State Estimation and Filtering for Aerospace Systems


Stanford School of Engineering

Aeronautics and Astronautics: State Estimation and Filtering for Robot Perception


How does an autonomous aircraft determine its velocity vector and position while taking into consideration GPS, airspeed, and IMU measurements? How does an autonomous car map its surrounding environment and determine its position relative to that environment with noisy data including camera and Lidar measurements? These are examples of a fundamental problem in engineering: state estimation. In this course you will study algorithms that are used to determine the state of a dynamical system over time while filtering out erroneous measurements. By exploring examples from robotics, including state estimation for drones, SLAM for autonomous cars and mobile robots, and attitude estimation for autonomous spacecraft, you will learn how to use filters to solve mathematical problems. You will develop an understanding of state estimation in the larger context of Bayesian estimation, which is relevant to a range of topics in machine learning, artificial intelligence, and signal processing.

What you will learn

  • How to develop state estimation algorithms
  • How to optimize parameters using experimental data
  • How to apply state estimation strategies to real world problems
  • How to advance your skills solving both traditional math problems as well as implementation exercises


A conferred Bachelor’s degree with an undergraduate GPA of 3.5 or better.

The course assumes knowledge of concepts from state space control and linear systems (ENGR205 and EE263), and basic familiarity with the Kalman filter. A high level of mathematical maturity is expected.

Topics include

  • Dynamical systems and probability review
  • Linear-Gaussian systems
  • Kalman and Bayesian filtering
  • Nonlinear architectures
  • Iterated filters and optimization
  • Rigid body dynamics


Course Availability

The course schedule is displayed for planning purposes – courses can be modified, changed, or cancelled. Course availability will be considered finalized on the first day of open enrollment. For quarterly enrollment dates, please refer to our graduate education section.

Pre-register Now

Dates:March 29 - June 4, 2021
Units: 3.00
Instructors: Mac Schwager
Delivery Option:
For Credit $4,056.00
Notes: Pre-registration Dates: February 1, 2021 at 9:00am to March 12, 2021 at 5:00pm

Pre-registration for this course will secure your enrollment request and ensure timely processing of your application for potential course approval. Please note: course enrollment will be confirmed after March 19, 2021; after completing your pre-registration, no further action is required on your part.


This course may not currently be available to learners in some states and territories.