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I'm working on a Kalman filter for estimating the position of a point in 3D space. I know that I can measure its 3D position directly with a variance of about 2 mm (in other words: the variance of the norm of the measured x, y, z vector is about 2 mm).

I'd like to fill my measurement noise covariance matrix based on this, so my question is:

How does this relate to the variance of the individual x, y, z measurements? I'm looking for three equal variances, assuming independency.

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  • $\begingroup$ I don't understand what you're asking. You can't touch the covariance matrix. It holds the uncertainty in your system. $\endgroup$
    – CroCo
    Commented Oct 27, 2016 at 12:23
  • $\begingroup$ I'm talking about the measurement noise covariance matrix R which the user should define, not the state error covariance matrix P. $\endgroup$
    – SHG
    Commented Oct 27, 2016 at 13:10
  • $\begingroup$ you only define the sigmas at the start point. During the process, you shouldn't modify these matrices (i.e. the process and the measurement covariance matrices). $\endgroup$
    – CroCo
    Commented Oct 28, 2016 at 20:01

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Take a bunch of measurements of your system while states are static and compute the noise matrix yourself. As long as recording measurements is relatively straightforward this should be a painless process. It will also verify that your measurements are as accurate as you believe.

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