DISCRETE TIME LINEAR DYNAMIC SYSTEMS = Kalman Filter
The estimation of the state vector of a stochastic linear dynamic system is considered.
The state estimator for discrete-time linear dynamic systems driven by white noise — the (discrete-time) Kalman filter — is introduced.
Estimation of Gaussian random vectors.
For linear systems, white noise Gaussian processes
Linear equations used for state prediction, prediction of the
measurement and for measurement update.
Exact propagation and measurement update equations for a priori
and a posteriori covariances
All pdfs stay exactly Gaussian, no need for approximations