Calculate Prediction Step Quiz Explanation

The equations for updating x, y and the yaw angle when the yaw rate is not equal to zero:

$x_f = x_0 + \dfrac{v}{ \dot{\theta}}[sin(\theta_0 + \dot{\theta}(dt)) - sin(\theta_0)]$

$y_f = y_0 + \dfrac{v}{ \dot{\theta}}[cos(\theta_0) - cos(\theta_0 + \dot{\theta}(dt))]$

$\theta_f = \theta_0 + \dot{\theta}(dt)$

Plugging in all the numbers should give:

$102+\frac{110}{\frac{\pi}{8}}[sin(\frac{5\pi}{8}+\frac{\pi}{8}(0.1))-sin(\frac{5\pi}{8})] = 97.59$

$65+\frac{110}{\frac{\pi}{8}}[cos(\frac{5\pi}{8})-cos(\frac{5\pi}{8}+\frac{\pi}{8}(0.1))] = 75.08$

$\frac{5\pi}{8}+ \frac{\pi}{8}(0.1)= \frac{51\pi}{80}$