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}