| 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 |