Calendar

Lec # Topics

1

Introduction

Content of the Course

2

Examples of Inverse Problems, Static and Time Dependent

3

Basic Vector/Matrix Notation

Algebraic Formulation

4-6

Over/Underdetermined Problems

Varieties of Least-Squares

7

Basic Statistics

Concepts and Notation

8

Variances/Covariances

Biases of Solutions

9

Special Case of Eigenvector Solutions

10-11

Singular Value Decomposition and Singular Vector Solutions

12-13

Recursive Least-Squares

Gauss-Markov Estimation; Recursive Estimation

14

Time-dependent Models

Whole Domain Least-Squares

15-16

Sequential Methods (Kalman Filter/RTS Smoother)

16-17

Control Problems

Lagrange Multiplier (adjoint) Methods

Non-linear Problems

18

Stationary Processes

Numerical Fourier Series/Transforms; Delta Functions

19

Statistics of Fourier Representations

Sampling

Periodograms

20

Convolution

Power Density Spectral Estimates

21

Coherence; Multiple Linear Regression

22

Filtering, Prediction Problems

23-24

Special Topics, Spillover