EE638: Estimation and Identification (Autumn 2026)

Instructor: Dr. Debraj Chakraborty

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

Office: 1^st floor, EE

Lecture Hours: Monday + Thursday 8-9:30am

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

TA: Naveen Mukesh N ( 214070006 )

• Prerequisite: Familiarity with Probability theory, Stochastic processes, Linear Systems and Linear Algebra ( e.g. EE601 AND (EE640 or (EE302 AND EE635)) )

Syllabus

1. Parameter Estimation:

a. Minimum Variance Unbiased Estimation, Cramer-Rao Lower Bound

b. Maximum Likelihood Estimation, EM algorithm

c. Complete Sufficient Statistics, RBLS Theorem

d. Bayes Estimation, MAP

e. Best Linear Unbiased Estimators

f. Least Squares Estimation: Deterministic and Stochastic

g. Applications: Linear Regression/Polynomial Fitting, Bearing only target motion analysis

2. Signal Estimation:

h. Finite Horizon Weiner-Hopf Filter: The Innovations Process

i. The Kalman Filter: State Space Models, Various forms, Consistency, Initialization, Sensitivity, Computational Aspects, Prediction, Application to Kinematic Models.

j. Estimation for non-linear Systems: EKF, Applications

k. Adaptive Estimation: VSD, IMM

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. Bar-Shalom, Yaakov and Kirubarajan, Thiagalingam and Li, X.-Rong, Estimation with Applications to Tracking and Navigation, 2002, John Wiley and Sons

5. Peter Maybeck, Stochastic Models, Estimation and Control – vol 1, Academic Press 1979.

Evaluation:

2 Quizzes (15+15 %), Mid-Sem (30%), End-Sem (40%). Regular Assignments will be given out, but solutions will be corrected only on specific request from students.

Lecture Notes (old)

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

Old 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, Tuesday 25^th 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, Thursday 10th September.