6.432 | Spring 2004 | Graduate
Stochastic Processes, Detection, and Estimation


The calendar below provides the lecture (L) and recitation (R) sessions for the course.

L1 Overview; Problem Review; Random Vectors PS 1 Out
R1 Course Information; Review of Linear Algebra

L2 Covariance Matrices; Gaussian Variables

L3 Gaussian Vectors; Bayesian Hypothesis Testing PS 1 Due
PS 2 Out
R2 Diagonalization of Symmetric Matrices; Symmetric Positive Definite and Semidefinite Matrices

L4 Binary Hypothesis Testing; ROCs

R3 More on Symmetric Positive Definite Matrices; Hypothesis Testing for Gaussian Random Vectors

L5 ROCs; M-ary Hypothesis Testing PS 2 Due
PS 3 Out
L6 Bayesian Estimation; LS; MAP

R4 Binary Hypothesis Tests: Receiver Operating Characteristic (ROC); Geometry of M-ary Hypothesis Tests

L7 Bayes and Linear LS PS 3 Due
PS 4 Out
L8 Vector Spaces

R5 Bayes’ Least Squares Estimation; Vector Spaces and Linear Least Squares

L9 Nonrandom Parameter Estimation CRB PS 4 Due
PS 5 Out
L10 ML Estimation

R6 Nonrandom Parameter Estimation

L11 QUIZ #1 (through Lecture 8, PS# 1-4)

L12 Stochastic Processes PS 5 Due
PS 6 Out
R7 Linear Systems Review

L13 Second-Order Descriptions

L14 PSD’s PS 6 Due
PS 7 Out
R8 Examples of Stochastic Processes; Second Order Statistics and Stochastic Processes

L15 Whitening, Shaping; K-L

L16 K-L; Freq, Domain Representation PS 7 Due
PS 8 Out
R9 Discrete Time Processes and Linear Systems; Discrete Time Karhunen–Loeve Expansion

L17 Detection and Estimation in White Noise

L18 Nonlinear Estimation PS 8 Due
PS 9 Out
R10 Binary Detection in White Gaussian Noise; Detection and Estimation in Colored Gaussian Noise

L19 Det/estimation in Colored Noise; LLSE of Processes

R11 Linear Detection from Continuous Time Processes; Karhunen–Loeve Expansions and Whitening Filters

L20 QUIZ #2 (through Lecture 16, PS# 5-8)

L21 Wiener Filtering

R12 Discrete–Time Wiener Filtering; Prediction and Smoothing

L22 Innovations, State Models PS 9 Due
PS 10 Out
L23 Kalman Filtering

R13 State Space Models and Kalman Filtering

L24 KF; Estimation of Statistics PS 10 Due
PS 11 Out
L25 Estimation of Statistics; Modeling

R14 Estimation and Detection Using Periodograms

L26 Modeling

Final Exam