I have 2 position estimates (along with their measurement error) and a difference in time between estimates. I estimate velocity usingVelocity = (PosA - PosB)/DeltaTI 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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I have 2 position estimates (along with their measurement error) and a difference in time between estimates. I estimate velocity usingVelocity = (PosA - PosB)/DeltaTI am trying to estimate the error in my velocity estimate, but I can&#039;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&#039;s relative to DeltaT and/or abs(PosA - PosB). What is the velocity measurement variance/standard deviation?

Cristian Hamilton · Accepted Answer

σ    v    =                                          σ            A                          2            +                                    σ            B                          2                    Δ      T      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  =            (      B      −      A      )              Δ      t        =      1          Δ      t        B  −      1          Δ      t        A      σ    V    2    =      ∑    i    n        a    i    2        σ    i    2    =  (      1          Δ      t            )    2        σ    B    2    +  (      1          Δ      t            )    2        σ    A    2    =  (      1          Δ      t            )    2    (      σ    A    2    +      σ    B    2    )      σ    V    =      (          1              Δ        t                    )      2        (          σ      A      2        +          σ      B      2        )    =                    σ        A        2            +              σ        B        2                    Δ      t

I have 2 position estimates (along with their measurement error) and a difference in time between es

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