John Doe's Portfolio

---

Code for this project is not available. Providing it publicly would be in violation of Georgia Institute of Technology's plagiarism rules.

The only  prior knowledge given about the system is the motion model;

x(t) = C_pos + t * C_vel (t^2/2) * C_acc 

Where, C_pos, C_vel, and C_acc are the position, velocity, and acceleration of the asteroid respectively  in either the ex or y direction 

There no need to try and explain what is  a  common control system.  I recommend the following resources to understand the material better:

Phil's Lab - https://www.youtube.com/watch?v=hQUkiC5o0JI

Wikipedia - https://en.wikipedia.org/wiki/Kalman_filter

For this implementation, the covariance of process noise matrix was omitted. The covariance of observation noise was iteratively tuned to achieve desirable performance.

The prediction step is performed first so the system can make an educated guess for the position of each asteroid. Given the current position of all known asteroids and the  prior knowledge of the system, which allows us to construct a state transition matrix, we are able to determine where any given asteroid should be during the next time step. 

Each measurement step contributes to the models understanding of the system, and is treated with varying degrees of trust. If, for example, the system accelerates much quicker than expected for a time step than that date will not be trusted; however, if the system continues to accelerate quicker than expected for many time steps continuously than the high-acceleration model will prevail and the Kalman filter will adjust to the new beliefs. 

The prediction and measurement steps are repeated ad infinitum, until the simulation is complete.