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From Wikipedia:

If the output signal slowly changes independent of the measured property, this is defined as drift

So my question is, if I have a gyroscope with sensor drift does that mean that $E\left\{f(x)\right\} \neq 0$ ? I have an excercise where it is written, that the sensor has drift but also that the $E\left\{f(x)\right\} = 0$. But to me one statement seems excludatory of the other one.

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I assume you set the first momentum of your true measure to $\mu=0$, so your question actually reads

gyroscope with sensor drift does that mean that $E[f(x)] \ne \mu$?

No. It might still be the case that the sensor value, in the long term, drifts centred around the true value.

The thing is that $f(x)$ is a random variable with non-zero variance and a time dependency. That means: If there's drift, that random variable is not a stationary process.

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  • $\begingroup$ Ah I see. So would an example of this be a thermometer that measures the temperature over a whole year. It has E[f(x)] = some_mean But it would have a drift in Summer and Winter respectively? Maybe my confusion stems from the contrieved example of a gyro having a drift. Or is that a realisitc case? $\endgroup$ – Hakaishin May 29 '17 at 12:13
  • $\begingroup$ Your thermometer example doesn't work, because the actual temperature does change between summer and winter. $\endgroup$ – Marcus Müller May 29 '17 at 12:37

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