Exponential Noise on Factors not Diminishing Effects

[Jay Elrod]

Hi gtsam users,

I have some custom factors for which I want to scale the noise model according to an exponential curve and am getting some unexpected results.

For example, when detecting a fiducial printed on a piece of paper, if the vector normal to the camera lens and the vector normal to the back side of the fiducial detection have angular distance greater than or equal pi/2 between them, the lens ought to have not been able to observe it at all.

As the above theoretical limit is approached, among other similar ones, the accuracy of the detection does in fact degrade, and I have implemented some exponential noise models in my code used to scale the noise applied to factors according to some configurations. My initial assumption was that after a particular inflexion point, the factors being applied would basically have no effect whatsoever, but in practice that does not seem to be the case.

I am applying these exponential noise models as measurement noise of the form `gtsam::noiseModel::Diagonal::Sigmas((gtsam::Vector( ... ) << ..., ...).finished())`, and even factors with sigmas as high as `4245211377070.561523` for all measurement dimensions appear to still have a marginal impact on the optimized factor graph. Sometimes this very very high noise does seem to adequately squash these very noisy factors, but omitting them from the factor graph entirely has a much more drastic effect. Am I applying these in the wrong way, or is my understanding of the application of noise to a factor flawed? Ultimately, I would like to still include these noisy factors according to my own noise function as described above but have their effects diminish with increased noise at a certain point, but I have been unable to find any amount of noise that seems to be sufficient, even in the presence of other highly accurate factors.

Thanks in advance!

Jay

[Jay Elrod]

(I suppose I should explicitly mention that my first attempts at marginalizing these factors with noise as their accuracy degrades did actually use reasonable values for noise, reflective of the actual spatial inaccuracies of the measurements, like 60cm, etc.)