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In the below picture, the measurements are inside the $\pm 3 \sigma$ bounds. In my experiment, the measurements sometimes go out of the uncertainty bounds.

enter image description here

This is a snapshot of my plot where the red is $\pm 3 \sigma$ bounds (i.e. $true \pm 3\sigma$ ), the black is the measurements, the blue is the true value and the green is the EKF. Is there something wrong with my results?

enter image description here

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The meaning of $±3σ$ is that for a given distribution of the measurements, most of the measurements (which have values of up to three time the standard deviation around the average) will be in that boundary. By definition there will be values out side the boundary.

You need to make some specific computations to find out if in your implementation there is a deviation from your expected performance.

I wonder what is the distribution of the values you assumed? How you determine for each measurement the average and the boundaries - you have a kind of dynamic behavior which places a challenge on defining the various values.

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