Adaptive Filtering

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EECE-595, Section II, Adaptive Filtering:

Instructor: Balu Santhanam

Pre-requisites: EECE-539, EECE-541, knowledge of MATLAB

Course Materials:

1. Flier for the course
2. Course Outline/Syllabus

Review material:

Class Notes

Preliminaries :

Lecture I notes
1. Lecture II notes
2. Hilbert Space View of Random Signals
3. On Signals with Rational Power Spectra
4. Power Spectrum Factorization
5. On Autoregressive Processes
6. On Linear Prediction and Autoregressive Processes

LMS Algorithm and Variants:

1. Steepest Descent: AR(2) Example
2. Steepest Descent Versus Newton's Algorithm
3. Lecture Notes on the LMS Algorithm
4. Lecture Notes on the NLMS Algorithm
5. NLMS: Minimum Norm/SVD solution
6. AR(2) Example: (a) Average Tap-weights and (b) Learning Curve
7. Lecture Notes on Affine Projection Algorithm
8. Lecture Notes on Variants of the LMS

RLS Algorithm and Variants:

1. On Least Squares Inversion
2. On the Least Squares Algorithm
3. Exponentially Weighted RLS Algorithm
4. RLS Algorithm: Design Guidelines
5. AR(2) Example: RLS Tap-weights

Kalman Filter and Variants:

1. Discrete Kalman Filter
2. Relation Between the DKF and RLS
3. DKF AR(2) Prediction Example: State estimate Kalman gain vector MMSE learning curve
4. On Wiener and Kalman Filters
5. Extended Kalman Filter (EKF)
6. Iterated Extended Kalman Filter (IEKF)

Order Recursive Adaptive Filters:

1. Gradient Adaptive Lattice
2. Least Squares Lattice

Problem Sets :

1.Problem Set # 1.0

2.Solutions to Problem Set # 1.0

3.Problem Set # 2.0

4.Sample output from Problem Set # 2.0

5. Solution to Problem Set # 2.0

MATLAB Files:

1. LMS Algorithm
2. Normalized LMS Algorithm
3.Recursive Least Squares (RLS) Algorithm
4.Script for AR(2) example : I (NLMS)
5.Script for AR(2) example : II (RLS)
6.Script for AR(2) example : III (DKF)
7.Discrete Kalman Filter
8.EKF for Tracking Example