Author Archives: crsimpson

Spring 2019/Lecture 1/Orbit Determination Concepts – 23 Jan 2019

The inherent characteristics of an orbit determination (OD) problem are introduced. Dynamic state estimation, observations, linearization, and the state transition matrix are discussed. At the end, I have left a practice problem that we will review on Friday, 8 June. We throw a satellite up and watch it come down while introducing some important concepts.

Lecture Slides:

Orbit Determination Concepts – Lecture 1

Cesium Demo Using STK Scenario/TLE Data

Orbit Determination — A Short Course

SA · ORBIT DETERMINATION · SHORT COURSE · 14JUN26

Orbit Determination

A short course.

A twelve-lecture introduction to orbit determination — from orbital mechanics and the two-body problem through coordinate systems, measurement simulation, and fitting real measurements into a state estimate. Taught by Dr. Christopher R. Simpson. Free, self-paced, with lecture notes and video.

Who it is for

Students and engineers who want a working understanding of how a state estimate is built from measurements. Some calculus and basic orbital mechanics help, but the course builds from first principles.

Syllabus

  1. Lecture 1 — Orbit determination concepts
  2. Lecture 2 — Orbital mechanics
  3. Lecture 3 — Problem solution and review
  4. Lecture 4 — The two-body problem
  5. Lecture 5 — Perturbed motion
  6. Lecture 6 — Coordinate systems and time
  7. Lecture 7 — Ideal and conceptual measurements
  8. Lecture 8 — Simulating ideal measurements
  9. Lecture 9 — Conceptual measurements
  10. Lecture 10 — Conceptual example, part 1
  11. Lecture 11 — Conceptual example, part 2
  12. Lecture 12 — Real measurements

Problem sets & assessment

How to follow along

Work the lectures in order. Each builds on the last. Questions are welcome on each lecture’s video page — discussion is the point.

Originally taught Spring 2019; refreshed and re-launched 2026.

Updates: Ph.D. Candidate

I’ve officially passed my qualifying exams. I took my qualifiers in both Intermediate Dynamics and Space Systems. Having passed both I am officially a Ph.D. Candidate. Time to begin preparing for my thesis proposal.

Next semester will see the completion of a satellite ground station at Alabama (more on that later), the publishing of an Orbit Determination course, and my proposal.

I can’t wait to return to my research! It’s been languishing as I focused on qualifiers.

IGARSS 2018: CubeSat Constellation

I attended the 2018 International Geoscience And Remote Sensing Symposium (IGARSS 2018) in July; presenting on the recently proposed 50 CubeSat constellation to sound the Antarctic ice sheets. There are still large gaps in ice thickness data despite more than 50 years of airborne radar sounding. A satellite mission presents an opportunity to gain complete coverage of the ice sheets. Some key features of the constellation include a 50 m and 1 m along-track and cross-track separation, respectively, a Ka-band radar and downlink device, and a 150 MHz sounder.

Abstract-In spite of more than 50 years of airborne radar soundings of Antarctic ice by the international community, there are still large gaps in ice thickness data. We propose a CubeSat satellite mission for complete sounding and imaging of Antarctica with 50 CubeSats integrated with a VHF radar system to sound the ice and image the ice-bed. One of the major challenges in orbital sounding of ice is off-vertical surface clutter that masks weak ice-bed echoes. We must obtain fine resolution both in the along track and cross track directions to reduce surface clutter. We can obtain fine resolution in the along track direction by synthesizing a large aperture by taking advantage of the forward motion of a satellite. However, we need a large antenna-array to obtain fine resolution in the cross track direction. We propose a train of 50 CubeSats with optimized offset position to obtain a 500-m long aperture and also coherently combine data from multiple passes of the train to obtain a very large aperture of 1-2 km in the cross track direction. Our initial analysis shows that we can obtain measurements with horizontal resolution of about 200 m and vertical resolution of about 20 m. The CubeSat will carry a transmitter and receiver with peak transmit power of about 50 W. We will synchronize all transmitters and receivers with a Ka-band system that serves as a communication link between the earth and Cubesats to downlink data and as command and control for the CubeSats.

Paper: A CubeSat Train for Radar Sounding and Imaging of Antarctic Ice Sheet

Presentation: Simpson_CubeSatTrain_Presentation_IGARSS2018

Image credit: (2018/Charles O’Neill)

Lecture 3 – Orbital Mechanics Review B

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Lecture

I pick up again by reviewing the solution to the problem assigned during Lecture 1. (The link will take you to a solution using C++ on GitHub). A few common coordinate systems and reference frames are introduced, orbital perturbations are introduced, and an example problem to be solved in Lecture 4 is given to the class to start on.

[youtube https://www.youtube.com/watch?v=FlcF9AoNBUo]

Previous Lectures

Lecture 2

Lecture 1

Resources

Lecture 3 – Review Of Orbital Mechanics B

Lecture 2 – Orbital Mechanics Review A

Lecture 1 – Orbit Determination Concepts (slides)

AppendixA-ProbabilityAndStatistics

OD – HW 1 Solution

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Solution to Homework 1

Problem 1 provides the solution for us. We are learning how to use iterative methods to estimate the state vector. In this case we will use the Newton-Raphson root-finding method to solve for the problem. An Excel sheet is provided that walks through the first three iterations as an illustration. C++ code is provided on GitHub that will solve for the final solution and show the number of iterations.

Homework Solution 1

Excel – Visual Iterative Solution

C++ Solution

 

OD – Postponement/Ans.

I’ve been traveling and haven’t been able to finish the last part of Orbital Mechanics Review. Feel free to review Dr. Russell’s work, prior to Monday. Full solution will be posted Monday as well. If you’re answers don’t match up; start a discussion in the comments below.

Answer for the practice problem:

X0 1
Y0 8.0
Xdot 2.0
Ydot 1
g 0.5
Xs 1.0
Ys 1.0

Lecture 2 – Orbital Mechanics Review A

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Lecture

We review orbital mechanics and Newton’s law of gravitation to prepare for orbit determination. We will cover the two body problem, orbital elements, and perturbing accelerations. We won’t finish the entire lecture today. We will continue on Monday.

[youtube https://www.youtube.com/watch?v=eBekNtOqy-k]

Previous Lectures

Lecture 1

Resources

Lecture 2 – Orbital Mechanics Review A

Lecture 1 – Orbit Determination Concepts (slides)

AppendixA-ProbabilityAndStatistics