I am currently working with an IMU and I need the sensor Error Model.
The documentation provided only includes spectral densities in all the three exes for the following: misalignment, accelerometer, gyroscope, velocity and position.
The problem is that I use an algorithm that implements the error model in the form of a linear mathematical model:
(Sensor output)=u+Cx+Dv
where x_dot=Ax+Bw is the sensor error, u is thetrue kinemativ variable that sensor is expected to measure and Dv is the addtive white noise.
In order to use my algorithm, I would need to get, separately, the parameters A, B, C and D.
So, I would like to know if there is a way of obtaining that type of error model from the spectral densities.
Thanks in advance.
PS: Please, take into account that my area is computer science and I am in need of this information for a specific problem. I am not a physic or a telecommunication engineer.
you can get the autocorrelation time series from the spectral density using an inverse fft (in matlab etc), which is a second order measure of your noise.
https://www.mathworks.com/help/signal/ug/power-spectral-density-estimates-using-fft.html
another approach is to convert your signal of interest to the frequency domain and use the noise spectral densities directly there (multiplicative effect)
IMHO.It seems what is needed is a kalman filter or a linear predictor or ANN.
Cheers
Thank you all for your answers.
Narasim Ramesh, the truth is that I need the error model to implement Kalman for another use so it would be really counterproductive to implement Kalman to get the error model.
Vikas Ramachandra, thanks for your answer. I would look into that but I don't think I can get the parameters A,B,C and D from that function. I should have said before in the question I needed them. I have corrected that. However, if you know a way to obtain them, I would be eternally grateful.
Again, thanks for answering.
Am I correct in interpreting that you are basically looking for System identification with known data ? See System modeling in Proakis and Manolakis P 882 . In any case with time series data it should be possible to estimate A, B ,C , D of the plant.However the problem stated is that only spectral densities are available. So it is necessary to estimate the time series from PSD or at least the coefficient matrices. There might not be an unique solution as PSD is derived from |x(n)|^2 . However some trials done in ref below might be of help.
" Generate a time series from a PSD
http://in.mathworks.com/matlabcentral/newsreader/view_thread/236071 "
Good Luck
Cheers
Further it seems what you are seeking is spectral decomposition F(z)= H(z) (~H(z) ).There is no unique solution for H(z) without additional imposed constraints e.g. minimum phase etc.
Cheers
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