Motivation

I try to build some novel application for GP and find a interesting application on maneuvering error modeling. In Napoleonic Wars age, soldiers are lined to fire on their foe. They’re trained to maintain a straight batthleline but that line will not be that perfect straight at all. We can build a generative model to simulate it using GP to help realistic animation in war game.

Why GP?

A i.i.d benchmark can be considered, it will look like this:

i.i.d movement

We can assign time and space correlation to them naturally using GP. A squared exponential can be specifed to denote the fact that more closer two points (X,Y,T) in time and space, the more positive correlation their “error” term hold.

We may expect at same time unit which are close to each other will have consistent deviating tendency, leading a smoother placement instead of a zigzag shape. In other hand, closing to each other at different timestamp having same tendency may imply a “unseen” terrain obstacle, which slow units passing it temporarily.

Result

Take 30 frames:

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Result of Gaussian Process

Links

Original post with detailed equations.

https://yiyuezhuo.github.io/blog/tech/2019/12/07/emperor-gaussian-process.html