First off a reminder about the difference between speed and velocity, and how these two parameters relate to statistical uncertainty. We distinguish between the term velocity (which involves direction of motion aswell as the rate) and speed, which only involves the rate and not direction.
Velocity: v(t) = dx/dt = x'(t)
Speed is the absolute value of the velocity:
Speed: s(t) = |v(t)| = |dx/dt|
If we have a velocity component U, then the mean:
<U> = sum(U)/N
sig(<U>) = sig(U)/sqrt(N)
U = single ping velocity component
<U> = mean
N = number of pings
sig = standard deviation (gives a measure of how spread out the variance of the mean is. The smaller the standard deviation, the more of the variance is concentrated close to the mean)
That is; the mean is an arithmetic mean and the uncertainty in the mean is the uncertainty of each separate measurement divided by number of measurements. That means that the uncertainty in the velocity measurement gets smaller and smaller towards zero as long as one continue to measure. Therefore, there is no limit to how low the measurement uncertainty you can get.
If we work with speed, then: (ref. Pytagoras)
speed = sqrt(U^2 + V^2 +eps),
eps = sig(U)^2 + sig(V)^2
The uncertainty will get very low if we first take the mean of U and V. Doing that we can get good speed estimates. If, instead, one takes the mean of each speed measurement, we will not get rid of the uncertainty and speed will not converge towards zero even though both velocity component does. Depending on instrument setup, the sig(U) and sig(V) can be relatively large so that the error may be larger than one initially would expect.
Regarding the definition of accuracy (ref. instrument specific data sheet):
-0.5 cm/s + 0.99 Um < U < 0.5 cm/s + 1.01*Um
where Um is the measured velocity component and U is the correct velocity.