# estimate accuracy of (aruco) marker position tracking

I'm planning a concept for calibrating a robot model. For this purpose I want to use computer vision approaches. Since I'm not that experienced in that field I have some basic questions on the accuracy of NON STEREO approaches like the famous Aruco markers aruco marker description.

Using a simple pin hole camera model where $$x_{img} = \frac{f_x}{z_C} x_C$$ where $$C$$ denotes the cameras coordinate frame.

I know the size of a pixel of my camera ( $$\Delta x_{img}\approx10\mathrm{\mu m}$$) and the focal length ($$f_x\approx664\mathrm{m}$$). Somehow I'm having problems to estimate the accuracy I can expect. Especially in the depth ($$z_C$$) direction.

My fist approach was to use the distance between two pixels in the image frame to calculate a distance in z-direction but i) this depends on the $$x_C$$ coordinate, and ii) this leads to unrealistic values $$\Delta z_C \approx 6.64e7 x_C$$.

Now I'm seeking for help.