Adaptive Filtering

Review material &

Class Notes :

Preliminaries

Lecture I notes

Lecture II notes

Hilbert Space View of Random Signals

On Signals with Rational Power Spectra

Power Spectrum Factorization

On Autoregressive Processes

On Linear Prediction and Autoregressive Processes

LMS Algorithm and Variants:

Steepest Descent: AR(2) Example

Steepest Descent Versus Newton's Algorithm

Lecture Notes on the LMS Algorithm

Lecture Notes on the NLMS Algorithm

NLMS: Minimum Norm/SVD solution

AR(2) Example: (a) Average Tap-weights and (b) Learning Curve

Lecture Notes on Affine Projection Algorithm

Lecture Notes on Variants of the LMS

RLS Algorithm and Variants:

On Least Squares Inversion

On the Least Squares Algorithm

Exponentially Weighted RLS Algorithm

RLS Algorithm: Design Guidelines

AR(2) Example: RLS Tap-weights

Kalman Filter and Variants:

Discrete Kalman Filter

Relation Between the DKF and RLS

DKF AR(2) Prediction Example: State estimate Kalman gain vector MMSE learning curve

On Wiener and Kalman Filters

Extended Kalman Filter (EKF)

Iterated Extended Kalman Filter (IEKF)

Order Recursive Adaptive Filters:

Gradient Adaptive Lattice

Least Squares Lattice

Problem Sets :

Problem Set # 1.0

Solutions to Problem Set # 1.0

Problem Set # 2.0

Sample output from Problem Set # 2.0

Solution to Problem Set # 2.0

MATLAB Files:

LMS Algorithm

Normalized LMS Algorithm

Recursive Least Squares (RLS) Algorithm

Script for AR(2) example : I (NLMS)

Script for AR(2) example : II (RLS)

Script for AR(2) example : III (DKF)

Discrete Kalman Filter

EKF for Tracking Example