Probabilistic Estimation and Tracking

AAE59000

Credit Hours:

3

Learning Objective:

The goal of this course is twofold: 1) understand the fundamentals of probabilistic estimation theory needed to conduct novel research and 2) learn practical techniques needed to apply estimation algorithms to real engineering problems.
At the conclusion of this course, successful students will be able to:

  1. Identify problems and applications suitable for state estimation based solutions.
  2. Model key dynamic and measurement processes for continuous and discrete stochastic dynamical systems.
  3. Understand the most commonly used probabilistic state estimation algorithms, their advantages, and their limitations.
  4. Test, troubleshoot, and evaluate state estimation algorithm performance.
  5. Independently apply the covered techniques to a unique problem of their interest.

 

Description:

Probabilistic estimation and tracking theory, with a focus on aeronautics and astronautics applications. Topics include extended/unscented Kalman filtering, Gaussian mixture filtering, particle filtering, multi-sensor fusion, and target tracking.

Fall 2025 Syllabus

 

Topics Covered:

This is an experimental course being offered for the first time. Topics are subject to change based on pace and student feedback.

  1. Review of linear algebra and probability concepts
  2. Parameter estimation and least squares
  3. Kalman filtering
  4. Practical considerations
  5. General Gaussian filtering
  6. Smoothing
  7. Gaussian mixture filtering
  8. Particle filtering
  9. Multisensor fusion
  10. Introduction to multiobject tracking

 

Prerequisites:

AAE 340, STAT 511(or equivalent probability and statistics course)

Necessary Background

  • Basic probability and statistics
  • Linear algebra
  • Differential equations
  • Formulation and solution of state space equations

 

Web Address:

https://purdue.brightspace.com

 

Homework:

  1. Approximately 5-6 homework assignments. Each homework will consist of a mix of theory questions and application problems.
  2. All homework is to be submitted via Gradescope. The assignments must be uploaded at the time indicated on the homework sheet. Although late homework assignments are graded for the benefit of the student, homework submitted after the due date/time will receive a score of zero.
  3. Homework rules
    • must be neat and legible
    • on 8. x 11-inch letter paper or electronic equivalent (any style)
    • adhere to the formatting outlined in the separate documents.
    • The result must be boxed and clearly marked.
    • It must be your own work (copying will result in a grade divided by the number of students involved). Points will be taken off for not following all these rules.
    • All computer code must be attached to the homework submission.
    • Code should be thought of as an appendix to your work. All equations, assumptions, approximations, derivations, etc. should be written in the handwritten/typed portion of your submission and not hidden in your code.
    • A discussion should accompany every plot. Potential questions to answer are: are your results satisfactory? Why or why not? What are the convergence properties? What is the overall behavior of the plot? Are there any anomalies? If so, what might have caused them? How might your plots change if the problem or model was varied slightly?
  4. Solutions for selected problems will be available on the course site on Brightspace.

 

Projects:

Student-designed independent project, including a proposal and final report.

 

Textbooks:

Course notes
The course notes will be published on Brightspace. However, taking your own notes is highly encouraged and will improve learning and class performance.

Some suggested texts are:

  • Särkkä, Simo. Bayesian Filtering and Smoothing. 1st ed. Cambridge University Press, 2013. (free pdf available online courtesy of author)
  • Crassidis, John L., and John L. Junkins. Optimal Estimation of Dynamic Systems, 2004.
  • Bar-Shalom, Yaakov and X. Rong Li. Estimation with Applications to Tracking and Navigation. John Wiley & Sons, Inc, 2001.
  • Tapley, Byron D., Bob E. Schutz, and George H. Born. Statistical Orbit Determination. Amsterdam ; Boston: Elsevier Academic Press, 2004.
  • Grewal, Mohinder S., and Angus P. Andrews. Kalman Filtering: Theory and Practice Using MATLAB. Fourth edition. Hoboken, New Jersey: John Wiley & Sons Inc, 2015.

 

Computer Requirements: