Course Objective: The purpose of this course is to give students a background in stochastic system approach and the analysis. Stochastic optimal linear filter, prediction, and smoothing algorithms for discrete-time systems are the main focus.
Syllabus:
Elements of probability theory
-random variables-Gaussian distribution-stochastic processes-characterizations and properties-Gauss-Markov processes-Brownian motion process-Gauss-Markov models
Optimal estimation for discrete-time systems
-fundamental theorem of estimation-optimal prediction
Optimal filtering
-Weiner approach-continuous time Kalman Filter-properties and implementation-steady-state Kalman Filter-discrete-time Kalman Filter-implementation-sub-optimal steady-state Kalman Filter-Extended Kalman Filter-practical applications
Optimal smoothing
-optimal fixed-interval smoothing optimal fixed-point smoothing-optimal fixed-lag smoothing-stability-performance evaluation
References:
- ‘Stochastic Optimal Linear Estimation and Control’
– James S Meditch
– McGraw-Hill , New York
- ‘Lessons in Estimation Theory for Signal processing, Communication, and Control’
– Jerry M Mendel
– Prentice-Hall Inc, New Delhi
- ‘Kalman Filtering; Theory and Practice’
– Mohinder S Grewal, Angus P Andrews
– Prentice-Hall Inc, Englewood
- ‘Optimal Control and Stochastic Estimation; Theory and Applications’
– Grimble M J, M A Johnson
– Wiley, New York
- ‘Stochastic Models, Estimation, and Control’
– Peter S Meybeck
– Volume 1 & 2, Academic Press, New York
- ‘Probability, Random Variables, and Stochastic Process’
– Papoulis Athanasios
– 2nd Edition, McGraw-Hill , New York
- ‘Optimal Estimation’
– Frank L Lewis
– Wiley, New York
- ‘Stochastic Systems and State Estimation’
– Mcgarty J P
– John Wiley, New York
Prerequisite: Second level course in control systems
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