# How do I compare the accuracy of two measurement devices when one of them is the reference?

I'm currently trying to compare the measurement accuracy of two devices. However, I am using one of the devices as a "gold standard" to say something about the accuracy of the other device.

The quantity I am trying to measure is the distance (depth) to a point in a scene (image). I am using a laser scanner which gives me (x,y,z) coordinates for a point and I am using optical geometry to give me (x,y,z) coordinates for the same point. My base (or reference) measurement is the laser scanner measurement. I am using this as a gold standard. I now have a corresponding measurement from the optical geometry based measurement system. I have corresponding measurements for 1000's of points. I average the error in the difference between these and get a mean error. This error, however, neglects the fact that the laser scanner too is a measurement system and has its own error. It comes with an accuracy of +/- 5mm for an object at 10m range. How do I incorporate this into an accuracy metric for the optical geometry based system?

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I see, so you are saying Var(X-Y) = $\frac{\sum_{i=1}^{N} (X_i - Y_i)^2}{N}$ ? And that Var(X) = Var(X-Y) - Var(Y)? –  Mustafa Jul 3 '12 at 20:44