Equations to Implement

Generating Updated Position

Basic Equation

$\text{Original Position}+{\int }_0^{\Delta t}v(x)\mathrm{d}x+{\int }_0^{\Delta t}a(x)\mathrm{d}x$

Given Position, Velocity, and Acceleration

$\text{Original Position}+(\Delta t\ast \text{current velocity})+(\Delta t\ast \text{current acceleration})$

Estimating with Rotation

We’ll use rotation matrices for this, with the $x$ and $y$ directions.