Course Details
Subject {L-T-P / C} : EE6333 : Estimation of Signals and Systems { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Dr. Abhishek Dey
Syllabus
Module 1: Introduction to Probability (3 hours)
Module 2: Random Variables: Discrete and Continuous, Probability Mass and Density functions, Joint and Conditional Distribution, Expectation, Variance and Moments, Function of Random Variables, Limit Theorems (8 hours)
Module 3: Random Processes: continuous and discrete, Brownian motion, Gaussian process, Markov Process, White noise, Stochastic difference and differential equation Strict Sense and Wide Sense Stationary Processes. (6 hours)
Module 4: Deterministic and Stochastic Estimation: Least Squares (LS) and Least Mean Squares (LMS) , Weighted Least Squares (WLS), Orthogonality principle. (5 hours)
Module 5: Estimation for static and dynamic systems: Least Square (LS) and Maximum Likelihood Estimation (MLE), Parameter estimation in AR, ARX, ARMAX model, Yule-Walker equation, one step ahead estimation. (5 hours)
Module 6: Goodness of estimator: unbiased estimator, Minimum Variance Unbiased Estimator (MVUE), Best Linear Unbiased Estimator (BLUE), Cramer Rao Lower Bound. (2 hours)
Module 7: Recursive Estimation: Recursive Least Square (RLS), Kalman Filter- discrete, continuous, hybrid, propagation of mean and variance, Extended Kalman Filter (EKF). (6 hours)
Course Objectives
- Introducing stochastic modeling of dynamical systems.
- Explaining various estimation methods, such as LS, LMS, MLE, MAP and Kalman Filtering.
- Evaluating the goodness of an estimator.
- Obtaining state and parameter estimates of a dynamical system.
Course Outcomes
At the end of the course, students will be able to <br /> <br />CO1: Demonstrate basic knowledge of probability theory and random variables. <br />CO2: Demonstrate ability to model stochastic processes. <br />CO3: Apply the concepts of conditional probability and independence in random variables and random processes. <br />CO4: Formulate estimation problems and find state and parameter estimates of dynamical systems. <br />CO5: Evaluate performance of different estimators for given systems. <br />CO6: Use computational tools to implement various estimation algorithms in MATLAB/Python.
Essential Reading
- Dimitri P. Bertsekas and John N. Tsitsiklis, Introduction to Probability, 2nd Ed., Athena Scientific , https://ocw.mit.edu/courses/res-6-012-introduction-to-probability-spring-2018/pages/part-i-the-fundamentals/
- T. Kailath, A. H. Sayed and B. Hassibi, Linear Estimation, Prentice Hall
Supplementary Reading
- Athanasios Papoulis and S. Unnikrishna Pillai, Probability, Random Variables and Stochastic Processes, McGraw Hill
- Dan Simon, Optimal State Estimation: Kalman, H8, and Nonlinear Approaches, Wiley
Journal and Conferences
- Kalman, R. E. (1960). "A New Approach to Linear Filtering and Prediction Problems." ASME. J. Basic Eng. March 1960 82(1): 35–45. https://doi.org/10.1115/1.3662552
- Sorenson, H. W. (1970). "Least-squares estimation: from Gauss to Kalman". IEEE spectrum, 7(7), 63-68.