Instructor Notes

Note that for a vector $\mathbf{v} = \text{(x,y)}$ , $\vert \mathbf{v} \vert$ is used here to denote the vector length or magnitude = $\sqrt{x^2 + y^2}$ .

For a difference between two vectors, $\mathbf{v} = {(x_v,y_v)}$ and $\mathbf{w} = {(x_w,y_w)}$ , the magnitude $\vert \mathbf{v - w} \vert$ is also the Euclidean distance between these two vectors = $\sqrt{(x_v - x_w)^2 + (y_v - y_w)^2}$

In this case $\sqrt{\vert p_i - g \vert}$ is meant to note the root squared error of a particular particle, resulting in the general form described in the quiz:

$\sqrt{(x_p - x_g)^2 + (y_p - y_g)^2}$

where:

• Position RMSE = $\sqrt{(x_p - x_g)^2 + (y_p - y_g)^2}$
• Theta RMSE = $\sqrt{(\theta_p - \theta_g)^2}$

Root Squared Error Quiz

Given that the car’s ground truth position was (x, y, theta) = (5.2 m, 19.3 m, pi/16) and the best particle’s position was (x, y, theta) = (5 m, 18.7 m, pi/8), what is the error?

Position RMSE = $\sqrt{(x-x_{meas})^2+(y-y_{meas})^2}$

Theta RMSE = $\sqrt{(\theta-\theta_{meas})^2}$