EE638:
Estimation and Identification (Autumn 2023)
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: TBA
2023 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
4: MVUE using Sufficiency
5.
Lecture
5: BLUE
6.
Lecture
6: Least Squares: Deterministic and Stochastic
7.
Lecture
7: Wiener Filter
8.
Lecture
8: Kalman Filter Part 1
9.
Lecture
8a: Kalman Filter Part 2
10.
Lecture
9: System Identification: Basic
theory
11.
Lecture
10: 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, Wednesday 23th 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 13th September.
.
Homework 3: Kailath,
Sayed and Hassibi 2000: 2.6, 2.9, 2.10, 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 Deadline for submission: Hardcopy
only, in class, Wednesday 27th September. (Mid-Sem
Syllabus until 4.8)
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. Deadline for submission: Hardcopy only, in class, Wednesday
18th October.
Homework 5: Kailath,
Sayed and Hassibi 2000: 9.3, 9.5, 9.6, 9.9, 9.10,
9.12, 9.15. Hardcopy only, in class, Wednesday Nov 8th.
Practice problems for System ID: L. Ljung 1999: 2G4, 2E4, 3D2, 4E1, 4E12 (submission
not necessary)
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