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I have a localization data estimated and GPS_truth and generated [3x3] covariance matrix along with them.

What i would like to do is to see if the covariance is correct or not?

Can we check it by plotting the covariance?

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  • $\begingroup$ You can plot the 2 and 3 $\sigma$ gates around the means to see if it visually and intuitively makes sense. If you have access to the raw data before it was filtered, you can calculate the residuals and follow robotics.stackexchange.com/questions/6639/… $\endgroup$
    – Gouda
    Aug 21, 2016 at 12:13
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    $\begingroup$ Good answer @Gouda. Why don't you make it a real answer so we can upvote it? $\endgroup$
    – Ben
    Aug 22, 2016 at 0:23
  • $\begingroup$ Is this localisation in 2D or 3D? $\endgroup$ Aug 24, 2016 at 9:41
  • $\begingroup$ It is a 3D localization of a UAV obtained through SLAM $\endgroup$ Aug 24, 2016 at 15:25

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You can plot the 2 and 3 σ gates around the means to see if it visually and intuitively makes sense.

If you have access to the raw data before it was filtered, you can calculate the residuals and follow how to plot $\pm 3 \sigma$ of a landmark in EKF-SLAM

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  • $\begingroup$ Im really sorry to open this question again, But as you suggested i tried plotting σ and 3σ around the mean to visualize whether the ground_truth is well within the limits (which is well outside). but as the value of std. deviation (σ) is very low is really difficult to even see the difference between μ+σ and μ-σ imgur.com/a/qMgX1 $\endgroup$ Sep 8, 2016 at 4:01
  • $\begingroup$ Did you forget to take the square root of the diagonal elements of the position covariance matrix? That would change the size considerably. You should plot $\mu \pm 3\sigma$. $\endgroup$
    – Gouda
    Sep 10, 2016 at 3:08
  • $\begingroup$ well i did take the sqrt of the diagonal elements the matrix is, $$ \begin{bmatrix} 0.000266161 & 8.05408*10^-5 & -8.42415*10^-5 \\ 8.05408*10^-5 & 0.000604004 & -0.00037067 \\ -8.42415*10^-5 & -0.00037067 & 0.000388194 \\ \end{bmatrix} $$ so the values i get are $$\sigma _x = 0.0163144 $$ $$\sigma _y = 0.0245764 $$ $$\sigma _z = 0.0197026 $$ $\endgroup$ Sep 10, 2016 at 14:29
  • $\begingroup$ Those sigmas look like good precision for a SLAM solution. The next step in validation is to check the sigmas of the measurements and make sure they match the covariance parameters of your SLAM. Can you tell us more on: How is your ground truth measured? What other sensors are used for the SLAM estimate? And also look at the RMS error between the estimates and the ground truth. An image of the plot would help too. $\endgroup$
    – Gouda
    Sep 11, 2016 at 3:25
  • $\begingroup$ The ground truth is the localization information obtained from GPS. For SLAM the sensors used are IMU, Laser range finder and a Monocular camera. The RMS error is 3.690156 Trajectory Plots: VSLAM vs. GPS (x): imgur.com/i5z8G2N VSLAM vs. GPS (y): imgur.com/BYzayrY VSLAM vs. GPS (z): imgur.com/zChgxOA VSLAM vs. GPS (3D): imgur.com/hLLQMam $\endgroup$ Sep 12, 2016 at 12:41

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