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Inference from Data and Models >> Content Detail



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Lec #Topics
1Introduction

Content of the Course
2Examples of Inverse Problems, Static and Time Dependent
3Basic Vector/Matrix Notation

Algebraic Formulation
4-6Over/Underdetermined Problems

Varieties of Least-Squares
7Basic Statistics

Concepts and Notation
8Variances/Covariances

Biases of Solutions
9Special Case of Eigenvector Solutions
10-11Singular Value Decomposition and Singular Vector Solutions
12-13Recursive Least-Squares

Gauss-Markov Estimation; Recursive Estimation
14Time-dependent Models

Whole Domain Least-Squares
15-16Sequential Methods (Kalman Filter/RTS Smoother)
16-17Control Problems

Lagrange Multiplier (adjoint) Methods

Non-linear Problems
18Stationary Processes

Numerical Fourier Series/Transforms; Delta Functions
19Statistics of Fourier Representations

Sampling

Periodograms
20Convolution

Power Density Spectral Estimates
21Coherence; Multiple Linear Regression
22Filtering, Prediction Problems
23-24Special Topics, Spillover

 








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