Let's take two constants, $\alpha$ and $\beta$, both are given by two functions $f_1(\vec{\theta})$ and $f_2(\vec\theta$) (the model). These functions are known: we have an analytical closed expression, that for a given set of values $\vec\theta$, $\alpha$ and $\beta$ are retrieved.
PROBLEM:
The components of $\vec\theta$ are noisy measurements, so, the variance of $\alpha$ and $\beta$ is high: for different measurements, we have quite different values for them... though our model defines them as constants. Furthermore, the model is not actually realistic, and obviously it imposes some assumptions.
formulation:
The observed values are $\vec\theta = [\beta, \dot\psi, \delta, A, B, C]$
\begin{equation} \alpha = \frac{\dot\beta + \dot\psi}{-2A\beta + B\dot\psi A\delta} \end{equation} \begin{equation} \beta = \frac{\alpha K\beta + \alpha C\dot\psi + \alpha D\delta}{\ddot\psi} \end{equation}
(The derivatives are computed using finite differences)
NOTE: the observed values of $\vec\theta$ are not independent since they come from the same sensing unit (which little do we know about), so I think assuming statistical independence won't work here...
QUESTIONS:
Are there common approaches in Machine Learning to mitigate the effect of the noise? Can Machine Learning help to get the true values? Can Machine Learning model the variance of the estimators? By Machine Learning I mean algorithms that are not as known as Kalman filtering.
MOTIVATION AND CONSIDERATIONS:
I was asked this question by a colleague at my job office, since I work on Machine Learning. I personally think that a better approach is to face it from the estimation theory (ref.). For instance, modeling the noise of the sensors and try to get Maximum Likelihood estimators, and if possible, derive a bound for their variance (CRLB) or a closed expression for the bias. For handling the noise, I suggested u-Kalman, Particle Filtering... But other terms that came to my mind were: "fuzzy", "GMM", "EM"...
EDIT:
I think what my colleague wants is a "data-driven/black-box" approach that can help him skip the math, since he has not the enough background...