Shahriar Talebi | MECH&AE 271A (cross-listed 175A)

A rigorous and computational introduction to probability, stochastic processes, and estimation in dynamical systems, with emphasis on applications in autonomy, robotics, and physical AI. The course develops estimation from first principles as probabilistic inference under uncertainty. Starting from probability spaces, random variables, conditional expectation, and stochastic processes, we develop minimum mean-square estimation, state-space models, Bayesian filtering, Kalman filtering and smoothing, nonlinear filtering, and sequential Monte Carlo methods. Time permitting, we also study inference when the underlying model is uncertain or learned from data, including joint state and parameter estimation, expectation-maximization, differentiable state estimation, model mismatch, and distribution shift. Throughout the course, mathematical foundations are paired with computational modules in which students implement and investigate estimation algorithms on dynamical systems.

Instructor's bio: Shahriar Talebi is an Assistant Professor in the Department of Mechanical & Aerospace Engineering at the UCLA Samueli School of Engineering (since July 2025). Before UCLA, he was a Postdoctoral Research Fellow at Harvard University and a contributor to the NSF AI Institute in Dynamic Systems (Dynamics AI). He received a Ph.D. in control theory from the University of Washington in 2023—focusing on constrained decision-making and control in complex systems—and an M.Sc. in Mathematics (differential geometry) from UW.

Course Logistics

Course: MECH&AE C271A (cross-listed as MECH&AE 175A), 4 units
Concurrent course: MECH&AE C175A
Instructor: Dr. Shahriar Talebi, s.talebi@ucla.edu, office: Eng IV, 38-137F
Prerequisites: Familiarity with linear algebra, differential equations, and undergraduate probability. Prior exposure to dynamical systems and linear systems is helpful.
Lectures: MW 12:00 PM-1:50 PM in Boelter Hall 9436
Office hours: TBD

Main Textbook

J. L. Speyer and W. H. Chung, Stochastic Processes, Estimation, and Control, Society for Industrial and Applied Mathematics, 2008 — applications of probability and stochastic strategies to model uncertainty for estimation problems.

Additional Resources

R. Durrett, Probability: Theory and Examples, 5th ed., Cambridge University Press, 2019 — graduate mathematics for probability-theoretic foundations and stochastic processes.
T. D. Barfoot, State Estimation for Robotics, 2nd ed., Cambridge University Press, 2024 — Applied modern state estimation, nonlinear estimation, robustness, and robotics applications.
S. Särkkä and L. Svensson, Bayesian Filtering and Smoothing, 2nd ed., Cambridge University Press, 2023 — a Bayesian perspective to filtering and estimation.
T. Kailath, A. H. Sayed, and B. Hassibi, Linear Estimation, Prentice Hall, 2000 — classical reference for projection, orthogonality, innovations, and linear estimation.
Selected research papers and instructor notes will be distributed throughout the course.

Course Philosophy

The course is organized around a unifying view of estimation as inference about hidden quantities from incomplete and noisy information. Classical methods such as least squares and Kalman filtering and modern approaches based on Monte Carlo inference and learned dynamical models are developed within the same probabilistic framework. Particular emphasis is placed on understanding the assumptions behind an estimator, how uncertainty is represented and propagated, and how those assumptions fail in real dynamical and autonomous systems.

The mathematical progression of the course is:

Probability → Conditional Expectation → Stochastic Dynamics → Bayesian Inference → Kalman Filtering → Nonlinear Inference → Learning → Autonomous Systems

Learning Objectives

By the end of this course, students will be able to formulate uncertainty in dynamical systems using probability spaces, random variables, stochastic processes, and state-space models; work with conditional expectation and interpret minimum mean-square estimation as an orthogonal projection in an appropriate Hilbert space; analyze Gaussian random vectors and derive optimal estimators from conditional distributions and covariance information; formulate filtering, prediction, and smoothing as Bayesian inference problems; derive and implement the Kalman filter and smoother from both probabilistic and minimum-variance perspectives; construct approximate estimators for nonlinear and non-Gaussian systems using linearization, sigma-point, and Monte Carlo methods; formulate joint state and parameter estimation and likelihood-based learning problems for dynamical systems; assess estimator consistency, robustness, and sensitivity to model mismatch; and combine model-based and data-driven components in modern state-estimation architectures for autonomous systems. Students will also develop computational proficiency by implementing estimation algorithms from first principles and evaluating their behavior on simulated and physical dynamical systems.

Topics

Probability and conditional inference — Probability spaces, random variables, expectation, Gaussian random vectors, conditional probability, conditional expectation, MMSE estimation, orthogonality, and linear minimum mean-square estimation.
Stochastic processes and dynamical models — Stochastic sequences and processes, covariance functions, Gaussian and Markov processes, state-space models, and propagation of uncertainty through dynamical systems.
Bayesian and linear-Gaussian estimation — Bayesian filtering recursion, Kalman filtering, innovations, covariance and information forms, numerical considerations, smoothing, and trajectory estimation.
Nonlinear and non-Gaussian estimation — Extended Kalman filtering, sigma-point and unscented filtering, Monte Carlo inference, importance sampling, particle filtering, and limitations of approximate inference.
Learning and adaptive estimation — Joint state and parameter estimation, identifiability, adaptive estimation, maximum likelihood, expectation-maximization, and learning state-space models from data.
Estimation for autonomous systems — Differentiable estimation, hybrid physics-learning models, estimator consistency, model mismatch, distribution shift, robustness, and integration of probabilistic inference into modern autonomous systems.

Grading

Problem Sets — 0%
Computational Assignments — 0%
Reading Assignments — 0%
Midterm Exam — 40%
Final Exam + Final Project — 60%

Syllabus PDF