Category Archives: Statistical Orbit Determination

Spring 2019/Lecture 5/Perturbed Motion – 6 Feb 2019

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Sorry for the missed lectures on Friday and Monday. I was out sick. Assignments are due on Friday. We covered perturbations to orbital motion. We examined contributions from gravitational and nongravitational sources to the two-body motion.

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Slides: L5 Slides – Perturbed Motion

[youtube https://www.youtube.com/watch?v=HZjksLbF4go&w=560&h=315]

Previous lectures:

 

 

Spring 2019/Lecture 4/Two Body Problem – 30 Jan 2019

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We resumed today with orbital mechanics. We covered the two-body problem, introduced Kepler’s problem (time doesn’t relate well to true anomaly), and sprinted to the state transition matrix. We will resume with perturbations and additional bodies considered on Friday.

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Slides: L4 Slides – Two Body Problem

[youtube https://www.youtube.com/watch?v=Mx6PEYk_RQE&w=560&h=315]

Previous lectures:

 

 

Spring 2019/Lecture 3/Problem Solution and Review – 28 Jan 2019

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Re-recorded lecture from Monday, January 28. I cover the 2D Uniform Gravitational Field (parabolic trajectory) problem solution. I also reviewed linearization and the state transition matrix because I felt that I didn’t cover them adequately in lecture 1. We will pick back up with additional review of orbital mechanics before moving on to observations.

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The problem solution can be found on GitHub at https://github.com/simpsonchristo/Soln-HW1-SimpsonAerospace.

The pdf write-up of the solution and the slides can be found here:

Write-up: soln_hw1

Slides: 3-problemsolutionlinearization_spring2019

[youtube https://www.youtube.com/watch?v=8oFZBRa2yp8&w=560&h=315]

Spring 2019/Lecture 2/Orbital Mechanics – 25 Jan 2019

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We review orbital mechanics to prepare for orbit determination. We will cover the two body problem, orbital elements, and perturbing accelerations. We will continue on Monday. Be ready to turn in your solution for the practice problem.

Lecture Slides:

Review of Orbital Mechanics – Lecture 2

[youtube https://www.youtube.com/watch?v=Hu86dlxZ6-o&w=560&h=315]

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

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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

[youtube https://www.youtube.com/watch?v=WKOjZB9IPO0&w=560&h=315]

Cesium Demo Using STK Scenario/TLE Data

Spring 2019 – Orbit Determination Course

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Thanks to those of you that have been following the orbit determination course.

  1. This course is being revamped/restarted. We will follow a typical semester schedule. We had our first lecture today.
  2. I apologize to those following previously. Things got hectic with my father’s illness and qualifying exams for my Ph.D.
  3. Looking forward to hearing from all of you!

 Check It Out!

Before we get started, just a few things:

  • If you’re working through the material and have a question, please leave it on the lecture page on YouTube! The goal is to encourage discussion!
  • I appreciate feedback! I want to make it as easy as possible for you to learn from me.

Finally,

Thank you for signing up and wanting to learn more about OD!

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.

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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