I'm developing a Simulink model for noise according to the description of the algorithm of Accelerometer in this page: IMU simulation model.
My system takes the RandomWalk (defined in [unit], being unit [g] for accelerometer, [m] for a distance and so no), the NoiseDensity (in [unit/sqrt(SensorSampleRate[Hz])] ) and BiasInstability in (in [unit*sqrt(SensorSampleRate[Hz])] ).
At the moment it is still not clear if those data will be given as one-sided or a two-sided noise.
Anyway according to the Matlab page I've implemented the model so that to use the 's' parameter set to 1 for one-sided noise and 2 for two-sided noise.
The problem comes when I run the simulation to validate the simulation results.
The expectation is that running the model and analysing output as if it was recorded by a real instrument I should be able to demonstrate that the noise obtained has the given NoiseDensity, BiasInstability and RandomWalk.
In order to do that I've firstly run some cases with only NoiseDensity (both one-sided and two-sided) and what I've found is that I can obtain the expected value in two ways:
by doing the sqrt(s*var(y)/SensorSampleRate[Hz]) being 's' set as described above
by using the method descibed in What should be the correct scaling for PSD calculation using $\tt fft$ replacing the following line
psdx = (2/(Fs*S)) * psdx
with this one
psdx = (s/(Fs*N)) * psdx; being 's' set as described above (I've replaced the original 'S' parameter at denominator with N which is the number of samples in the signal).
Is it correct that I have to 'scale' the result to take into account if the noise is single or double sided?
Finally the big question: in order to validate the noise also with BiasInstability and RandomWalk I've implemented the code of Allan analyses (Inertial Sensor Noise Analysis Using Allan Variance), but apparently it gives good results only if noise is one sided. The same happens using the code from Allan variance calculation (core of AVAR application).
The two algorithms give the same results and the results are correct only for single sized noises (in both cases the BiasInstability is underestimated by roughly 20% and I've not yet understand way, but I do not expect the Allan analysis to give me back exactly the sensor parameter values ... NoiseDensity and RandomWalk are some percent off for reference).
Is there something I'm doing badly? Should I modify the Allan estimation to take into account the 's' parameter for the two different types of noise? If yes, how? If not, why I get correct results only for the one sided one?
