How does noise scale with turbidity?

[CamDavidsonPilon]

Our Kalman Filter is non stationary, and so we should feel okay scaling our matrices as the experiment progresses. One important parameter is the observation noise covariance. For example, at low turbidity (with zero growth in the process, i.e. a sterile media), there is some noise due to whatever. When the turbidity increases, the noise increases as well - but by how much? This is the factor we should be scaling the observation noise covariance by.

Quick tests show that scaling the matrix by the OD states works somewhat well.

But it may also make sense to scale with the growth rate - high gr => more noise?

[CamDavidsonPilon]

variance seems to rise near the peak of growth and immediately after

Below is log-scale of rolling OD-mean vs OD-variance

Scatter plot of the relationship is pretty strong, which suggests the variance should scale linearly with OD:

[CamDavidsonPilon]

Another one: