# Noise of a fiber optic gyro

I have not much experience with noise handling or calculations, furthermore in my researches couldn't find a similar problem, so here is my attempt:

Having a fiber optic gyro that is rated with a noise performance "RW" (not familiar with the term, its from the specs) of $0.0791 \frac{deg}{\sqrt{hr}}$. I'm not sure if the value is given for $1\sigma$ or 3sigma, but I can use my value for the same certainty.

• How much deviation has to be expected in terms of angular rate ($\dot{deg}$) if the gyro delivers data in $0.1s$ intervals? I need this value for monitoring to detect if the device becomes faulty (sensor redundancy).

My personal attempt so far was:

Calculate the absolute error that will emerge after some time, in this case $0.1s$ (square-root multiplication because of unit comparison)

$0.0791 \frac{deg}{\sqrt{3600s}} *\sqrt{0.1s} = 4.16894*10^{-4}\left [deg\right ]$

to get the amount of deviation in degrees after $0.1s$.

For the angular rate deviation I divide the result by $0.1s$ to figure out how much was the rate of change for this interval (calculating it like an average).

$\frac{4.16894*10^{-4}deg}{0.1s}=4.16894*10^{-3}\left [\frac{deg}{0.1s} \right ] = 4.16894*10^{-3}\left [\frac{\dot{deg}}{0.1} \right ]$

• Is this calculation the right approach? (I cannot compare it to the real values yet to even see if I'm in the right magnitude)
• Are the two values of $4.16894*10^{-4}\left [deg\right ]$ and $4.16894*10^{-3}\left [\frac{\dot{deg}}{0.1} \right ]$ amplitudes or the peak to peak ranges?

• Bias (zero point error): $2.644 \frac{deg}{hr}$
• Update rate: $5Hz-1000Hz$
• Scale factor (including non-linearities) +100deg/s: $-152ppm$
• Scale factor (including non-linearities) -100deg/s: $-116ppm$
• Operational: $\pm1000\frac{deg}{s}$

Side-note from the manual: Two equivalent units of measurement are used to describe this performance: "deg/√h" or "deg/h/√Hz". The conversion factor between the two is a factor of 60 (deg/√h = 60*deg/h/√Hz). Unit deg/√h is used here.

• From a cursory look, the RW probably stands for Random Walk, in which the variance (in square degrees) increases linearly with time. This would make your approach the right one, I think, as long as you're re-setting the value every 0.1s. – Emilio Pisanty Oct 7 '14 at 14:33
• Great! What value is needed to be re-setted? And is the angular rate deviation an amplitude or peak-to-peak? – Stefan Oct 7 '14 at 15:26
• If the number is given in $deg/\sqrt{hr}$, then it's a low frequency noise component. There is no guarantee, that this noise density extends to a 0.1s sampling interval. What other data do you have about the device? – CuriousOne Oct 7 '14 at 16:07
• You can't really describe noise with a single number. The 0.0791 number you have is an integral of the noise spectral density from 1/hour and above in frequency. If you're probing the gyro at 0.1s intervals you are sensitive to noise at higher frequencies, 10Hz and above. This will almost certainly give you less drift than the low frequency number you quoted. To really answer your question we need more information from the gyro's spec sheet. – DanielSank Oct 7 '14 at 16:11
• Added some more specs. I can understand that noise isn't so simple to put in numbers, but I'm pretty sure it will never output +10000deg/s caused by noise (1 or 3 sigma). I would be really happy to learn more, feel free to add an answer below. At least in my naive vision those numbers should represent something with practical use? If you need more let me know which ones I should be looking for, think those should be the "performance" ones. – Stefan Oct 7 '14 at 17:22