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whatever

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Maybe my math/stat is very poor. I'm having trouble manipulating the standard deviation. Here's the thing.

I have radar mounted on a car. For each detection, the radar returns these variables.

- relative distance between the object/host vehicle in forward direction (in vehicle body-fixed coordinates)

- standard deviation of the relative forward distance

- relative distance between the object/host vehicle in left/right direction (in vehicle body-fixed coordinates)

- standard deviation of the relative left/right distance

I'm trying to do coordinate transform of the above data, so that I get relative distance/standard deviation in global coordinates (North, South, East, West)

Distance is easy since it only requires to rotate the axis by the amount of angle between the vehicle body-fixed axis and the global axis.

How about standard deviation? How do I transform the standard deviation from the vehicle body-fixed axis to global axis?