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