I'm trying to simulate an IMU (inertial measurement unit) using a simple model:
$$ \tilde a(t) = a(t) + b(t) + c(t) $$
where $\tilde a$ is the measured value, $a$ is the true value, $b$ is the random walk bias simulated as Wiener process and $c$ is Gaussian white noise:
$$ \dot b(t) = \sigma_b w(t)\\ c(t) = \sigma_c w(t) $$
where $w(t)$ is Gaussian white noise process with mean 0 and standard deviation 1.
This is modeled as
P=TransformedProcess[b[t]+c[t],
{b\[Distributed]WienerProcess[0,0.1],
c\[Distributed]WhiteNoiseProcess[]},t];
However, MMA complains that the discrete and continuous model cannot be mixed when I plot the data
ListPlot[RandomFunction[P, {0, 10, 0.01}]]
The processes in {[FormalP]1[Distributed]WienerProcess[0,0.1],[FormalP]2[Distributed]WhiteNoiseProcess[NormalDistribution[0,1]]} should be all continuous-time or all discrete-time.
Of course, we can generate the data separately using WienerProcess
and WhiteNoiseProcess
, but I'm wondering what is the correct way to do this symbolically so that I can utilize all the functions associated with the random process (RandomFunction
, CovarianceFunction
, etc.) to analyze the model?
a[t]
come from? $\endgroup$