Lecture 10: Inference in Gaussian Linear State Space Models:
Filtering & Smoothing
John MacLaren Walsh, Ph.D.
March 11, 2015
References
Inference in Hidden Markov Models, Olivier Cappe, Eric Moulines
Homework #7 Solution
ECE S523
1. Let 1 be the decision based on feature 1 and let 2 be the decision based on feature 2. k, k = 1,
2, takes the value 1 or 0 depending on whether H1 or Ho is picked, and
ECE S523
Homework # 7
1. Let 1 be the decision based on feature 1 and let 2 be the decision based on feature 2. k,
k = 1, 2, takes the value 1 or 0 depending on whether H1 or Ho is picked, and let p(H
ECE 523
Homework 5
Spring 2015
2
1. Let =
=0 + , where is (0, ), = 1,2, , , is white noise.
a. Assume that 0 , 1 , . . , and 2 are known, how would you determine the best
, 0 ?
b. Find the MLE for 0
Homework # 4
1. You are given a set of n independent identically distributed random vectors ri = (xi, yi), i = 1,
2, ., n from a normal bivariate distribution (0, 0, 1, 1, ).
(a) Find the minimal suff
Homework # 3
1. If = (1 , 2 , . , ) are i.i.d. distributed with (| ) = 2 x , 0, > 0.
a) Find the minimum sufficient statistics associated with .
b) Is the minimum sufficient statistics complete? Why?
Homework # 2
1. If x1, x2, ., xN are i.i.d. Poisson distributed with (| ) = , 0, > 0.
!
a) Show that (| x1 ) = (x1 = ), = 0, 1, is unbiased estimator for (| ) based on
one observation x1, where (x1 =
ECE S-523
Detection and Estimation
Spring 2014
Homework # 1
1. For a two class problem two-dimensional problem let the class conditional
0
1
distribution p(x|i) ~ (i,), i = 1,2, where
( ), 1 , 2 ,
1
ECES 690/435 - Winter 2015
Instructor: Matthew Stamm
Drexel University
Assignment 4 - Part 1
This assignment is due by 11:59 p.m. on Thursday, March 5. All reports should be submitted as PDFs. Only on
ECES 690/435 - Winter 2015
Instructor: Matthew Stamm
Drexel University
Assignment 4 - Part 2
This assignment is due by 11:59 p.m. on Thursday, March 5. All reports should be submitted as PDFs. Only on
ECES 690 Homework 3
Sagar Patel , Suman Satish
February 20, 2015
1
1
Part 1
The code for watermarking the image using Spread Spectrum Watermarking
has been appended in the end.
2
Part 2
The code for e
ECES 690/435 - Winter 2015
Instructor: Matthew Stamm
Drexel University
Assignment # 3, Part 1
This assignment is due by 11:59 p.m. on Thursday, Feb 19. All reports should be submitted as PDFs. Only on
ECES 690/435 - Winter 2015
Instructor: Matthew Stamm
Drexel University
Assignment # 2, Part 1
This assignment is due by 11:59 p.m. on Thursday, Feb 12. All reports should be submitted as PDFs. Only on
ECES 690 Homework 1
Sagar Patel , Suman Satish
January 30, 2015
1
1
1.1
Part 1
Subsection 1-A
A MATLAB function that performs gamma correction on a greyscale digital
image is attached in the appendix
ECES 690/435 - Winter 2015
Instructor: Matthew Stamm
Drexel University
Assignment # 1
This assignment is due by 11:59 p.m. on Wednesday, January 29. All reports should be submitted as PDFs. Only
one r
Week 1: Dening Stochastic Processes, Stationarity, & Wide Sense
Stationarity
John MacLaren Walsh, Ph.D.
1
What is a Stochastic Process? How do I Dene it?
A discrete time stochastic process can be thou
Week 2: MMSE Linear Prediction & Filtering for Wide Sense
Stationary Random Processes
John MacLaren Walsh, Ph.D.
1
Causal Linear MMSE Prediction
Suppose we wish to predict the value of a zero mean DT-
Week 4: Discrete Time Markov Chains, II:
State Classication, Stationary Distributions, & Limiting Behavior
John MacLaren Walsh, Ph.D.
1
References
Markov chains are a widely taught subject, and hence
Week 8: Renewal Processes, Stopping Times, Walds Equation
John MacLaren Walsh, Ph.D.
1
References
R. Gallager, Stochastic Processes: Theory for Applications, Cambridge University Press, 2014.
A. Leo
Week 6: Continuous Time Homogenous Markov Chains & Basic
Queuing
John MacLaren Walsh, Ph.D.
1
References
A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, 2nd ed., Addison
ECE S681 Homework # 1
A weaving machine capable of generating horizontal streak defects (of one pixel width) at random
locations needs to be tested using an FIR sensor that ideally sees the defects as
ECE-S 681 Homework #2 Solution
Part 1: Theoretical Questions
1. If y = f(x) = m x + d is the nonparametric explicit linear polynomial representing a curve, and
(x(t), y(t), with x(t) = a1 t + b1 and y