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I have $2$ sensors allowing me to measure angles of arrival. These sensors are a distance $d$ ($d \simeq 10$ m) apart and the target to be located is at a distance $R$ with $d<<R$. In the literature we see the formulation for the angle of arrival: $\theta_i=\theta_{i0}+n_i $ with $\theta_{i0}$ the true angle for sensor $i$ and $n_i$ the noise.

I asked myself the following question: as the sensors are close is it reasonable to assume that for all $i$, $n_i=n$ i.e. the noise is the same at each sensor.

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    $\begingroup$ Most likely that's not a reasonable assumption. It's more likely that the two noises are uncorrelated. $\endgroup$
    – MBaz
    Jan 6 at 15:50

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No that would not be a reasonable assumption in my opinion. This would depend on the source of the noise and what you mean by "the same". If the noise in the signal itself being measured in dominant and similarly received by each sensor, then the noise in each can be identical if compensated for delay and gain offsets. However if the local noise in the sensor itself is dominant, then the two noise processes could be independent unless the source of that noise is shared between the sensors.

If there is a way to mask the sensors input (terminate or block depending on what kind of sensor it is), then the local noise in each can be measured and cross-correlated to determine similarity and independence, and this would be a measure of the sensor's noise floor. Then using a low level signal (to keep the sensor in the same linear operating region) the measurement can be repeated. From this it can be determined the received noise relative to the local noise and degree of similarity.

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