Why the unit of angular random walk of Gyroscope is °/√s or °/√hr rather than °/s or °/hr ?
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You just integrate a random number, so it’s just as likely to go up as it is to go down, so it doesn’t go up and up with time.
its the standard deviation of the gyro. Equation for standard deviation is √(1/sampleTime *Sum((actualDegrees-expectedDegrees)^2 )
so you have √(°^2 /s) or °/√s
In a random walk, you take random steps forward or backward at the flip of a coin and ask how far you are from your starting point at the end. If I take 4 steps, they *could* be all in the same direction so I could be 4 steps from the start, but that’s really unlikely. Much more likely to have about as many forward steps as backward, for a final distance 0, 1, or 2 away from the start.
As I take more steps, my most likely distance from the start increases, but not in proportion. [It turns out](https://en.m.wikipedia.org/wiki/Random_walk) that if I take N steps, my most likely distance from the start is about sqrt(N).
Thus, real-world processes that behave like random walks have deviations that increase not with time, but with the square root of time.
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