# Get variance of white noise from Accelerometer data

i have a static accelerometer data. So i assume that all signal are from noise. So i model it like this,

$$X(k) = X(k-1) + U(k)$$

But I plot the $$U(k)$$ autocorrelation function seems it is not white noise,

So, I model it as $$\mathrm{AR}(1)$$ like

$$U(k) = a U(k-1) + W(k)$$

And from MATLAB I got a = -0.24 and I get $$W(k)$$. When I plot $$W(k)$$ it still not white noise. How can I get variance of white noise from my accelerometer data?

• Welcome to DSP.SE! I don't understand how you get $U(k)$ from your signal. How do you split your original data into the noise-free signal and the noise itself? – Tendero Oct 11 at 14:43
• A static acclerometer should measure the specific force which is the sum of inertial acceleration, bias (if these are MEMS-based sensors), and noise. So, what you are essentially observing is bias + noise. – Maxtron Oct 11 at 15:22
• @Tendero : sorry i'm still new in DSP, so i cant get U(k) from accel data that i model it to X(k) = X(k-1) + U(k), is that U(k) = diff(X(k))? – EM Farih Oct 12 at 8:03
• @Maxtron : So i cant get variance of noise (purely white noise) from accel data? – EM Farih Oct 12 at 8:04
• No. Because it is a combination of both bias and sensor noise. These are two different terms. Please look at this tutorial for more details. Link – Maxtron Oct 12 at 14:53