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content/zettels/sensor_noise_estimation.md
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@@ -12,13 +12,13 @@ Tags
Measuring the noise level of inertial sensors is not easy as the seismic motion is usually much larger than the sensor's noise level.
A technique to estimate the sensor noise in such case is proposed in ([Barzilai, VanZandt, and Kenny 1998](#org4702c9a)) and well explained in ([Poel 2010](#orgeaef46f)) (Section 6.1.3).
A technique to estimate the sensor noise in such case is proposed in ([Barzilai, VanZandt, and Kenny 1998](#org65ed433)) and well explained in ([Poel 2010](#org02bd600)) (Section 6.1.3).
The idea is to mount two inertial sensors closely together such that they should measure the same quantity.
This is represented in Figure [1](#org030f5c0) where two identical sensors are measuring the same motion \\(x(t)\\).
This is represented in Figure [1](#orgbc58a8d) where two identical sensors are measuring the same motion \\(x(t)\\).
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{{< figure src="/ox-hugo/huddle_test_setup.png" caption="Figure 1: Schematic representation of the setup for measuring the noise of inertial sensors." >}}
@@ -76,7 +76,7 @@ Now suppose that:
- sensor noises are modelled as input noises \\(n\_1(t)\\) and \\(n\_2(s)\\)
- sensor noises are uncorrelated and each are uncorrelated with \\(x(t)\\)
Then, the system can be represented by the block diagram in Figure [2](#orgec7c79b), and we can write:
Then, the system can be represented by the block diagram in Figure [2](#org1dabfe7), and we can write:
\begin{align}
P\_{y\_1y\_1}(\omega) &= |H\_1(\omega)|^2 ( P\_{x}(\omega) + P\_{n\_1}(\omega) ) \\\\\\
@@ -90,7 +90,7 @@ And the CSD between \\(y\_1(t)\\) and \\(y\_2(t)\\) is:
\gamma^2\_{y\_1y\_2}(\omega) = \frac{|C\_{y\_1y\_2}(j\omega)|^2}{P\_{y\_1}(\omega) P\_{y\_2}(\omega)}
\end{equation}
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{{< figure src="/ox-hugo/huddle_test_block_diagram.png" caption="Figure 2: Huddle test block diagram" >}}
@@ -116,6 +116,6 @@ If we assume the two sensor dynamics to be the same \\(H\_1(s) \approx H\_2(s)\\
## Bibliography {#bibliography}
<a id="org4702c9a"></a>Barzilai, Aaron, Tom VanZandt, and Tom Kenny. 1998. “Technique for Measurement of the Noise of a Sensor in the Presence of Large Background Signals.” _Review of Scientific Instruments_ 69 (7):2767–72. <https://doi.org/10.1063/1.1149013>.
<a id="org65ed433"></a>Barzilai, Aaron, Tom VanZandt, and Tom Kenny. 1998. “Technique for Measurement of the Noise of a Sensor in the Presence of Large Background Signals.” _Review of Scientific Instruments_ 69 (7):2767–72. <https://doi.org/10.1063/1.1149013>.
<a id="orgeaef46f"></a>Poel, Gerrit Wijnand van der. 2010. “An Exploration of Active Hard Mount Vibration Isolation for Precision Equipment.” University of Twente. <https://doi.org/10.3990/1.9789036530163>.
<a id="org02bd600"></a>Poel, Gerrit Wijnand van der. 2010. “An Exploration of Active Hard Mount Vibration Isolation for Precision Equipment.” University of Twente. <https://doi.org/10.3990/1.9789036530163>.