# Ridgy software and algorithms

### Extension to the observation model

The new landmark design and recognition gives the distance*d*to the landmark, the angle

*θ*between the robot and the center of the landmark and the angle $\stackrel{~}{\alpha}$ between a line

*l*, from the center of the robot to the center of the landmark, and the landmark plane normal vector.

Using the fact that the height

*h*of an observed landmark is constant for any angle of the landmark plane (for a constant distance

*d*), and the width

*w*variates with the angle, the observed angle $\stackrel{~}{\alpha}$ of the landmark plane can be calculated as: $$\stackrel{~}{\alpha}=\mathrm{arccos}\frac{w}{h}$$