How does a missile calculate it’s deviation and where it shouldn’t be?
In: Engineering
Start small, understand 3D positioning:
https://www.intmath.com/vectors/7-vectors-in-3d-space.php
Then understand GPS, which is much more complex but essentially the same, 3D Geometry once you know points in space is trivial.
But there’s a lot underlying GPS to get to this point.
Have fun!
I might add that very sophisticated mathematics are used to get estimates as precise as possible of the missile’s position. Interestingly enough, statistical methods that are also commonly found in economic and financial models are used (they are also found elsewhere in the sciences). If you have a solid foundation of statistics, you can look up Kalman filter on wikipedia. There might even be an ELI5 on this stuff somewhere on the web.
Here’s my ELI5: You cannot directly observe the missile’s position because it is very far away so you have to make due with the technology at hand. Since the path of the missile is subject to randomness/noise/error and the sensors on the missile that guess its position are subject to randomness/noise/error you have a very special dynamical system here. This duality of noise requires a special mathematical treatment i.e. Kalman filtering. Kalman filtering makes use of your previous guess of the missile’s position (say one second ago) and what the sensors tell you right now to give an educated guess of the missile’s current position. This process is then continued a step further and repeats. The appropriate “weighting” of past guess vs. current sensor’s guess to determine the missile’s current position is learned by the algorithm because it too is something that is important to the system but cannot be directly observed. This problem has been solved and has made missiles, spaceflight, and more possible.
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