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I have 2 position estimates (along with their measurement error) and a difference in time between estimates. I estimate velocity using

Velocity = (PosA - PosB)/DeltaT 

I am trying to estimate the error in my velocity estimate, but I can't seem to find any ways to calculate this. I assume it has to use Sigma_PosA and Sigma_PosB. I would also assume it's relative to DeltaT and/or abs(PosA - PosB). What is the velocity measurement variance/standard deviation?

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    Bet$a$: I'm not sure if they are. They are the same o$b$ject, but th$a$t's the only relationship $b$etween the 2 me$a$surements.2011-08-31

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sigmav = sqrt((sigmaA)2 + (sigmaB)2) / (DeltaT)

EDIT:

(Corrected an error above-- DeltaT should not be squared.)

It sounds as if the measurements are independent, so the errors are uncorrelated. We want the standard deviation of a linear combination of (two) variables:

$V = \frac{(B-A)}{\Delta_t} = \frac{1}{\Delta_t}B - \frac{1}{\Delta_t}A$

$\sigma_V^2= \sum_i^n a_i^2\sigma_i^2 = (\frac{1}{\Delta_t})^2\sigma_B^2 + (\frac{1}{\Delta_t})^2\sigma_A^2 = (\frac{1}{\Delta_t})^2(\sigma_A^2 + \sigma_B^2)$

$\sigma_V = \sqrt {(\frac{1}{\Delta_t})^2(\sigma_A^2 + \sigma_B^2)} = \frac{\sqrt{\sigma_A^2 + \sigma_B^2}}{\Delta_t}$

(I'm new to math.stackexchange-- gotta say I'm lovin' the MathJax.)

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    It looks like that would work, but I would like to see some explanation.2011-09-01
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You want the propagation of error, or propagation of uncertainty. Since you're subtracting them, the formula is

sqrt(sigma_posA * sigma_posA + sigma_posB * sigma_posB)

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    I don't think this would work. I know that if the 2 measurements are far apart (in time/space) then the velocity estimate improves.2011-08-31