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I'm getting two error variance values from two third-party sensors, and need to multiply these variances with the position state estimates of the target they're tracking. Once that's done, the combined variance has to be sent back to the sensors.

The problem here is, how to get a combined variance? Obviously (variance1 + variance2)/2 won't work. Is there no practical way to calculate the combined variance if the mean and sample values aren't known?

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    $\begingroup$ Have you considered the pooled variance (weighted mean of the variances, with weights equal to the sample sizes)? $\endgroup$
    – ocram
    Mar 9 '15 at 7:01
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    $\begingroup$ @DilipSarwate This was, of course, a typo. Thanks for pointing that out. I deleted it. Indeed, the variance of the sum of two random variables $X$ and $Y$ is $Var[X+Y]=Var[X]+Var[Y]+2Cov[X,Y]$. $\endgroup$
    – random_guy
    Mar 9 '15 at 15:28

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