Hi Everyone. I am implementing a Kalman filter for an accelerometer. As you know,the accelerometer can be modeled as a Random Walk process and the output of a random walk process is assumed to be coming out of an integrator driven by white noise. This is described in "Random signals and applied kalman filtering, Brown,Hwang" chapter 2&5. The book describes that to find the Process Noise Covariance matrix 'Q' ,you need to know the Power spectral density of the input function, which is white noise here.
My question here is how do i do that? I have measured the power spectral density of the noise in the acceleration signal from the accelerometer, which is very close to the value stated in datasheet. But on the other hand this PSD is from the noise contained in the 'output' of the accelerometer and the Random Walk model says that this output is the integrated white noise. Should i differentiate the acceleration signal and find the PSD of the differentiated signal or Use the value that i already measured?
One more thing. In a research paper i read, the researcher just assumed the PSD to be 1 (m/s^2)^2 per rad/sec. Which i don't understand why. Any help would be greatly appreciated.