EE638: Estimation and Identification (Autumn 2024)

 

Instructor: Dr. Debraj Chakraborty

Email: dc [AT] ee.iitb.ac.in

Office: 1st floor, EE

Lecture Hours: TBA

Website: http://www.ee.iitb.ac.in/~dc/EE638

 

TAs: Naveen Mukesh N ( 214070006 )

Syllabus

1.     Parameter Estimation:

a.    Minimum Variance Unbiased Estimation

b.    Cramer-Rao Lower Bound

c.    Sufficient Statistics

d.    Best Linear Unbiased Estimators

e.    Maximum Likelihood Estimation

 

2.     Signal Estimation:

f.     Least Squares Estimation: Deterministic and Stochastic

g.    Finite and Infinite Horizon Weiner-Hopf Filter: The Innovations Process, Canonical Spectral Factorization

h.    The Kalman Filter: State Space Models, Various forms, EKF

i.     Case Studies: Sensor Fusion using Kalman Filter, Orientation Estimation from IMU data

 

3.     Identification (If time permits): Nonparametric and parametric methods for LTI systems, Introduction to Subspace methods

Text Book

No Text Book is prescribed. Lecture Notes will be provided.

Reference Books

1.     Steven M. Kay, Fundamentals of Statistical Signal Processing: Estimation, Prentice-Hall, 1993.

2.     G. Casella and R. Berger, Statistical Inference, Duxbury Thomson Learning, 2002.

3.     T. Kailath, A.H. Sayed and B. Hassibi, Linear Estimation, Prentice- Hall, 2000.

4.     L. Ljung, System Identification-Theory for the User, Prentice-Hall, 1999.

5.     P.V. Overschee, B.D. Moore, Subspace Identification for Linear Systems, Kluwer Academic, 1996

Evaluation:

Assignments (20%), Mid-Sem (30%), End-Sem (40%), Term Project (10%)

Lecture Notes (updated)

1.     Lecture 1 : Introduction

2.     Lecture 2: MVUE

3.     Lecture 3: MLE

4.     Lecture 3a: EM Algorithm

5.     Lecture 4: MVUE using Sufficiency

6.     Lecture 5: Bayes Estimation

7.     Lecture 6: BLUE

8.     Lecture 7: Least Squares: Deterministic and Stochastic

9.     Lecture 8: Wiener Filter

10.  Lecture 9: Kalman Filter Part 1

11.  Lecture 9a: Kalman Filter Part 2

12.  Lecture 10: System Identification: Basic theory

13.  Lecture 11: Stochastic System Identification

Class Notes by Tanmay Dokania

Homework Assignments

Homework 1: Steven Kay, 93: 2.6, 2.8, 2.9, 2.11, 3.4, 3.9, 3.10, 3.13, 3.15, 7.5, 7.8, 7.9, 7.11, 7.21. Deadline for submission: Hardcopy only, in class, Friday 30th August.

 

Homework 2: Steven Kay, 93: 4.4, 4.13, 4.14, 5.1, 5.4, 5.5, 5.6, 5.9, 5.10, 5.11, 5.12, 5.13, 5.14, 5.15, 5.17, 5.18, 6.7, 6.8, 6.9, 6.11 Deadline for submission: Hardcopy only, in class, Wednesday 11th September.

 

Homework 3: Kailath, Sayed and Hassibi 2000: 2.6, 2.9, 2.10.

G. Casella and R. Berger Second Edition 2002: 7.22, 7.24, 7.27, 7.28. Not to be submitted before mid-sem. Submission deadline Oct 23rd in class

 

Homework 3a: Kailath, Sayed and Hassibi 2000: 3.1, 3.4, 3.9, 3.12, 3.16, 3.17, 3.19, 3.21, 4.1, 4.4, 4.5, 4.8, 4.9a, 4.10 1st part, 4.11(a,b), 4.12: Submission deadline for Homework 3 and 3a: Oct 23rd in class.

 

Homework 4: Kailath, Sayed and Hassibi 2000: 6.1, 6.5, 6.9, 7.4, 7.5, 7.8, 7.11, 7.13, 7.17. Submission Deadline October 25th in class.

 

Homework 5: Kailath, Sayed and Hassibi 2000: 9.3, 9.5, 9.6, 9.9, 9.10, 9.12, 9.15. Submission Deadline, Wednesday Nov 6th.

 

 

Term Project:

Estimate the instantaneous orientation from the recorded gyro + accelerometer+magnetometer data. You can check the accuracy of your estimation by comparing with the orientation estimates given in the same dataset. The order of the Kalman filter, architecture of the filter and the choice of states is to be decided by you. Please submit a short report (<= 10 pages) and your code by email.

The project datasets: 5 separate recordings of IMU data onboard the self-balancing robot (courtesy Sajal Deolikar and Adityaya Dhande) for around 30-40 seconds each with corresponding videos are kept in the linked google drive folder. You need to login with LDAP/SSO to access the data:

Google drive folder: https://drive.google.com/drive/folders/1pNSZ3eaYMRaEbs_h3U9ciXlA6t-JH0js?usp=sharing