Course Catalog 2010-2011
Postgraduate

Basic Pori International Postgraduate Open University

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Course Catalog 2010-2011

MAT-51266 Stochastic Processes, 6 cr

Person responsible

Robert Piche

Lessons

Study type P1 P2 P3 P4 Summer Implementations Lecture times and places
Lectures
Excercises
 4 h/week
 2 h/week
+4 h/week
+2 h/week


 


 


 
MAT-51266 2010-01 Monday 14 - 16, TD308
Tuesday 14 - 16, Td308

Requirements

Exam, or exam and homework
Completion parts must belong to the same implementation

Learning outcomes

Stochastic (i.e. random) processes are probabilistic models of information streams such as speech, audio and video signals, stock market prices, data from medical instruments, the motion of a GPS receiver, and many more. A solid understanding of the mathematical basis of these models is essential for understanding phenomena and processing information in many branches of science and engineering including physics, communications, signal processing, automation, and structural dynamics. In this course, we focus on linear stochastic system theory for estimation and prediction. After studying this course, the student can compute the response of linear continuous and discrete-time systems with random inputs; derive the Kalman filter and apply it to estimate random state parameters in simplified versions of practical engineering problems; demonstrate his/her understanding of the underlying theory by proving theorems, deriving formulas, devising counterexamples, and solving computational problems; write short Matlab programs to analyse, simulate and estimate the parameters of systems with random inputs

Content

Content Core content Complementary knowledge Specialist knowledge
1. deterministic dynamic systems: linear time-invariant continuous-time state space models (differential equations), LTI discrete-time state space models (difference equations) models; response; stability   solution uniqueness; sampling; observability; transfer function models; Lyapunov equation; frequency response: z-transform, Laplace transform, Fourier transform; system analysis and simulation using Matlab    
2. probability: vector random variables, joint distribution, conditional distribution, multivariate gaussian density, functions of vector random variables, expectation, covariance, conditional expectation   moment generating function; characteristic function; Chernoff bound; Chebyshev inequality; Schwarz inequality    
3. random sequences: convergence (sure, almost sure, mean square, stochastic, distribution), Markov chains, Markov sequence, Brownian motion, Wiener process, stationarity, ergodicity; response of LTI discrete-time system to random input   central limit theorem; laws of large numbers; Poisson process; Chapman-Kolmogorov matrix equation; Lyapunov equation; martingale; simulations with Matlab    
4. random processes: mean-square stochastic calculus (continuity, differentiation, integration); power spectral density; white noise; stationarity; ergodicity; Fourier transform of random process   Karhunen-Loève expansion    
5. estimation: Bayesian estimation of parameters in linear multivariate gaussian model, Kalman filter,   Kalman filter special questions: information form, noiseless measurements, square root filter; hidden Markov models; particle filters; implementing and simulating filters in Matlab   navigation (GPS, inertial, Doppler)  

Evaluation criteria for the course

exam, or exam + homework.

Assessment scale:

Numerical evaluation scale (1-5) will be used on the course

Partial passing:

Completion parts must belong to the same implementation

Study material

Type Name Author ISBN URL Edition, availability, ... Examination material Language
Other online content   course home page   RP       Lecture slides, lecture recordings, course notes, problems      English  

Prerequisites

Course Mandatory/Advisable Description
MAT-20501 Todennäköisyyslaskenta Mandatory    
MAT-31096 Matrix Algebra 1 Mandatory    

Prerequisite relations (Requires logging in to POP)



Correspondence of content

Course Corresponds course  Description 
MAT-51266 Stochastic Processes, 6 cr MAT-51262 Stochastic Processes, 7 cr  

Additional information

Suitable for postgraduate studies

More precise information per implementation

Implementation Description Methods of instruction Implementation
MAT-51266 2010-01 Lectures Mondays and Tuesdays 2-4pm in Td308 during periods 1-2 in 2010.        

Last modified27.09.2010