# Reading noise from allan variance plot for MEMS sensor per IEEE Std 952-1997

I am following the Standard Sensor Performance Parameters from the "MemsIndustryGroup" to test some Gyroscopes:

I conducted a test and plotted the square root of AVAR (Allan Deviation) against Time per IEEE Std 952-1997 using MATLAB:

I am confused however, by how I can read the Quantization Noise, Angle Random Walk, Bias Instability, and Rate Random Walk from this plot. The Standard Sensor Performance Parameters state to read them when T = 3^1/2, T = 1, Slope = 0, T = 3.

When I read these values, my results look like this:

I was wondering if I am doing this correctly. The example plots from both Standard Sensor Performance Parameters and IEEE involve slope lines that do not have anything to do with reading my plot:

EX1

EX2

What is the proper way to read these noise parameters from my Allan Variance/Allan Deviation plot?

Is my approach of reading the values correct, or should I try to make my graphs use the slopes as seen in the two examples? Etc.

In your first figure, the root AV curve appears to follow a slope of $-0.5$ from the start of the curve and all the way up to an integration time of a few hundred s. A simple way to extract angular random walk (ARW) is to make a straight line through the part of your curve with slope of $-0.5$ and find where this line crosses $\tau = 1$s. In some cases this line will not follow your AV curve when it crosses $\tau = 1$s, but in your case it does. (Which means white noise is dominating for integration times less than a few hundred seconds). In your case it seems you have already found that the curve crosses $\tau = 1$s at $178.182^{\circ}$/h. This means that your ARW = $178.182 / 60^{\circ}/\sqrt{h} = 2.97^{\circ}/\sqrt{h}$.
The quantization noise seems not to influence your root AV curve at all. (I can see no part with slope of -1). Thus it seems negligible. Perhaps you use a very high resolution ADC to sample the gyro data or you decimate the data before you perform your AV calculations? I've never worked with the quantization noise, but I suppose you would do it the same way as with ARW; i.e. you find the part of the curve with slope of -1, if neccessary extend this with a straight line so it passes $\tau = 3^{0.5}$ seconds, and convert to proper units.
The same goes for rate random walk. Don't read the value of the curve itself at $\tau = 3$ seconds, but draw a straight line through the part of the curve with slope of +0.5, extend this line all the way to $\tau = 3$ seconds, read the value and convert to proper units.